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In both cases, the refracted rays are parallel to the principal axis. C. A ray directed to the optical centre of the lens. In both cases, the rays pass undeviated. NB: in ray diagrams, the following symbols are used for the two lenses: Converging lens Diverging lens Note that in ray diagrams:FORM 4 PHYSICS LESSON NOTES 2018 Page 3 of 70 1. Real rays, real objects and real images are represented using continuous lines. 2. Virtual rays and virtual images are represented using broken lines. 3. To locate an image, there must be at least two rays intersecting, whether real or virtual. Sometimes, a scale may be used in ray diagrams. If used, then the scale chosen for object and image distances need not be necessarily equal to that of the object and image heights but the two must be given on the diagram. 1.4:Image formation by thin lenses 1.4.1:Image formation by a converging lens. This is summarized by the table below: Position of object Ray diagram Characteristics of image Between F and the lens I O Image is: - Virtual - Upright erect - Magnified - On same side as the object At F O Image is: - Real - Inverted - At infinity Between F and C O I Image is: - Real - Inverted - Magnified - Beyond C At C Image is: - Real - Inverted - Same size as object - At C Beyond C Image is: - Real - Inverted - Diminished At infinity Image is: - Real - Inverted - Diminished - At F 1.2:Image formation by a diverging lensFORM 4 PHYSICS LESSON NOTES 2018 Page 4 of 70 Generally, a diverging lens forms a virtual, upright and diminished image regardless of the position of the object. 1.5:The lens formula and magnification The equation 1 f 1 u 1 v where f is the focal length of the lens, u is the object distance and v the image distance, is called the lens formula. The equation takes into account the signs of u, v and f and holds for both the converging and diverging lens. The ratio of the image size to the object size is called magnification of the lens. When the magnification is less than one the image is diminished while when it is more than one, the image is magnified.
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When a converging lens is used such that the object is found between its principal focus and the lens, it forms a virtual, upright and magnified image. When used this way it serves as a simple microscope. A compound microscope It consists of two converging lenses, objective lens and eyepiece lens both of short focal lengths. The lens closer to the object is called the objective lens while that closer to the eye is called the eyepiece lens. The focal length of the eyepiece lens is longer than that of the objective lens. FORM 4 PHYSICS LESSON NOTES 2018 Page 9 of 70 The object is found between F and C of the objective lens. O I 2F0 F0F0 2F0 FeFe The first image formed by the objective lens is real, inverted and magnified. This image then acts as the object for the eyepiece lens. The eyepiece lens forms a final image which is greatly magnified. Assuming the magnification of the objective lens is mo and that of the eyepiece lens is me , then the total magnification of the compound microscope m mo me. Example 1.2 1. In a compound microscope, the focal length of the objective lens is 2.0cm and that of the eyepiece lens is 2.2cm and they are placed at a distance of 8.0cm. A real object of size 1.00mm is placed 3.0cm from the objective lens. A Use the lens formula in turn for each lens to find the position of the final image formed. B Calculate the magnification produced by the arrangement of these lenses and the size of the final image viewed by the eye. The lens camera A camera is a device that is used to take photographs. It consists of a converging lens, a light- sensitive film enclosed in a light-tight box blackened on the inside and a shutter. Light from the object enters the camera through the shutter which closes automatically after a given length of time. The amount of light reaching the lens is controlled by the diaphragm stop . The light reaching the lens is refracted to form a real, inverted and diminished image on the film. To clearly focus the image, the distance between the lens and film is adjusted accordingly. The film has some light- sensitive chemicals which change on exposure to light. This can then be developed and printed to get a photograph.
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To clearly focus the image, the distance between the lens and film is adjusted accordingly. The film has some light- sensitive chemicals which change on exposure to light. This can then be developed and printed to get a photograph. The human eyeFORM 4 PHYSICS LESSON NOTES 2018 Page 10 of 70 Sclerotic layer white Choroid layer black Ciliary muscles Retina Suspensory ligaments Vitreous humourFovea Iris Lens Cornea To central nervous System Blind spot Aqueous humour Pupil The human eye is a natural optical instrument. It comprises of the following parts: Sclerotic layer- encloses the eye. The front part cornea is transparent to allow in light. It is the white part of the eye. Aqueous humour- it is a clear fluid liquid found between the cornea and the lens. This helps to maintain the shape of the eye. Iris- it is responsible for the colour of the eye. It has the pupil in the middle which allows for passage of light. By changing the size of the pupil, the iris controls the amount of light entering the eye. Lens- it is a natural converging lens. With the help of the ciliary muscles, its focal length can be adjusted for fine focusing. Vitreous humour- it is a jelly-like substance and transparent in nature found between the lens and retina. Retina- images are formed here. It has light-sensitive cells. Fovea- it is the central part of the retina. This is where the eye has the best details and colour vision. Blind spot- has cells which are non-sensitive to light. Ciliary muscles- they suspend support the lens. It is also responsible for controlling the shape of the lens. When the muscles relax, the focal length of the lens increases. This enables the eye to focus a distant object. Contraction of the muscles on the other hand reduces tension in the lens, thus reducing its focal length. This enables it focus near objects. This automatic adjustment of the eye lens to bring to focus on the retina images of both distant and near objects is referred to as accommodation. The closest shortest distance a normal eye can focus clearly is known as its near point while the farthest distance a normal eye can focus clearly is known as its far point.
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This enables it focus near objects. This automatic adjustment of the eye lens to bring to focus on the retina images of both distant and near objects is referred to as accommodation. The closest shortest distance a normal eye can focus clearly is known as its near point while the farthest distance a normal eye can focus clearly is known as its far point. For a normal eye, the near point is usually 25cm. Note that the distance between the retina and the eye lens is always constant. 1.9.1:Eye defects Despite the adjustments made by the eye, some eyes cannot produce clear images within the normal range of vision. There are two common eye defects namely myopia shortsightedness and hypermetropia long-sightedness . Myopia shortsightedness FORM 4 PHYSICS LESSON NOTES 2018 Page 11 of 70 Having this defect means clear vision for near objects but images of distant objects are formed in front of the retina. The cause of the defect is the eyeball being too long or shorter focal length. The defect is corrected by using a diverging lens of appropriate focal length so that the rays reaching the eye lens appear as if they are coming from a near object. Defect Correction Hypermetropia long-sightedness A person who is long-sighted has clear vision of distant objects but cannot see clearly closer objects clearly. It is caused by the eyeball being too short or longer focal length so that the image of a closer object is formed behind the retina. The defect is corrected by using a converging lens of appropriate focal length. Defect Correction 1.9.2: Similaritiesanddifferences between the eye and lens camera Similarities 1. Both use converging lenses. 2. In both cases, the amount of light allowed in can be controlled. The eye does it through the iris while the camera does this through the diaphragm. 3. In both, a real, inverted and diminished image is formed. For the eye, the image is formed on the retina while for the camera, it is formed on a light-sensitive film. 4. In both cases the inner part is black; for the eye, there is the choroid layer which is black and for the camera, the inner part is painted black. This is to absorb stray rays. Differences 1. The focal length of the eye lens changes while that of the lens camera is constant. 2.
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An object of mass 10kg is whirled round a horizontal circle of radius 4m by a revolving string inclined to the vertical. If the uniform speed of the object is 5m s, calculate: a The tension in the string b The angle of inclination of the string to the vertical Ans. T 118N, 70 2.6: Case examples of circular motion 2.6.1: movement of cars round a flat level bend In this case, the centripetal force is provided by the frictional force between the tyres and the road, i.e. FR FC mv2 r If the road is slippery, then the frictional force may not be sufficient to provide the required centripetal force. Hence skidding may occur. To avoid skidding, the speed of the car should not exceed a certain speed limit critical speed . The critical speed depends on the radius of the bend; the larger the radius the higher the critical speed. Other factors which affect friction also significant here. These include the nature of the road surface and the nature of the tyres. Example 2.5 1. A car of mass 1200kg is moving with a velocity 25m s round a flat bend of radius 150m. Determine the minimum frictional force between the tyres and the road that will prevent the car from sliding off. FR mv2 r 1200 252 150 5000N 2. A glass block of mass 100g is placed in turn at various distances from the centre of a table which is rotating at a constant angular velocity. It is found that at a distance 8cm from the centre, the block just starts to slide off the table. If the frictional force between the block and the table is 0.4N, determine: a The angular velocity of the table FR mr 2 0.4 0.1 0.08 1 2 7.07rads-1 b The force required to hold the block at a distance of 12cm from the centre of the table.
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X c.o.g y Mg FR For a flat road surface, frictional force between the tyres and the road provides the centripetal force; FR FC mv2 r In cases when the frictional force is not sufficient, the cyclist is likely to skid. To avoid this, the cyclist is advised to lean inwards. Thus the frictional force, FR and the normal reaction, R produce a turning effect about the centre of gravity. Thus taking moments about the c.o.g.,. We get; Clockwise moment Rx And anticlockwise moment FRy For no skidding to occur, clockwise and anticlockwise moments should be equal; Rx FRy FR R x y But tan x y and R mg Therefore tan FR mg FORM 4 PHYSICS LESSON NOTES 2018 Page 21 of 70 Where is the coefficient of friction. Hence skidding only occurs when tan is greater than tan . Example 2.7 1. A cyclist who is travelling at 20m s negotiates a bend of radius 45m. he inclines at an angle to the vertical. Calculate: a The centripetal acceleration a v2 r 202 45 8.889m s2 b The angle of inclination tan v2 rg tan-1 202 45 10 41.65 2.7: Applications of circular motion 2.7.1: Centrifuges A centrifuge is a device that is used to separate substances of different densities e.g. immiscible liquids or solids suspended in liquids. The mixture is put in tubes which are then set into rotation. At a particular speed, the more dense particles or substance move further away from the centre of rotation while the less dense particles move inwards towards the centre of rotation. R2 R1 R3 Lighter particles Heavier particles Since centripetal force varies directly as the mass and inversely as the radius, for a larger radius the mass must be higher for the same amount of centripetal force. Hence denser particles are far away from the centre of rotation. When the rotation stops, the tubes return to the vertical position with the denser particles at the bottom.
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R2 R1 R3 Lighter particles Heavier particles Since centripetal force varies directly as the mass and inversely as the radius, for a larger radius the mass must be higher for the same amount of centripetal force. Hence denser particles are far away from the centre of rotation. When the rotation stops, the tubes return to the vertical position with the denser particles at the bottom. 2.7.2: Satellites When two bodies of mass m1 and m2 are separated by a distance r, there existsattractional force between them given by; F Gm1m2 r2 Where G is the universal gravitational constant. The above equation is referred to as Newton s law of universal gravitation. Consider a satellite of mass m orbiting the earth at a distance of r metres away. Suppose the mass of the earth is M, then the centripetal force that keeps the satellite on the circular path is provided by the gravitational force of attraction. Hence FC mv2 r GMm r2 And v GM r 1 2FORM 4 PHYSICS LESSON NOTES 2018 Page 22 of 70 Where v is the velocity of the satellite. When a satellite has the same periodic time as that of the earth, it will appear stationary when viewed from the earth s surface. Such satellites are said to be in a parking orbit. They are widely used in weather forecasting and in telecommunication. 2.7.3: Speed governor Fuel control valve Arm Collar Pivot To drive shaft As the shaft rotates, the masses also rotate with increasing angular velocity. Thus the angle enlarges. The collar is then pulled upwards by the arms which in turn pulls the lever up. The lever is connected to the fuel steam valve which regulates the flow of fuel or steam which in turn controls the speed of the engine. MmFORM 4 PHYSICS LESSON NOTES 2018 Page 23 of 70 TOPIC 3: ELECTROMAGNETIC SPECTRUM 3.1: Introduction We have seen that waves can be categorized either electromagnetic or mechanical in nature. Electromagnetic waves are waves resulting from the interaction of oscillating electric and magnetic fields. They include visible light, radio waves, x-rays, infrared, ultraviolet, microwaves and gamma radiations. When these waves are arranged in a certain pattern e.g in the order of increasing frequency or wavelength then we get an electromagnetic spectrum.
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Electromagnetic waves are waves resulting from the interaction of oscillating electric and magnetic fields. They include visible light, radio waves, x-rays, infrared, ultraviolet, microwaves and gamma radiations. When these waves are arranged in a certain pattern e.g in the order of increasing frequency or wavelength then we get an electromagnetic spectrum. 3.2: The electromagnetic spectrum Increasing frequency f Hz 103 108 1010 10141015 1022 R M IR V UV X G m 105 100 10-3 10-6 10-8 10-10- 10-11 10-13 Decreasing wavelength Where R- Radio waves M- Microwaves IR- Infra red V- Visible light UV- Ultraviolet X- X-rays G- Gamma radiation Hint: Roast R maize M is IR a very V unusual UV x-mass X gift G . 3.3: Properties of electromagnetic waves The following properties are common to all electromagnetic waves: Travel in a vacuum with a speed of 3.0x108m s. Do not require material medium for their propagation. Transverse in nature. Posses and transfer energy. The amount of energy possessed by an electromagnetic wave of frequency f is expressed as E hf, where h is Plank s constant and is equal to 6.63x10-9Js. The wave equation c f also apply for electromagnetic waves. Carry no charge not charged and are not deflected by a magnetic or electric field. Undergo reflection, refraction, diffraction, interference and polarization effects. FORM 4 PHYSICS LESSON NOTES 2018 Page 24 of 70 Can be emitted, transmitted and absorbed by matter. 3.4: Production, detection and applications of electromagnetic radiations The table below summarizes the production, detection and applications of the various electromagnetic radiations: Radiation Production Detection Application Radio waves From oscillating electrical circuits. Antennae aerials , diodes, earphones. In telecommunication- radio broadcast, TV and satellite communication, cellular telephone, radar and navigation equipments etc. Microwaves From special vacuum tubes called magnetrons within microwave ovens. Crystal detectors, solid state diodes, antennae. Cooking in microwave cookers. In communication- mobile phones. In speed cameras.
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Calculate the wavelength of the signal. FORM 4 PHYSICS LESSON NOTES 2018 Page 25 of 70 c f 3.0x108m s 1.0x108x 3.0m 2 An X-ray machine produces a radiation of wavelength 1.0x10-11m. calculate: a The frequency of the radiation. C f 3.0x108m s fx1.0x10-11m f 3.0x1019Hz b The energy content of the radiation. Take h 6.63x10-9Js. E hf 6.63x10-9Js x3.0x1019Hz 1.989x10-14J. 3 Arrange the following radiations in order of increasing wavelength: infra red, blue light, UV light, radio waves and X-rays. X-rays, UV light, blue light, infra red and radio waves. FORM 4 PHYSICS LESSON NOTES 2018 Page 26 of 70 TOPIC 4: ELECTROMAGNETIC INDUCTION 4.1: Introduction When a conductor moves within a magnetic field at an angle greater than zero, current is produced in the conductor which can be shown by connecting a galvanometer in series with the conductor. This method of generating electricity is called electromagnetic induction. It was first discovered by Michael Faraday about the year 186. Electromagnetic induction has been widely used to produce in large scale electrical energy in power stations. 4.2: Factors affecting the size of the induced electromotive force and Faraday s law Light copper wire When the copper wire is moved vertically downwards between the poles of the magnet, the galvanometer is observed to deflect. However, the direction of deflection changes when the wire is now moved vertically upwards. When the conductor is kept stationary between the poles of the magnet, no deflection occurs. Similarly when the wire is placed parallel to the magnetic field, no deflection is observed. A deflection of the galvanometer indicates presence of induced electromotive force while absence of deflection indicates no induced electromotive force. The deflection is maximum when the angle between the wire and the field is 900, a stronger magnet is used and when the wire is moved very swiftly at a high speed .
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Similarly when the wire is placed parallel to the magnetic field, no deflection is observed. A deflection of the galvanometer indicates presence of induced electromotive force while absence of deflection indicates no induced electromotive force. The deflection is maximum when the angle between the wire and the field is 900, a stronger magnet is used and when the wire is moved very swiftly at a high speed . These factors can be summed up in Faraday s law which state: the magnitude of the induced emf is directly proportional to the rate of change of the magnetic flux linkage. Magnetic flux linkage refers to the number of magnetic field lines cut by the conductor per unit area. 4.3: Lenz s law Electromotive induction also occurs when a magnet is moved to and back within a solenoid as shown below: IN OUT a b c d SN S N GGSNGS NFORM 4 PHYSICS LESSON NOTES 2018 Page 27 of 70 When the magnet is pushed into the solenoid, the galvanometer is observed to deflect same to when it is brought out but in opposite directions. However, when the magnet is kept stationary in the solenoid no deflection occurs. Specifically, when the north pole of the magnet is brought into the solenoid the galvanometer deflects towards the left showing that current flows from b to a but deflects towards the right when the magnet is moved away from the solenoid showing that current flows from c to d. These observations are summarized in Lenz s law which state: the induced current flows in such away to oppose the change causing it. It is based on the principle of conservation of energy i.e the mechanical energy of the moving magnet is converted to electrical energy in the form of the induced current. The direction of the induced current can be predicted by Fleming s right hand rule: if the thumb, first and second fingers of the right hand are held mutually at right angles to each other with the First finger pointing the direction of the Field, thumb pointing the direction of the Motion then the seCond finger points in the direction of the Current. It is also called the Dynamo rule. Thumb motion 1ST Finger field 2ND Finger induced current 4.4: Mutual induction Mutual induction occurs when a varying current in one coil induces current in another close coil.
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The direction of the induced current can be predicted by Fleming s right hand rule: if the thumb, first and second fingers of the right hand are held mutually at right angles to each other with the First finger pointing the direction of the Field, thumb pointing the direction of the Motion then the seCond finger points in the direction of the Current. It is also called the Dynamo rule. Thumb motion 1ST Finger field 2ND Finger induced current 4.4: Mutual induction Mutual induction occurs when a varying current in one coil induces current in another close coil. The first coil in which current flows is called the primary coil while the second coil in which current is induced is called the secondary coil. The varying current in the primary coil produces a magnetic field which links with the secondary coil inducing current in it. Primary coil Secondary coil When the switch is closed, current in the primary coil increases from zero to maximum. As a result, the magnetic flux linking up with turns of the secondary coil also increases from zero to maximum. This changing magnetic flux induces current in the secondary coil which makes the galvanometer to deflect. Once the current has reached maximum value, there will be no further increase in the magnetic flux and the pointer goes back to zero. GFORM 4 PHYSICS LESSON NOTES 2018 Page 28 of 70 When the switch is open, the current falls from maximum to zero within a very short time. This implies that the magnetic flux of the primary coil takes a very short time to change. The shorter the time the higher the induced current and thus a larger deflection. Hence more current is induced during switching off than during switching on. The magnetic flux of the primary coil linking up with the secondary coil can be varied by: Switching the current on and off. Varying the current in the primary coil using a rheostat. Applying an alternating current. The direction of the induced current can be predicted applying the Right-hand grip rule and Lenz s law simultaneously. When doing so, the primary coil is treated as if it were a bar magnet moving into the secondary coil during switching on and as a bar magnet moving away from the secondary coil during switching off.
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Hence the voltage dropped across the cables lost through resistance IR V 10x200 2000V Therefore the voltage across the primary coil of T2 40,000-2000 38,000V. d The maximum power output of the transformer T2. Effeciency power output power input x100 95 power output 38000x10 x100 Power output 95x38000x10 100 361,000V Energy losses in transformers There are four main causes of energy losses in transformers: i. Flux leakage When part of the magnetic flux of the primary coil fails to reach the secondary coil, it is referred to as magnetic flux leakage. In order to minimize energy loss through flux leakage can be reduced by winding the primary and secondary coils next to each on a common core. Alternatively, the secondary coil can be wound on top of the primary coil. Ii. Resistance As current flows through the coils, heat is generated due to the resistance of the coils. The electrical power loss as a result of resistance is given by I2R. Energy loss through resistance can be minimized by using thicker cooper wires. Iii. Eddy currents As the current alternates the magnetic flux also keeps alternating in the soft iron core producing eddy currents. These currents are sufficient enough to generate heat within the core. The energy loss can be minimized by laminating the core i.e. using thin sheets of soft iron plates insulated from each other. Iv. Hysteresis lossFORM 4 PHYSICS LESSON NOTES 2018 Page 32 of 70 The process of magnetization and demagnetization any time current reverses do generate heat within the core. Energy loss in this way is referred to as hysteresis loss. Hysteresis loss can be minimized by using soft iron core which is easier to magnetize and demagnetize. Note that despite the above measures, some of significant heat is still generated within the transformers. This is further cooled using oil. 4.5.2: Alternating current ac generator It is also called the alternator. A generator is a device that converts mechanical energy into electrical energy. It consists of a coil that rotates between the poles of a strong magnet.
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When the coil is rotated in the clockwise direction as shown in figure a , the induced current flows in the direction abcdand through the load via the half split ring 2 and carbon brush Y. At the vertical position the carbon brushes touch the gaps between the commutators half split rings . When the coil goes past the vertical position, the half split rings automatically exchange the carbon brushes as shown in figure b above. Applying Fleming s right hand rule again, the induced current flows in the direction dcbaand through the load via the half split ring 1 and carbon brush Y. thus the direction of current through the load is in one direction only hence direct current generator. The graph of induced current emf by a dc generator appears as shown below: Induced emf Current 0 180 360 540 720 angle made with the field Note that the magnitude of the induced current and electromotive force produced by both the ac and dc generators can be increased in the following ways: Using a stronger magnet. Increasing the number of turns of the secondary coil. Increasing the speed of rotation of the coil. Winding the coil on a soft iron core. In some generators like the bicycle dynamo, the coil is kept stationary while the magnet rotates. 4.5.4: Induction coil An induction coil consists of a primary coil of fewer turns and a secondary coil of many turns, both wound on a soft iron core. When the switch is closed, the soft iron core becomes magnetized and attracts the soft iron armature. This breaks the contact and current stops flowing. The core is thus demagnetized. The armature is released and the contact is remade. The process is repeated as long as the switch is closed. FORM 4 PHYSICS LESSON NOTES 2018 Page 34 of 70 The changing magnetic flux during magnetization and demagnetization produces an induced emf and current in the secondary coil. The induced current in the secondary coil produces sparks as current flows through the air across the gaps at the ends of the secondary coil as the shown in the figure below: .. Sparks Primary coil Contact C Secondary coil Soft iron armature The capacitor is used to store charge and thus reduce sparking. The sparks produced can be used to ignite an air-petrol mixture such as in the car ignition system. 4.5.5: The moving coil microphone A moving coil loudspeaker converts sound energy into electrical energy.
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Sparks Primary coil Contact C Secondary coil Soft iron armature The capacitor is used to store charge and thus reduce sparking. The sparks produced can be used to ignite an air-petrol mixture such as in the car ignition system. 4.5.5: The moving coil microphone A moving coil loudspeaker converts sound energy into electrical energy. Magnet Diaphragm To amplifier Sound waves When a person speaks into the microphone, the sound waves set the diaphragm into vibration. This makes the coil to move forward and back cutting through the magnetic field inducing current in the coil. The induced current flows to the amplifier for amplification before it is relayed to the loudspeaker where it is converted back to sound energy. FORM 4 PHYSICS LESSON NOTES 2018 Page 35 of 70 TOPIC 5: MAINS ELECTRICITY 5.1: Introduction Mains electricity refers to the electrical power supplied to households. The power is generated at the power station and then transmitted to the consumers either through overhead transmission lines or underground cables. Some of the sources of mains electricity include water in high dams, geothermal, wind, solar energy, coal and diesel engine generators, nuclear energy and tidal waves. Note that the choice of the source of mains electricity to use is dependent on its availability and abundance as well as the implications it has on the environment. In Kenya, the most utilized source of mains electricity is hydroelectricity. Today, there is also increased usage of solar energy, geothermal energy, wind energy and coal. 5.2: Electrical power transmission This is process by which electrical power is relayed from the generation plant to the consumers at their homes, institutions, schools, industries, factories etc. In Kenya, electrical power is distributed using the national grid system. The national grid system is a network of cables connecting at a common point all the power generation plants and then distributed to the consumers. This way it ensures availability of power even when one of the stations is shut down. Before power is fed into the national grid system, it is stepped up i.e. voltage is stepped up but current is stepped down. Most power stations generate between 11kV and 25kV which is stepped up to between 17kV and 400kV. At the consumer end, a step down transformer is used to step down the voltage to about 11kV at a substation. However, this value is still large to be used the way it is.
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A power station produces 50kW at 240V. The power is transmitted through cables with a resistance of 0.4 . Calculate the percentage power loss during transmission. Power VI 50,000W 240VxI I 50,000 240 208.8A Hence, power loss 208.37x0.4 17,360.556W power loss 17360.556 50000 x100 9.72 5.3: Domestic wiring From the step down transformer near the consumer, power is transmitted by two cables; the live and neutral wire to the consumer s meter which measures and registers the amount of power consumed. The live wire is at full potential of 240V while the neutral wire is at zero potential since it has been earthed at the sub-station. From the meter, electricity enters the fuse box which comprises of the following: Main switch- controls all the live and neutral wires simultaneously. It is normally useful during repairs. Live busbar- it is a brass bar on which all the live wires of all the circuits have been connected. Each live wire is connected to the live busbar through a fuse. Neutral busbar- it is a brass bar to which all neutral wires of all the circuits have been connected. FORM 4 PHYSICS LESSON NOTES 2018 Page 37 of 70 Earth terminal- it is used to earth the circuit. This can be done by burying a thick copper wire deep underground or through a metallic water piping. A fuse is a thin wire with very low melting point such that if it is overheated it melts and the circuit gets disconnected. This way it is used to safeguard electrical appliances. Fuses are rated in amperes. Normally, the fuse rating is slightly above the maximum current requirement of the appliance. All fuses must be connected along the live wire. In domestic wiring, there are three important types of wires commonly used namely live wire, neutral wire and earth wire. Live wire- it transmits alternating current from the source to the appliance or plug. It is normally red or brown in colour. Neutral wire- it is the return wire i.e. it returns the current back to the source completing the circuit. It is usually at zero potential. It is normally blue or black in colour. Earth wire- it earths the circuit.
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It is usually at zero potential. It is normally blue or black in colour. Earth wire- it earths the circuit. It is normally green or yellow in colour However, at times the fuse may melt off and thus fail to serve its rightful purpose. Some causes that can lead to melting off of the fuse include: i. Short circuiting when bare conductors touch each other. Ii. Overloading the circuit with more appliances than the fuse can accommodate. Iii. Using a fuse of lower rating than the current requirement of the appliance. Iv. Using a faulty fuse whose wire could have been oxidized. Example 5.2 1. An electric cooker has an oven rated 3kW, a grill rated 2kW and two rings each rated 500W. The cooker operates from 240V mains. Would a 5A fuse be suitable for the cooker assuming that all the parts are switched on? Ioven 500 240 12.5A Igrill 2000 240 8.8A 2Irings 2x500 240 4.17A Total cooker current 12.5 8.8 4.17 25.0A With a fuse rated 5A, it is suitable. Note that a circuit breaker can also be used to serve the same purpose as the fuse. It should be noted that a circuit breaker is better than a fuse since for a fuse once it has blown off it must be replaced while for a circuit breaker, it does not need to be replaced. Instead, the strip just needs time to cool off and then the circuit will be complete once again. FORM 4 PHYSICS LESSON NOTES 2018 Page 38 of 70 The diagram below shows a typical house wiring system: Main supply cable Meter box Fuse box Socket Cooker Heater Lights Ring main circuit 5.3.1: The lighting circuit This is the circuit that controls all the lamps within the house. Lamps are always connected in parallel so that they are operated from the same mains voltage. This also ensures that the other lamps continue to work when one is faulty. The lighting circuit uses very low current and therefore thin wires are usable. This is also the reason why the lighting circuit needs not to have the earth wire. It also has a low rated fuse, mostly 5A fuse. A two-way switch circuit In this circuit, a lamp is operated by two switches i.e.
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One kilowatt-hour is also referred to as one unit; 1kWh 1unit The total cost of electrical energy consumed by a household is given by the product of the number of units consumed and the charges per unit; Total cost number of units used x cost per unit. Example 5.3 1. A six bulb arrangement in a house runs for 8hours every night for 5days. If each bulb is rated 100W and the cost of electrical energy is sh. 2.60 per unit, how much will the owner of the house pay at the end of the five days? Electrical energy consumed 6x0.1x8 x5 24kWh Total cost 24kWh x sh 2.60 ksh. 62.40 2. An electric cooker has an oven rated 3kW, a grill rated 2kW and two rings each rated 500W. The cooker operates from a 240V mains. What is the cost of operating all the parts for 5minutes if electricity costs Sh 1.50 per unit? Total units consumed 3 2 2x0.5 x5 60 3kWh Total cost 3kWh x sh 1.50 Ksh 4.50FORM 4 PHYSICS LESSON NOTES 2018 Page 40 of 70 TOPIC 6: CATHODE RAYS AND CATHODE RAY TUBE 6.1: Introduction When a metal surface is heated, the electrons gain energy and become excited. At very high temperatures, the electrons may break off from the force of attraction of the nuclei. When heat is used to extract electrons from the surface of a metal, it is referred to as thermionic emission. Cathode rays are streams of fast moving electrons emitted from the surface of a heated cathode inside a vacuum. 6.2: Production of Cathode Rays. Cathode Anode Cathode rays Heater E.H.T. Vacuum Fluorescent screen Fig.1 Cathode Ray Tube Cathode rays are produced in a cathode ray tube. The cathode is heated by the heater emitting electrons through thermionic emission. Note that the cathode rays are streams of negatively charged particles electrons . Thus once emitted at the cathode, the electrons will be attracted by the anode which is at a positive potential.
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The cathode is heated by the heater emitting electrons through thermionic emission. Note that the cathode rays are streams of negatively charged particles electrons . Thus once emitted at the cathode, the electrons will be attracted by the anode which is at a positive potential. Hence the role of the anode is to accelerate the electrons towards the screen. The anode is connected to an extra high tension EHT source. The tube is evacuated. This is to prevent the electrons from interacting with any particles before reaching the screen. The screen is coated using a fluorescent material that glows when struck by the electrons. 6.3: Properties of Cathode Rays 1. They travel in straight lines. When an opaque object is placed along the path of the rays, a sharp shadow of the object is formed on the screen. 2. They are charged. Hence they are deflected by both magnetic and electric fields. 3. They posses kinetic energy. 4. They can cause certain substances e.g zinc sulphide screen to glow or fluoresce. 5. They can produce X-rays when they are suddenly stopped by a metal target. 6.4: The Cathode Ray Oscilloscope CRO This is an electrical instrument developed from the cathode ray tube and which can be used to display and analyze waveforms. It can display both alternating current and direct current waveforms. Furthermore, it can be used to measure voltages that vary over time. FORM 4 PHYSICS LESSON NOTES 2018 Page 41 of 70 A cathode ray oscilloscope has three main components: The electron gun. The deflecting system. The display system. Anode Y-plates Cathode Grid X-plates Heater Electron gun Deflecting system Display system a The electron gun It consists of three parts namely the cathode, grid and anode. The cathode emits electrons through thermionic emission. The grid concentrates the electrons into a tight beam. It is connected to the negative terminal of the EHT and thus it is at a negative potential. When the negative voltage of the grid is raised, fewer electrons will move towards the screen and thus the spot will be less bright. However, when the grid voltage is lowered, more electrons will move towards the screen and thus the spot will be brighter. In general, the grid controls the rate of flow of electrons to the screen i.e. intensity.
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However, when the grid voltage is lowered, more electrons will move towards the screen and thus the spot will be brighter. In general, the grid controls the rate of flow of electrons to the screen i.e. intensity. The anode on the other side is at a positive potential and is used to accelerate the emitted electrons towards the screen. It also focuses the electrons to a point on the screen. B The deflecting system This system places the electron beam on the screen.it comprise of two pairs of parallel plates namely the Y-plates and X-plates. The Y-plates are responsible for the vertical deflection. When the upper plate is at a positive potential for instance, the beam is deflected upwards while if the lower plate is now at a positive potential, the beam is deflected downwards. However, when both plates are at a zero potential the beam will pass undeflected. Electron beamFORM 4 PHYSICS LESSON NOTES 2018 Page 42 of 70 The X-plates are responsible for the horizontal deflection of the electron beam. Electron beam There is no deflection when the potential difference across the plates is zero but deflects towards the plate at a positive potential when connected to a source of voltage as shown on the figure above. If an alternating voltage is applied simultaneously to both the Y and X-plates, then the spot on the screen would oscillate up and down and at the same time move across the screen from left to right tracing a wave on the screen. When the spot reaches the extreme end it flies back to the starting point and process is repeated. The speed with which the spot moves on the screen can be adjusted by the time base knob. 6.5: Uses of the CRO i. Used as a voltmeter. The time base is switched off while the voltage to be measured is fed through the Y-gain of the CRO. The applied voltage displaces the spot vertically on the screen. The Y-gain control knob can be used to amplify the display on the screen by setting it to a certain value. This is referred to as the sensitivity of the CRO. Hence the corresponding voltage to the signal on the screen is expressed as; Voltage V vertical deflection cm x Y-gain setting or sensitivity volts cm Consider the waveform shown in the figure below: The maximum vertical deflection of the signal is 3cm or 3divisions on either side.
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The Y-gain control knob can be used to amplify the display on the screen by setting it to a certain value. This is referred to as the sensitivity of the CRO. Hence the corresponding voltage to the signal on the screen is expressed as; Voltage V vertical deflection cm x Y-gain setting or sensitivity volts cm Consider the waveform shown in the figure below: The maximum vertical deflection of the signal is 3cm or 3divisions on either side. Suppose the Y-gain setting is 50V cm; Then the peak voltage represented by the signal vertical displacement cm x Y-gain setting V cm . 3cm x50V cm 150V When used as a voltmeter, a CRO has the following advantages over the ordinary voltmeters: Can measure both direct and alternating voltages. Can measure very large voltages without being damaged. FORM 4 PHYSICS LESSON NOTES 2018 Page 43 of 70 Does not take any current in the circuit since it has infinite resistance. It responds instantly. The pointer of ordinary voltmeters always swings about the correct value. Ii. Used to measure frequency The signal whose frequency is to be measured is fed into the Y-gain and the time base is switched on and adjusted so that the waveform appears stationary on the screen. Suppose the time base setting is 10ms cm, it implies that the wave takes 10ms to cover 1cm horizontally. This can be used to determine the time of one wave i.e period T. Recall: frequency 1 period T. In the example above, suppose the time base is set at 40ms cm; Then, period T number of divisions fitting one wave x time base setting 4cm x 40 1000 s cm 0.16s Hence frequency of the signal 1 0.16 6.25Hz Other uses of the CRO include: Measurement of small time intervals. Measurement of amplitudes of direct and alternating voltages. Display of electrical signals whose variations can be put in the form of voltage. 6.6: The television tube A television tube comprises of three electron guns, two sets of coils for deflection and a fluorescent screen. There are two types TV tubes namely the black and white tube and a coloured tube.
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Display of electrical signals whose variations can be put in the form of voltage. 6.6: The television tube A television tube comprises of three electron guns, two sets of coils for deflection and a fluorescent screen. There are two types TV tubes namely the black and white tube and a coloured tube. The signal is fed into the television through the control grid. This varying incoming signal regulates the number of electrons being emitted by the electron gun at any instant. This in turn regulates the brightness of the spot on the screen. The screen is coated using green, blue and red phosphors. When a red colour is required for instance, the red electron gun emits a red electron beam which strikes the red phosphor on the screen. The same happens for green and blue colours. For white colour, all the three electron guns simultaneously fire electrons to the screen. However, for black colour, no beam is fired to the screen. The rest of the colours are just obtained from a combination of any two of the three colours. The deflection of the beams is done by the two coils; one responsible for the vertical deflection and the other for the horizontal deflection. A current is fed into these coils producing a magnetic field. As the electrons pass between the coils, the resultant force on them causes them to deviate. A magnetic field is preferred to an electric field in a TV tube because it gives a wider deflection on the screen and thus a shorter tube can be used. FORM 4 PHYSICS LESSON NOTES 2018 Page 44 of 70 TOPIC 7: X-RAYS 7.1: Production of x-rays X-rays are produced when fast moving electrons are suddenly stopped by a metal target. At the time of their discovery by a German Physicist Ron6tgen, their nature was unknown and hence their name x-rays. Generally, x-rays are uncharged electromagnetic radiations of short wavelength and high penetrating ability power . X-rays are produced in an x-ray tube: E.H.T Glass tube Target Cathode Electron beam Oil out Low voltage Cooling fins Oil in Filament X-rays Copper anode Current in the filament emits electrons at the cathode by thermionic emission. These electrons are then attracted towards the anode by the high potential difference that exists between the cathode and anode. On striking the target, the electrons transfer their kinetic energy to the metal target.
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X-rays are produced in an x-ray tube: E.H.T Glass tube Target Cathode Electron beam Oil out Low voltage Cooling fins Oil in Filament X-rays Copper anode Current in the filament emits electrons at the cathode by thermionic emission. These electrons are then attracted towards the anode by the high potential difference that exists between the cathode and anode. On striking the target, the electrons transfer their kinetic energy to the metal target. About 99.5 of this energy is converted to heat at the target and only 0.5 of the energy is responsible for the production of x-ray radiations. As such, the material of the target must be one that has a high melting point like molybdenum or tungsten. The anode should also be a good thermal conductor like copper so as to ensure efficient dissipation of heat. Further cooling at the anode is enhanced by a circulation of oil around the anode and the presence of cooling fins. In some tubes, the target is made in such away to rotate so as to change the point of impact and thus reduce wear and tear. The target is inclined at an angle to direct the x-rays out of the tube. The glass tube is also evacuated to prevent interference with the electron beam before reaching the target. The cathode is concave in shape to focus the emitted electrons to the target. The high potential difference is used to accelerate the emitted electrons towards the anode. The x-ray tube is well shielded using lead which absorbs any stray rays thereby protecting the user. 7.2: Properties of X-rays - Travel in straight lines with the speed of light in air; 3.0x108m s. When an opaque object like a bone is placed on the path of x-rays a sharp shadow of the object is formed on the screen. -. They carry no charge. Hence x-rays are not deflected by either magnetic fields or electric fields. -. Ionize air molecules on their paths by knocking off electrons in them. -. They cause certain substances and salts to fluoresce. FORM 4 PHYSICS LESSON NOTES 2018 Page 45 of 70 - They cause photographing emulsion, a property used in x-ray photography. -. They cause photoelectric effect when incident on the surface of some metals. -. They can readily penetrate matter. The degree of penetration depends on the density of the material and the quality of the x-rays. -. They obey the wave equation v f .
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- They can readily penetrate matter. The degree of penetration depends on the density of the material and the quality of the x-rays. -. They obey the wave equation v f . -. They undergo interference, reflection, refraction and diffraction effects. 7.3: Energy and Quality of x-rays When an electron of charge e is accelerated by a voltage V applied across the tube, the electron gains an amount of energy equivalent to eV electron volts . This energy is converted into kinetic energy of the electron; i.eeV K.E eV m 2, where m- mass of the electron m 9.11x10-6kg and - the velocity of the electron. Also, according to Plank s theory, the energy of any electromagnetic radiation x-rays included is given by; Energy, E hf, where h- is Plank s constant and f- is the frequency of the radiation. Hence for x-rays; eV m 2 hf h . Generally, most energetic x-rays are those with higher frequency or shorter wavelength while the least energetic x-rays are those with lower frequency or longer wavelength. The energy of x-rays depends on the accelerating potential between the cathode and the anode. The higher the accelerating potential, the higher the energy of the electrons. Since it is the energy of the electrons that is converted into x-rays, the higher the energy of the electrons the higher the energy of the x-rays. X-rays produced by high energetic electrons or high accelerating voltage are referred to as hard x-rays. They are high quality x-rays, have very high frequency and high penetrating power. X-rays produced from low energy electrons or low accelerating voltage are called soft x-rays. They are low quality xrays, have low energy content, low frequency and low penetrating power. 7.4: Intensity of X-rays Intensity of x-rays refers to the number of x-rays produced per second. It depends on the number of electrons striking the target per second. This is controlled by the filament current. The higher the filament current the higher number of electrons emitted and hence the greater the intensity of the x-rays. 7.5: Detection of X-rays X-rays can be detected by: - Using a fluorescent screen. The screen glows when struck by the x-rays. -. Using a photographic plate. The plate is blackened when exposed to x-rays.
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The screen glows when struck by the x-rays. -. Using a photographic plate. The plate is blackened when exposed to x-rays. 7.6: Uses of X-rays In medicineFORM 4 PHYSICS LESSON NOTES 2018 Page 46 of 70 - Detection of fractures, displaced bones or other strange objects within the body. -. Destruction of cancerous growths and other malignant growths. -. Testing densities of bones. -. Detection of lungs with tuberculosis. In industries - Detection of flaws in metals and welded joints. -. Checking percentages of certain elements in an ore. -. For security checks in airports. -. To check the purity or genuineness of certain precious stones like gold, silver etc. -. To sterilize surgical equipment before packaging. -. Detection of leakages in water pipes. In crystallography - To study the crystal structure of substances. 7.7: Dangers of X-rays Excessive exposure of living body tissues to x-rays may lead to damage or killing of the cells. X-rays can cause deep rooted burns, mutation and serious diseases. These can be minimized by: 1. Limiting the exposure time of living tissues to x-rays. 2. X-ray sources should be well screened or shielded. Example 7.1 take h 6.63x10-9Js, e 1.6x10-19C, me 9.11x10-6kg and 3.0x108m s 1. Calculate the energy of x-rays whose frequency is 3x1016Hz. E hf 6.63x10-9Jsx3x1016Hz 1.989x10-17J 2. In an x-ray tube, an electron is accelerated by a potential difference of 1kV. a Determine the velocity of the electron as it is reaching the target. EV m 2 1.6x10-19Cx1000V x9.11x10-6kg x 2FORM 4 PHYSICS LESSON NOTES 2018 Page 47 of 70 2 3.5126x1014 b How much kinetic energy will the electron have acquired when it hits the target? EV K.E 1.6x10-19Cx1000V 1.6x10-16J 3.
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A Determine the velocity of the electron as it is reaching the target. EV m 2 1.6x10-19Cx1000V x9.11x10-6kg x 2FORM 4 PHYSICS LESSON NOTES 2018 Page 47 of 70 2 3.5126x1014 b How much kinetic energy will the electron have acquired when it hits the target? EV K.E 1.6x10-19Cx1000V 1.6x10-16J 3. Explain how you can increase: a Quality of x-rays. By increasing the accelerating potential between the cathode and the anode. B Intensity of the x-rays. By increasing the filament current so that more electrons are emitted per unit time. 4. An x-ray tube operates at 10kV and a current of 15mA. Calculate the number of electrons hitting the target per second. I ne 15x10-3A nx1.6x10-19C n 9.375x1016electrons. 5. An x-ray tube operates at 20kV. What is the shortest wavelength in its x-ray beam? EV h 1.6x10-19x20000V 6.63x10-9Jsx3.0x108 6.2156x10-11m 6. State any differences between x-rays and cathode rays. -. X-rays are uncharged while cathode rays are charged. -. X-rays are produced in an x-ray tube while cathode rays are produced in a cathode ray tube. FORM 4 PHYSICS LESSON NOTES 2018 Page 48 of 70 TOPIC 8: PHOTOELECTRIC EFFECT 8.1: Photoelectric emission We have already seen that when a metal surface is heated to a certain extent, electrons are dislodged. This is called thermionic emission. Similarly when a metal surface is irradiated using an electromagnetic radiation of a certain amount of energy, electrons are emitted. This process is called photoelectric emission or effect. The energy of the radiation is transferred to the electrons in the atoms of the metal. The electrons gain enough energy and get dislodged from the metal surface. These electrons are called photoelectrons.
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The energy of the radiation is transferred to the electrons in the atoms of the metal. The electrons gain enough energy and get dislodged from the metal surface. These electrons are called photoelectrons. Photoelectric emission can be shown by the following set-ups: 8.1.1: Using a galvanometer UV Radiation When the UV radiation is incident on the metal plate A, electrons are emitted which are then attracted towards plate B due to its positive potential. This completes the circuit and the galvanometer deflects. However, when a glass barrier is placed along the path of the UV radiation no deflection will be observed as the glass cuts off the radiation from reaching the metal plate hence no photoelectrons are emitted. 8.1.2: Using a clean zinc plate and uncharged electroscope. UV radiation Clean zinc plate When UV radiation is incident on the clean zinc plate, electrons are dislodged from the zinc plate. The zinc plate thus loses electrons. Some electrons are then attracted from the plate and leaf of the electroscope towards the zinc plate leaving the electroscope positively charged. Hence the leaf of the electroscope diverges. B AFORM 4 PHYSICS LESSON NOTES 2018 Page 49 of 70 8.1.3: Using a clean zinc plate and a charged electroscope UV radiation Clean zinc plate The UV radiation dislodges electrons from the surface of the zinc plate leaving it with a deficit of electrons. It then attracts some electrons from the leaf of the electroscope. This in effect discharges the electroscope and the leaf divergence reduces with time. However, when a positively charged electroscope is used, the UV radiation dislodges electrons which are immediately attracted back by the positive charges on the electroscope. Thus the leaf divergence remains unchanged. UV radiation Clean zinc plate 8.2: The quantum theory and Einstein s equation This theory was advanced by Max Plank. He says that electromagnetic radiations like light are propagated in small packets of energy called quanta singular- quantum . The amount of energy of a quantum is referred to as a photon. According to Plank, the energy of a photon is directly proportional to the frequency of the radiation; E f Thus, E hf: where h is Plank s constant i.e h 6.63x10-9Js .
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He says that electromagnetic radiations like light are propagated in small packets of energy called quanta singular- quantum . The amount of energy of a quantum is referred to as a photon. According to Plank, the energy of a photon is directly proportional to the frequency of the radiation; E f Thus, E hf: where h is Plank s constant i.e h 6.63x10-9Js . Since all electromagnetic radiations obey the equation c f ; E hc , where c is the velocity of the radiation in a vacuum and is the wavelength. Hence the larger the frequency the shorter the wavelength the greater the energy of a radiation. Note that all the energy of one photon is absorbed by one electron. This implies that the energy of the radiation must be sufficient to dislodge an electron from the surface of the metal otherwise no electron would be emitted. Electrons of various metals require different amounts of energy to be emitted. The minimum energy requirement of any metal to emit an electron is referred to as the workfunction, w0 of that metal. This implies that the radiation being used must meet a certain minimum frequency below which no photoemission occurs. This minimum frequency is called the threshold frequency, f0. FORM 4 PHYSICS LESSON NOTES 2018 Page 50 of 70 Hence workfunction, w0 hf0. For any radiation of frequency f which is less than the threshold frequency f0 of the metal surface, the energy, hf of the radiation will be less than the workfunction, w0 of the metal. Hence no photoemission takes place. However, when the frequency, f of the radiation is greater than the threshold frequency f0 of the metal, then the amount of energy equilavent to the workfunction of the metal will be used to emit an electron and the rest of the energy will be converted into kinetic energy of the electron. I.e energy of the radiation workfunction kinetic energy of the electron. E w0 k.e hf hf0 m 2, where m- mass of an electron 9.11x10-6kg and - the velocity of the electron. This equation is known as Einstein s equation of photoelectric emission. Alternatively, the radiation being used must not exceed a certain maximum wavelength for photoemission to occur recall w0 hf0 hc 0 .this is called threshold wavelength.
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Explain whether photoelectric emission will occur or not. Energy of the radiation hf 6.63x10-9x4.3x1014 1.602x10-19J 1.7796eV Since the energy of the radiation is less than the workfunction, no photoelectric emission will occur. Alternatively; Workfunction hf0 2.6x1.602x10-19 f0 2.6x1.602x10-19 6.63x10-9 6.74x1014Hz Since the frequency of the radiation is less than the threshold frequency of the metal, there is no photoelectric emission. 8.3: Factors affecting photoelectric emission There are three main factors affecting photoelectric emission namely: - Energy of the radiation - Intensity of the radiationFORM 4 PHYSICS LESSON NOTES 2018 Page 51 of 70 - Type or nature of the metal 8.3.1: Energy of the radiation The amount of energy of the emitted electrons is directly proportional to the frequency of the radiation. This can be shown by using radiations of different frequencies and investigating the stopping potential for each radiation. Stopping potential is the potential difference at which none of the emitted electrons reach the anode. Colour filter Various filters are used in turn to give light of different frequencies. For each filter, the variable resistor is used to vary the resistance until no current is registered by the micro-ammeter. Note that the source of d.c voltage is connected in such away that it opposes the flow of the ejected electrons i.e it works against the kinetic energy of the ejected electrons. The absence of a reading on the micro-ammeter indicates no flow of electrons. Hence, when no electron flows; eVs k.e eVs m 2. Substituted in the Einstein s equation, we obtain: hf hf0 eVs.
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The absence of a reading on the micro-ammeter indicates no flow of electrons. Hence, when no electron flows; eVs k.e eVs m 2. Substituted in the Einstein s equation, we obtain: hf hf0 eVs. V FORM 4 PHYSICS LESSON NOTES 2018 Page 52 of 70 Below is a typical result obtained by using different colour filters of different frequencies and their corresponding stopping potentials: Frequency, f x1014 Hz 1.65 1.9 1.17 1.00 Stopping potential, Vs V 0.20 0.40 0.60 0.98 When a graph of the stopping potential Vs against frequency is plotted, the graph would appear as shown below: Stopping potential Slope Vs f h e Vs 0 f0 Frequency, f x1014 Hz -w0 e 8.3.2: Intensity of the radiation It is defined as the rate of energy flow per unit area when the radiation is normal to the surface area ; Intensity E At But E t power, P. Hence, Intensity P t. Suppose the source of the radiation is a distance r from the metal plate, then the intensity of the radiation is inversely proportional to the square of the distance r; I 1 r2. Thus as the distance r decreases the intensity of the radiation increases and hence the value of the current is increased. FORM 4 PHYSICS LESSON NOTES 2018 Page 53 of 70 8.3.3: The type nature of the metal Each metal has its own workfunction and hence threshold frequency. If the energy of the radiation striking the metal is below its workfunction then no electron will be ejected despite its intensity. Example 8.2 1. The threshold wavelength of a photoemissive surface is 0.45 m. calculate: a. The threshold frequency of the surface. F0 c 0 3.0x108m s 0.45x10-6m 6.67x1014Hz. B. The workfunction of the surface in eV. W0 hf0 6.63x10-9x6.67x1014 1.602x10-19 2.76eV c.
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B. The workfunction of the surface in eV. W0 hf0 6.63x10-9x6.67x1014 1.602x10-19 2.76eV c. The minimum speed with which a photoelectron is emitted if the frequency of the radiation is 7.5x1014Hz. 6.63x10-9x7.5x1014 6.63x10-9x6.67x1014 x9.11x10-6x 2 12.081x1010 3.4754x105m s. 9.4: Applications of photoelectric effect 8.4.1: Photoemissive cell It consists of a cathode and an anode. When light falls on a photosensitive cathode, electrons are dislodged which are then attracted by the anode. This completes an external circuit and current flows. When a body passes between the cathode and the source of light, the light is cut off and no photoemission takes place. Such cells can be used in: Automatic opening of doors Burglar alarms for security Automated counting machine Reproduction of sound from a film. FORM 4 PHYSICS LESSON NOTES 2018 Page 54 of 70 Below is the symbol of a photoemissive cell. 8.4.2: Photovoltaic cells Gold film Copper oxide Copper Light strikes the cell on the gold film side which emits electrons from the copper oxide surface. The copper oxide thus acquires a negative potential and copper a positive potential. A potential difference is therefore created and a current flows through a wire connecting the gold film and the copper externally. Below is the symbol of a photovoltaic cell: 8.4.3: Photo-conductive cell It is also called the light dependent resistor. The resistance of the cell varies with intensity of the light falling on it. In darkness, the resistance of the cell is greatest and least on a bright light. Below is the symbol of the photo-conductive cell: Light dependent resistor can be used in operating street lights, fire alarms, detection and measurement of infra red radiation.
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The resistance of the cell varies with intensity of the light falling on it. In darkness, the resistance of the cell is greatest and least on a bright light. Below is the symbol of the photo-conductive cell: Light dependent resistor can be used in operating street lights, fire alarms, detection and measurement of infra red radiation. FORM 4 PHYSICS LESSON NOTES 2018 Page 55 of 70 TOPIC 9: RADIOACTIVITY 9.1: Introduction An atom X of mass number A and atomic number Z can be represented as . If the number of neutrons in the nucleus is N, then: A Z N. Some atoms have the same number of protons in the nucleus yet different mass numbers. Such atoms are referred to as isotopes. Examples of isotopes include carbon- 12 and carbon- 14. The energy holding the protons and neutrons together in the nucleus is called the binding or nuclear energy. When the ratio of the number of protons to the number of neutrons in a nucleus is about 1:1, the nuclide is said to be stable, otherwise it is an unstable. For unstable nucleus, it has to undergo disintegration a process called radioactivity. Radioactivity is the spontaneous disintegration of the nucleus of unstable atom to release radiations. In the process of radioactivity, there are three radiations which may be emitted namely alpha , beta and gamma radiations. Their behavior can be observed when they are passed through a magnetic or electric field. P Q R Radioactive source P- Beta radiation Q- Gamma radiation R- Alpha radiation Alpha radiations: Are positively charged. Are massive or heavy and thus have shorter range in air. They are slightly deflected by strong magnetic or electric field due to their higher mass. Cause the highest ionization effect on the particles on their paths compared to beta and gamma radiations, thereby losing most of their energy. Have the least penetrating ability or power compared to the other two radiations. They can be stooped by a thick sheet of paper. Beta radiations: Are negatively charged. Are lighter compared to alpha radiations. Hence they are greatly deflected by strong magnetic or electric field. Have longer range in air.
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Are lighter compared to alpha radiations. Hence they are greatly deflected by strong magnetic or electric field. Have longer range in air. FORM 4 PHYSICS LESSON NOTES 2018 Page 56 of 70 Cause less ionization compared to alpha radiations. Hence they have a higher penetrating ability or power. They can penetrate a thick sheet of paper but can be stopped by a thin aluminium foil. Gamma radiations: Are massless and do not have charge. Hence they are not deflected by both magnetic and electric fields. Are electromagnetic waves. Cause very little ionization. Hence most of their energy is intact. They have the highest penetrating ability or power of all the three radiations. They can penetrate thick paper and aluminium but is stopped by thick lead. 9.2: Radioactive decay and the decay equations The original atom before the decay process is referred to as the parent mother nuclide and the product is referred to as the daughter nuclide. A radioactive decay process consists of a parent nuclide, a daughter nuclide and the emitted radiation s . Emitted radiation s Where X- the parent nuclide Y- the daughter nuclide Note that a particular radioactive decay process must not necessarily emit all the three radiations. Suppose a radioactive decay process takes the form shown by the equation below: , where X is the parent nuclide, Y is the daughter nuclide and Q is the emitted radiation; Then, A m a and Z n b. Radioactive decay is not dependent on physical factors like pressure, temperature or chemical composition of the nuclide. There are three types of radioactive decay: 9.2.1: Alpha decay This decay process emits alpha radiation s . Alpha radiation is the nucleus of a helium atom represented by .
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Radioactive decay is not dependent on physical factors like pressure, temperature or chemical composition of the nuclide. There are three types of radioactive decay: 9.2.1: Alpha decay This decay process emits alpha radiation s . Alpha radiation is the nucleus of a helium atom represented by . If a nuclide decays by releasing an alpha particle, the mass number of the parent nuclide is reduced by 4 while atomic number is reduced by 2; Example 9.1 FORM 4 PHYSICS LESSON NOTES 2018 Page 57 of 70 9.2.2: Beta decay When an atom undergoes beta decay, it emits a beta particle. A beta particle is a fast moving electron represented by . The mass number of such a nuclide remains the same while its atomic number increases by one 1 . . Example 9.2 9.2.3: Gamma decay Gamma decay does not have any effect on the mass number or atomic number of the nuclide. Instead the nuclide attains stability by simply releasing energy in the form of gamma radiation.
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These can cause further ionization rendering the pulse registered incorrect. To counter this, bromine is used which acts as a quenching agent, absorbing the energy of the positive ions before they reach the cathode. This method is not suitable for detection of gamma radiations due to its low ionization effect. FORM 4 PHYSICS LESSON NOTES 2018 Page 59 of 70 9.3.4: The diffusion cloud chamber Black metal base Perspex lid Radioactive source Felt ring soaked in alcohol Light source Dry ice solid carbon iv oxide Sponge Wedge Removable base This detector uses the concept that when an ionizing radiation passes through air with saturated vapour, then the vapour is observed to condense on the ions formed. This explains why aeroplanes sometime leave trails of cloud behind them as they move through super saturated air. In the diffusion cloud chamber, alcohol vaporizes and diffuses towards black metal base. When a charged particle from the radioactive source; either alpha or beta particle, knocks the air particles ions are produced. The vaporized alcohol condenses on the formed ions. Since positive ions are heavy, they remain behind forming tracks which can be clearly seen through the Perspex lid. To enhance visibility, a source of light is used to illuminate the chamber. The dry ice is used to keep the black metal base cool while the sponge is used to keep the dry ice in contact with the black metal base. Each radiation will produce a specific track as shown below: Tracks due to alpha radiation They are: - Short, indicating their shorter range in air. -. Straight; due to their mass it is not easy to displace them from their path by air particles. -. Thick, to show they are heavy particles. Tracks due to beta radiation They are: - Long, indicating their longer range in air. -. Thin, indication of their lower mass. FORM 4 PHYSICS LESSON NOTES 2018 Page 60 of 70 - Irregular in direction not straight , meaning that they can be displaced by air particles. Tracks due to gamma radiation Tracks due to gamma radiation are generally scanty and disjointed. These tracks do not come directly from the source but from electrons released by the gas atoms when they are struck by gamma radiation. The electrons then produce their own tracks. 9.4: Background radiation Sometimes even in the absence of a radioactive source nearby, a GM tube may still register some radiations. This is called background radiation and it is present within the atmosphere.
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9.8: Applications of radioactivity In medicine: Gamma rays can be used to control cancerous growths in the human body. Gamma rays can be used to sterilize surgical equipment. Can be used to monitor blood circulation disorders and the functioning of thyroid gland. In carbon dating- it uses the ratio of carbon-12 to carbon-14 to estimate the ages of fossils. Pipe leakages- the content being transported through the pipe is mixed with some radioactive substance which can be detected by a radiation detector on the ground around the area of leakage. In Agriculture- a radiation detector can be used to monitor the uptake of minerals introduced to plants by mixing it with some weak radioactive substance. Gamma rays can also be used to kill pests or make them sterile. Determination of thicknesses of thin metal sheets, paper or plastics- a GM tube is used to measure the thickness of the metal plates, paper or plastic. The source of radiation is placed on one side while the GM tube is placed on the opposite side. The metal plate is passed between the source and the detector. The countrate registered is a measure of the thickness of the metal plate. To be more efficient, a thickness gauge can be adapted which automatically controls the thickness of the metal foils, paper or plastics. 9.9: Hazards of radioactivity and their remedy The effects of radiation on a human body depends on: The nature of the radiation, Dosage andFORM 4 PHYSICS LESSON NOTES 2018 Page 63 of 70 Part of the body irradiated. Excessive exposure of body cells to radiations can lead to burn effects or genetic damage. Extreme heavy doses can be fatal. There could also be delayed effects such as cancer, leukemia and hereditary defects. Gamma rays and beta radiation are more dangerous compared to alpha radiation due to their high degree of penetration. Precautions should therefore be taken when handling radioactive materials. These include: Always use forceps to handle radioactive materials. Never use bare hands to hold such materials. Keep radioactive materials in thick lead boxes. Use radiation absorbers in hospitals and research laboratories. Reduce time spent near radiation sources. FORM 4 PHYSICS LESSON NOTES 2018 Page 64 of 70 TOPIC 10: ELECTRONICS 10.1: Introduction This topic is about electronic circuits and their applications.
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Another electron in the valence band may jump into the hole formed creating another hole which may be filled by yet another electron and the process continues. The movement of the electrons generates electron current while that of holes constitute hole current. Thus the net flow of current in semiconductors is due to the flow of electrons and holes. Valence band Hole 2 1 e- e- e- e- e- e- e- e- e- e- e- e-FORM 4 PHYSICS LESSON NOTES 2018 Page 65 of 70 Forbidden gap Conduction band There are two types of semiconductors as discussed below: 10.2.1: Intrinsic semiconductors These are pure semiconductors whose electrical conductivity can be enhanced by increasing the temperature of the semiconductor. They include silicon, germanium etc. They have four electrons in their outermost energy level. Their electrical conductivity is dependent on the electron-hole pair movement. The electrons and the holes are referred to as charge carriers. At room temperature, intrinsic semiconductors are insulators. 10.2.2: Extrinsic semiconductors These are semiconductors obtained when a small amount of impurity is added to an intrinsic semiconductor. The process of adding an impurity to a pure semiconductor to improve its electrical conductivity is referred to as doping. Generally an extrinsic semiconductor is an impure semiconductor. The impurity can either be a group three element e.g boron, gallium and indium or a group five element e.g phosphorous, antimony etc. Doping using a group three element When silicon is doped using a group three element like boron, all the three electrons on the outermost energy level of boron atom participate in bonding with the neighboring atoms while silicon will have an extra electron. A vacancy will therefore exist due to the missing electron. This is treated as a hole. This hole is responsible for the electrical conductivity of the doped semiconductor. Hence holes are the majority charge carriers while electrons are the minority charge carriers. Such an impurity is called an acceptor impurity because they create a hole which can accept an electron. An extrinsic semiconductor in which the majority charge carriers are holes is called a p-type semiconductor.
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Hence holes are the majority charge carriers while electrons are the minority charge carriers. Such an impurity is called an acceptor impurity because they create a hole which can accept an electron. An extrinsic semiconductor in which the majority charge carriers are holes is called a p-type semiconductor. Boron Hole Doping using a group five element When a pure semiconductor is doped using a group five element like phosphorous having five electrons in their outermost energy levels, four of the electrons participate in bonding with the neighboring atoms while the remaining electron is used for electrical conductivity in the semiconductor. Hence electrons will be the majority charge carriers while holes will be the minority charge carriers. The impurity is referred to as a donor impurity since it donates an electron for electrical conductivity. SBSSSSPSSSeFORM 4 PHYSICS LESSON NOTES 2018 Page 66 of 70 The resultant semiconductor is known as an n-type semiconductor. Note that both p-type and n-type semiconductors are electrically neutral since the impurities added have the same number of electrons as there are protons. 10.3: A P-N Junction diode A p-n junction diode can be obtained when an intrinsic semiconductor is doped simultaneously using a trivalent and pentavalent impurities such that one half forms a p-type semiconductor while the remaining half forms an n-type semiconductor respectively. The boundary between the p-side and the n-side is referred to as a p-n junction. P-n junction p- type n-type Immediately the junction is formed, a region called depletion layer is formed which prevents the free movement of electrons and holes across the junction. Thus the depletion layer develops a potential barrier at the junction. It acts as an insulator. For holes to cross to the n-side and electrons to the p-side, the potential barrier must be overcome. The symbol of a p-n junction diode appears as shown below: When a p-n junction diode is connected to a power supply it is said to have been biased. A p-n junction diode allows current to flow only in one direction when the p-side is connected to the positive terminal of the power source and nside to the negative terminal of the power source. When connected this way, the diode is said to be forward biased. The cell provides the energy for the electrons to overcome the potential barrier and the holes are also able to cross over to the n-side thereby completing the circuit. The electrons and holes are attracted to the opposite ends.
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When connected this way, the diode is said to be forward biased. The cell provides the energy for the electrons to overcome the potential barrier and the holes are also able to cross over to the n-side thereby completing the circuit. The electrons and holes are attracted to the opposite ends. The thickness of the depletion layer is reduced and the charges flow with a lot of ease. However, when the terminals of the cell are reversed such that the n-side is connected to the positive terminal and the pside to the negative terminal of the cell, then the diode is said to be reverse biased. E- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e-FORM 4 PHYSICS LESSON NOTES 2018 Page 67 of 70 When the diode is connected in this manner, the holes in the p-type are attracted away from the junction by the external negative potential. Also, electrons are attracted away from the junction by the external positive potential. This increases the thickness of the depletion layer. Thus the potential barrier and hence the resistance of the function is increased. A very small current leakage current may flow in the circuit due to the flow of minority charge carriers. 10.4: Diode Characteristics This is the relationship between current and voltage across a diode when connected to a power source. The set up below shows a circuit in which a diode has been forward biased: When the switch is closed, current flows through the diode since it is forward biased and it is recorded by the milliammeter. The voltage across the diode is measured by the voltmeter. The variable resistor is used to vary the current through the circuit. When a graph of current against voltage is plotted, the graph will be a curve as shown below: Current mA VC Voltage V Initially as the forward voltage is increased from zero, no current is registered because the voltage is insufficient to overcome the potential barrier. When the potential barrier is completely overcome current start to increase. The voltage at which the potential barrier is overcome is referred to as the cut-in voltage Vc . Charges thereafter flow easily across the junction. Since the graph is non-linear, it implies that a diode is non-ohmici.e it does not obey Ohm s law.
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PTT Elaed EY CotPr CTetded EL odyBe Pun nNwit i KUNGSecondaryPHYSICSStudent s Book One Fourth Edition KENYA LITERATURE BUREAUP.O. Box 30022-00100, NairobiWebsite: www.kenyaliteraturebureau.comE-mail: info kenyaliteraturebureau.com Ministry of EducationAll rights reserved. No part of this book may be reproduced, stored in a retrieval system, ortranscribed, in any form or by any means, electronic, mechanical, photocopying, recordingor otherwise, without the prior written permission of the publisher. ISBN 978-9966-10-142-6First published 1988Second Edition 1995Third Edition 2004Reprinted 2006, 2007, 2008 twice , 2010, 2011Fourth Edition 2013KLB 10821 10m 2013Published and printed by Kenya Literature BureauContentsPrologueAcknowledgements1. Introduction to PhysicsPhysics as a scienceMeaning of physicsBranches of physicsRelationship between physics and other subjectsCareer opportunities in physicsBasic laboratory rules2. Measurement I LengthAreaVolumeMassDensityTimeRevision Exercise 23. ForceType of forcesGravitational forceTensionUpthrustCohensive and adhesive forcesFrictional forceMagnetic forceElectrostatic forceCentripetal forceSurface tensionAction and reactionMass and weightScalar and vector quantitiesRevision Exercise 34. PressureUnits of pressurePressure in liquidsLiquid levelsDerivation of fluid pressure formulaTransmission of pressure in liquidsHydraulic machinesAtmospheric pressureMercury barometerFortin barometerAneroid barometerPressure gaugesApplication of pressure in gases and liquidsRevision Exercise 45. The particulate nature of matterInvestigating matterThe smoke cell experimentDiffusionRevision Exercise 56. Thermal expansionTemperatureExpansion and contraction of solidsExercise 6.1Expansion and contraction of liquidsExpansion of gasesMeasuring temperatureRevision Exercise 67. Heat transferHeat and temperatureModes of heat transferFactors affecting thermal conductivityThermal conductivity in liquidsThermal conductivity in gasesSome applications of good and poor conductors of heatConvectionRadiationApplications of thermal radiationRevision Exercise 78.
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| 1,750,280,445.934013 |
The particulate nature of matterInvestigating matterThe smoke cell experimentDiffusionRevision Exercise 56. Thermal expansionTemperatureExpansion and contraction of solidsExercise 6.1Expansion and contraction of liquidsExpansion of gasesMeasuring temperatureRevision Exercise 67. Heat transferHeat and temperatureModes of heat transferFactors affecting thermal conductivityThermal conductivity in liquidsThermal conductivity in gasesSome applications of good and poor conductors of heatConvectionRadiationApplications of thermal radiationRevision Exercise 78. Rectilinear propagation and reflection at plane surfacesSources of lightRays and beams of lightTypes of beams of lightRectilinear propagation of lightShadowsEclipseThe pinhole cameraMagnificationReflection of lightRotation of a mirror through an angleFormation of images by plane mirrorsImages formed by mirrors at an angleApplications of plane mirrorsRevision Exercise 89. Electrostatics I Origin of chargeThe electroscopeCharges in airApplications of electrostatic chargesDangers of electrostaticsRevision Exercise 910. Cells and simple circuitsA simple electric circuitConnecting cells in series and parallelConductors and insulatorsSources of electricityRevision Exercise 10PrologueThis book is primarily meant to cover exhaustively the Form One Physicssyllabus as per the new 8-4-4 curriculum. It is by design also a versatilecompanion for those students taking related courses in technical colleges andother institutions. The book has been made more elaborate and the in-depth theoreticalcoverage boosted with numerous experiments to enhance a better understandingof concepts under study. Any student making full use of the title and by extension the KLBSecondary Physics series, will certainly acquire scientific knowledge and skillsuseful in answering the challenges of daily life. I am grateful to the panel of writers and everybody who took part in thepreparation and production of this edition. THE MANAGING DIRECTORKenya Literature BureauAcknowledgementsThe Managing Director, Kenya Literature Bureau, would like to thank thefollowing writers who participated in the revision of this book:Oliver MinishiErastus MuniHesborne OmoloGrace MwangashaIntroduction to PhysicsPhysics as a ScienceOne of the subjects offered in primary school is Science.
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Electrostatics I Origin of chargeThe electroscopeCharges in airApplications of electrostatic chargesDangers of electrostaticsRevision Exercise 910. Cells and simple circuitsA simple electric circuitConnecting cells in series and parallelConductors and insulatorsSources of electricityRevision Exercise 10PrologueThis book is primarily meant to cover exhaustively the Form One Physicssyllabus as per the new 8-4-4 curriculum. It is by design also a versatilecompanion for those students taking related courses in technical colleges andother institutions. The book has been made more elaborate and the in-depth theoreticalcoverage boosted with numerous experiments to enhance a better understandingof concepts under study. Any student making full use of the title and by extension the KLBSecondary Physics series, will certainly acquire scientific knowledge and skillsuseful in answering the challenges of daily life. I am grateful to the panel of writers and everybody who took part in thepreparation and production of this edition. THE MANAGING DIRECTORKenya Literature BureauAcknowledgementsThe Managing Director, Kenya Literature Bureau, would like to thank thefollowing writers who participated in the revision of this book:Oliver MinishiErastus MuniHesborne OmoloGrace MwangashaIntroduction to PhysicsPhysics as a ScienceOne of the subjects offered in primary school is Science. At secondary schoollevel and beyond, this subject is split into three main areas namely, Biology,Chemistry and Physics. The three, however, are interrelated since they are all human attempts toexplore the universe and its contents by establishing facts through observationand experiment. The primary school science syllabus covers topics such as Matter and itsProperties, Energy in its various forms, e.g., heat, light, sound and theircorresponding sources, Machines and the way they make work easier, Balancingand Weighing of various Shapes of objects, Electricity and Magnetism. All thesetopics form the basic foundation for Physics at secondary school level. Meaning of PhysicsPhysics is defined as the study of matter and its relation to energy. The subject isapplied in explaining phenomena like eclipse, lightning, rainbow, mirage andmany other wonders of nature. Physics explains the how and why behind the: falling of bodies towards the ground. Daily occurrence of tides in the sea. Rising up of a liquid through a drinking straw. Cracking sound produced when removing a nylon cloth from the body, andmany more. Rapid technological developments in communication, transport, medicine,among other disciplines.
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All thesetopics form the basic foundation for Physics at secondary school level. Meaning of PhysicsPhysics is defined as the study of matter and its relation to energy. The subject isapplied in explaining phenomena like eclipse, lightning, rainbow, mirage andmany other wonders of nature. Physics explains the how and why behind the: falling of bodies towards the ground. Daily occurrence of tides in the sea. Rising up of a liquid through a drinking straw. Cracking sound produced when removing a nylon cloth from the body, andmany more. Rapid technological developments in communication, transport, medicine,among other disciplines. Boeing 787, tablet, smart phone, I-pad and plasma TV.Through the study of Physics, the various forms of energy available can beharnessed for a more easily manageable and fulfilling life. Thus, a waterfall or ahot spring is seen as a source of electrical energy. On the other hand, radiowaves and microwaves as a means of energy propagation, have been put into usein the working of radio, television, satellites, computers and the telephone. As a subject, the study of Physics involves measurement of quantities andcollection of data. Through experimentation and observations, hypotheses aredrawn, tested and consequently laws and principles established. Branches of PhysicsPhysics as a study may be divided into the following key areas:MechanicsThis involves the study of motion of bodies under the influence of forces. Inmechanics, the characteristics of linear, circular and oscillatory motion areexplained. The equilibria of forces of bodies and fluids at rest and when inmotion are also explored. Electricity and MagnetismThis deals with the relationship between electric currents and magnetic fieldsand their extensive applications in the working of the electric motor, magneticrelay and telephone receiver, among others. ThermodynamicsThis is the study of transformation of heat to and from other forms of energy. Amajor reference is made to gas behaviour in which thermal exchanges and theaccompanying changes of pressure and volume are explained in line with theKinetic Theory of Matter. Geometrical OpticsUnder this title, the behaviour of light as it traverses various media is studied. Optical instruments such as telescopes, microscopes, periscopes and lawsgoverning their working form a major part of this branch of physics. WavesIn this area, the propagation of energy through space is discussed.
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Inmechanics, the characteristics of linear, circular and oscillatory motion areexplained. The equilibria of forces of bodies and fluids at rest and when inmotion are also explored. Electricity and MagnetismThis deals with the relationship between electric currents and magnetic fieldsand their extensive applications in the working of the electric motor, magneticrelay and telephone receiver, among others. ThermodynamicsThis is the study of transformation of heat to and from other forms of energy. Amajor reference is made to gas behaviour in which thermal exchanges and theaccompanying changes of pressure and volume are explained in line with theKinetic Theory of Matter. Geometrical OpticsUnder this title, the behaviour of light as it traverses various media is studied. Optical instruments such as telescopes, microscopes, periscopes and lawsgoverning their working form a major part of this branch of physics. WavesIn this area, the propagation of energy through space is discussed. In addition,effects such as reflection, refraction and diffraction of light and sound areexplained using the wave theory. Atomic PhysicsThis involves the study of the behaviour of particles constituting the nucleus andthe accompanying energy changes. It is within this area that radioactivity,nuclear fission and fusion are dealt with. Relationship between Physics, other Subjects and TechnologyPhysics and ReligionSystems in the universe reveal great orderliness which can be traced back to thecreator. The study of Physics comes up with findings that are in total agreementwith this orderliness. The earth faithfully maintains its rotation so that the sunwill always rise from the East and never from the West. Among the manywonders of creation in Physics is the anomalous expansion of water and itsimplications on aquatic life. Physics and HistoryCarbon dating, an application of radioactivity, serves as a crucial tool tohistorians in establishing fossil ages and hence past patterns of life. Earlyexplorers like Vasco da Gama made use of the magnetic properties of lodestoneto determine direction. Physics and GeographyEstablishment of weather patterns relies on the accurate use of instruments likethe thermometer, wind-vane and hygrometer. Heat transfer by convectionexplains the formation of convectional rainfall and pressure variations thatdetermine wind patterns. All these are concepts in Physics. Physics and Home SciencePhysics knowledge has been applied in the design and manufacture of domesticequipment.
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Earlyexplorers like Vasco da Gama made use of the magnetic properties of lodestoneto determine direction. Physics and GeographyEstablishment of weather patterns relies on the accurate use of instruments likethe thermometer, wind-vane and hygrometer. Heat transfer by convectionexplains the formation of convectional rainfall and pressure variations thatdetermine wind patterns. All these are concepts in Physics. Physics and Home SciencePhysics knowledge has been applied in the design and manufacture of domesticequipment. Examples are pressure cookers, microwave ovens, refrigerators andthe energy saving jiko and light bulb. Physics and BiologyKnowledge of lenses has helped in the making of the microscope which hasassisted in the study of the cell, the basic unit of life. Similarly, the knowledge oflevers helps to explain locomotion in Biology. Physics and ChemistryPhysics has helped in explaining forces within atoms and therefore, atomicstructure. It is this structure of the atom that then determines the reactivity of theatom as explained in Chemistry. Physics and MathematicsPhysics relates strongly to Mathematics. Many concepts in Physics are expressedmathematically. In manipulations involving extreme quantities like the mass ofthe earth or the charge on an electron, a good grasp of mathematical skills isessential. Physics and TechnologyIn the field of medicine, X-rays, body scanners and lasers are applications ofPhysics used in diagnosis and treatment of diseases. Even in the continuingresearch necessitated by the challenge posed by such diseases as Ebola andHIV AIDS, the development of high precision equipment employing theprinciples of Physics remains necessary. Information technology has reduced the world to a global village throughthe use of satellites and microwave dishes which relay information overextremely long distances in fractions of a second. The wide range of applications of Physics is used in industrial developmentfor the improvement of material well-being of the human race. In the entertainment industry, Physics has contributed to the refinement ofsound and colour mixing techniques to create special effects in stagepresentations. The defence industry has also become highly technological. Wars can nowbe fought using laser-guided bombs of extremely high precision. However, if technology is not used responsibly, it can lead to social andenvironmental problems. Notable cases are the Chernobyl nuclear disaster inUkraine of 1986 and the Hiroshima and Nagasaki atomic bomb attacks duringthe Second World War. Career Opportunities in PhysicsThere is a wide range of opportunities involving Physics. The following is a listof courses offered at university level that require sound knowledge of Physics: 1. Bachelor of Arts Buiding Economics .
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Notable cases are the Chernobyl nuclear disaster inUkraine of 1986 and the Hiroshima and Nagasaki atomic bomb attacks duringthe Second World War. Career Opportunities in PhysicsThere is a wide range of opportunities involving Physics. The following is a listof courses offered at university level that require sound knowledge of Physics: 1. Bachelor of Arts Buiding Economics . 2. Bachelor of Science Construction management . 3. Bachelor of Architecture. 4. Bachelor of Medicine. 5. Bachelor of Dental Surgery. 6. Bachelor of Pharmacy. 7. Bachelor of Science Nursing . 8. Bachelor of Science Environmental Health . 9. Bachelor of Science Bio-medical Science Technology .10. Bachelor of Education Home Science and Technology .11. Bachelor ofScience Agricultural Education .12. Bachelor of Science Agricultural and Home Economics .13. Bachelor of Science Animal Production .14. Bachelor of Science Dairy and Food Technology .15. Bachelor of Science Fisheries .16. Bachelor of Science Food Technology .17. Bachelor of Science Food Science and Technology .18. Bachelor of Science Horticulture .19. Bachelor of Science Natural Resources .20. Bachelor of Science Range Management .21. Bachelor of Science Tourism .22. Bachelor of Science Wildlife and Management .23. Bachelor of Science Wood Science Technology .24. Bachelor of Veterinary Medicine.25. Bachelor of Science Hotel and Institution Management .26. Bachelor of Science Environmental Studies .27. Bachelor of Science Textiles Design and Merchandising .28. Bachelor of Science Applied Aquatic Science .29. Bachelor of Science Food Nutrition and Dietetics .30. Bachelor of Education Agriculture and Home Economics .31. Bachelor of Science Agricultural Engineering .32. Bachelor of Science Civil Engineering .33. Bachelor of Science Electrical Engineering .34. Bachelor of Science Surveying .35. Bachelor of Science Electrical and Electronic Engineering .36. Bachelor of Science Electrical and Communication Engineering .37. Bachelor of Technology Electrical and Communication Engineering .38. Bachelor of Technology Production Engineering .39. Bachelor of Technology Chemical and Process Engineering .40. Bachelor of Technology Civil and Structural Engineering .41. Bachelor of Technology Textile Engineering .42. Bachelor of Science Water and Environmental Engineering .43. Bachelor of Science Manufacturing and Engineering Technology . 44.
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Bachelor of Science Water and Environmental Engineering .43. Bachelor of Science Manufacturing and Engineering Technology . 44. Bachelor of Science Instrumentation and Control Engineering .45. Bachelor of Science Computer Science .46. Bachelor of Education Technology .47 Bachelor of Science Computer Electronics, Science and Technology .48. Bachelor of Home Economics Food, Nutrition and Dietetics .The above courses are also offered at diploma and certificate levels. Basic Laboratory RulesThe laboratory is a facility designed and equipped for conducting scientificresearch, experiments and measurements. An average laboratory has electrical energy supply, water and gas pipingsystems, workbenches and cabinets for storage of equipment and chemicals. Some of the chemicals and equipment are particularly dangerous. An individualworking in a typical laboratory will be exposed to a number of dangers includingpoisons, flammable materials, explosive materials, extreme temperature, movingmachinery and high voltage electricity. The following precautions must,therefore, be taken when working in the laboratory: i Proper dressing must be put on. Shirts and blouses must be tucked in andlong hair tied up. Closed shoes must be worn. This is to avoid looseclothing or body parts such as hair getting accidentally tangled up inmoving machinery. In addition, safety glasses or face shields must be wornwhen working with hazardous or poisonous materials. Shorts and sandalsmust never be worn in the laboratory, and lab coats, if in use should alwaysbe buttoned. Ii The locations of electricity switches, fire-fighting equipment, First Aid kit,gas supply and water supply systems must be noted. These will beextremely useful in case of any emergency within the laboratory. Access toall these facilities must remain unobstructed, this includes emergencyshowers and eye washes, where these are available in the laboratory. Iii While working in the laboratory, windows and doors should be kept open. This is to prevent inhalation of dangerous materials or gases and also toallow for easy escape evacuation in case of an emergency. Similarly,corridors or pathways within the laboratory should not be used as workingor storage areas. Iv Any instructions given must be followed carefully. Never attempt anythingwhile in doubt. In case of any doubt or queries, consult your teacher or thelaboratory assistant.
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Similarly,corridors or pathways within the laboratory should not be used as workingor storage areas. Iv Any instructions given must be followed carefully. Never attempt anythingwhile in doubt. In case of any doubt or queries, consult your teacher or thelaboratory assistant. Additionally, if any equipment fails to function, thisshould be reported immediately to the teacher or the laboratory technician. Never try to fix a problem on your own as this could cause a seriousaccident or damage to the equipment v Never taste, eat or drink anything in the laboratory. Food should also neverbe stored in the laboratory. This is to avoid the risk of consumingdangerous or poisonous materials or substances. Related to this, neverpipette anything by mouth a bulb should be used instead . Smelling ofgases is also highly discouraged. Vi Ensure that all electrical switches, gas and water taps are turned off whennot in use. This is to avoid wastage in addition to averting the risk of fire orother hazards. Vii When handling electrical apparatus, hands must be dry. Do not splashwater where electrical sockets are located. Water to some extent is anelectrical conductor and when in contact with exposed power cables, cancause severe electric shock. Viii Never plug foreign objects into electrical sockets. Apart from damaging thesocket, this can also cause an electric shock. Ix Keep floors and working surfaces dry. Any spillage should be wiped offimmediately. Liquid on the floor surface can cause skidding, resulting inserious injuries. Some corrosive liquids will damage the floor or workingsurfaces. X All apparatus must be cleaned and returned to the correct location ofstorage after use. This facilitates easy re-use of the apparatus, apart fromensuring good order in the laboratory. Xi Laboratory equipment should not be taken out of the lab. This is tominimise the risk of damage to the equipment, or even loss. Xii Any waste after an experiment must be disposed of appropriately. This isbecause waste from certain experiments can be quite hazardous to the bodyand to the environment. Xiii Hands must be washed before leaving the laboratory. Experiments should never be left unattended. Similarly, the bunsen burnershould be adjusted to give a luminous flame, or turned off, when not in use. Never should an open flame be left unattended. This is to minimise the riskof fire or other serious accidents. Volatile and flammable compounds should only be used in the fumecupboard.
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This isbecause waste from certain experiments can be quite hazardous to the bodyand to the environment. Xiii Hands must be washed before leaving the laboratory. Experiments should never be left unattended. Similarly, the bunsen burnershould be adjusted to give a luminous flame, or turned off, when not in use. Never should an open flame be left unattended. This is to minimise the riskof fire or other serious accidents. Volatile and flammable compounds should only be used in the fumecupboard. The same applies to procedures that should result in hazardousfumes or any inhalable material. One should never look directly down into the liquid being heated in a testtube. The tube should also not be pointed towards anyone nearby. Corrosive chemicals should be kept separately. This is to prevent damageto other laboratory appliances especially the metallic type. First Aid MeasuresAccidents or emergencies are prone to occur any time and it is, therefore, theuser s responsibility to be conversant with the safety and fire alarm postersstrategically positioned within the laboratory premises. These must be followedstrictly during an emergency. The locations of vital emergency equipment suchas fire extinguisher must be known and easily accessible to all, and users mustbe continually reminded of building evacuation procedures. In case of injuries in the laboratory, the teacher in charge or the laboratorytechnician must be immediately informed and necessary action taken withoutdelay. Common laboratory injuries include burns, cuts and bruises sometimesresulting in bleeding , poisoning and foreign matter in the eyes. These casesshould be handled in the following way. Those offering first aid should ensurethey are in the first place safe from the danger .CutsThese may result from poor handling of glass apparatus or cutting tools likerazors and scalpels. In case the cut results in bleeding, pressure or direct compression should beapplied directly to the wound and proper dressing applied as medical assistanceis sought. BurnsBurns may result from naked flames or even splashes of concentrated acids andbases. Burns should generally be treated by flushing cold water over the affectedarea. Acid burns could alternatively be treated with sodium hydrogen carbonate baking soda , and base burns with boric acid or vinegar. PoisoningThis may result from inhaling poisonous fumes or swallowing of poisonouschemicals or materials. In case this happens, the poisoning agent should be notedwhile urgent medical assistance is sought.
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Those offering first aid should ensurethey are in the first place safe from the danger .CutsThese may result from poor handling of glass apparatus or cutting tools likerazors and scalpels. In case the cut results in bleeding, pressure or direct compression should beapplied directly to the wound and proper dressing applied as medical assistanceis sought. BurnsBurns may result from naked flames or even splashes of concentrated acids andbases. Burns should generally be treated by flushing cold water over the affectedarea. Acid burns could alternatively be treated with sodium hydrogen carbonate baking soda , and base burns with boric acid or vinegar. PoisoningThis may result from inhaling poisonous fumes or swallowing of poisonouschemicals or materials. In case this happens, the poisoning agent should be notedwhile urgent medical assistance is sought. For a poison ingested through themouth, the recommended antidote should be given to the victim, and vomitingshould not be induced unless recommended by a medical practitioner. If the poison is in form of a gas, the first step should be to remove thevictim from the area and take him her to an area with fresher air. If the poison iscorrosive to the skin, the victim s clothing should be removed from the affectedarea, and cold water run over the area for at least 30 minutes. If the poison getsto the eye, the same should be flushed with clean water for at least 15 minutes,and the patient advised not to rub the eyes. Electric ShockThis may result from touching exposed wires or using faulty electricalappliances. Without getting in contact with the victim, the first thing to do is to cut off thecurrent causing the shock by: i Turning off the current at the main switch, or, ii Using a non-conducting object, such as wooden rod, to move the victimaway from the conductor. In the meantime, urgently seek medical assistance. If the victim has a pulse butis not breathing, offer mouth to mouth resuscitation as you await assistance. If for some reason a laboratory user faints or loses consciousness, he she shouldbe promptly and gently moved to an area with fresh air and placed in a recoveryposition with the head slightly lower than the rest of the body . If necessary,mouth to mouth resuscitation should be offered. Measurement I Up to 1960, scientists were using different units of measurement depending onthe immediate environment.
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If the victim has a pulse butis not breathing, offer mouth to mouth resuscitation as you await assistance. If for some reason a laboratory user faints or loses consciousness, he she shouldbe promptly and gently moved to an area with fresh air and placed in a recoveryposition with the head slightly lower than the rest of the body . If necessary,mouth to mouth resuscitation should be offered. Measurement I Up to 1960, scientists were using different units of measurement depending onthe immediate environment. Some of the common units were the inch 2.54 cm ,the mile 1.61 km , acre 0.41 Ha , pint 0.57 litres , gallon 4.55 litres , pound 0.45 kg and tonne 1 000 kg . Others used grams, centimetres and seconds. There was need to harmonise the units of measurement. The metric system is adecimalised system expressing quantities in larger or smaller multiples of theunit, e.g, milligramme grammes kilogrammes or millimetre centimetre metre. Consenquently, scientists agreed on one international system of units to be used,the Systeme Internationale d Unites International System of Units , shortened toSI units, in all languages. This system has seven basic physical quantities andunits as shown in table 2.1.Table 2.1: The seven basic physical quantities and unitsBasic physical quantitySI unitSymbol of unitsLengthMassTimeElectric currentThermodynamic temperatureLuminous intensityAmount of substanceMetreKilogramSecondAmpereKelvinCandelaMolemkgsAKCdmolThese quantities cannot be obtained from any other physical quantities. On theother hand, there are quantities obtained by multiplication or division of basicphysical quantities. These are called derived quantities, for example, area,volume and density. This chapter will deal with the measurements of length,mass, time and their derived physical quantities. LengthLength is a measure of distance between two points. Breadth, width, height,radius, depth and diameter are all lengths. The SI unit of length is the metre m .
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This chapter will deal with the measurements of length,mass, time and their derived physical quantities. LengthLength is a measure of distance between two points. Breadth, width, height,radius, depth and diameter are all lengths. The SI unit of length is the metre m . One metre is the distance between twomarks on a standard platinum-iridium bar kept at a constant temperature of 0 C.The bar is kept at Sevres, near Paris, France. Table 2.2 shows the multiples and sub-multiples of the metre. Table 2.2: Multiples and sub-multiples of the metreUnitSymbolEquivalence in metresKilometreHectometreDekametreDecimetreCentimetreMillimetreMicrometrekmHmDmdmcmmmm100.10.010.0010.000001Measurement of LengthLength can be determined by estimation or accurately by using a measuringinstrument. There are various instruments for measuring length. The choice ofthe instrument is determined by the level of the accuracy desired and the size ofthe object to be measured. Some instruments used to measure length are meter rule and tape-measure. Metre RulesFor day-to-day work in Physics, metre rules and half-metre rules are used. Theyare graduated in centimetres and millimetres. The following procedure should always be followed when using a metrerule: i Place the metre rule in contact with the object. Ii Place the end of the object against the zero mark on the scale. Iii Position your eye perpendicularly above the scale, as shown in figure 2.1 a . Fig. 2.1: a Accurate use of a meter ruleFig. 2.1: b Inaccurate positioning of the eyeFigure 2.2 shows other ways of inaccurate use of the metre rule. In figure 2.2 a ,arrangement will not give a fair result because, the rule is not in contact with theobject. While in b the object is not aligned to the zero mark on the scale. Fig. 2.2: a Rule not in contact b Rule not alignedFigure 2.2 shows the inaccurate use of the rule.
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In figure 2.2 a ,arrangement will not give a fair result because, the rule is not in contact with theobject. While in b the object is not aligned to the zero mark on the scale. Fig. 2.2: a Rule not in contact b Rule not alignedFigure 2.2 shows the inaccurate use of the rule. The arrangement will not give anaccurate result because: i the rule is not in contact with the object. Ii the object is not aligned with the zero mark on the scale. Iii the position of the eye is not perpendicular to the scale. Note that when the eye is not perpendicular to the scale, there is an errordue to parallax. Reading a metre ruleConsider the reading shown by the arrow in figure 2.3 rule not to scale .The reading is more than 1.6 cm but less than 1.7 cm. The second decimalplace is approximated. It is 1.67 cm. It could even be 1.66 cm. Fig: 2.3: The reading on a metre ruleThe second decimal place cannot be accurately determined. However, it isimportant to note that the readings from a metre rule may be written up to thesecond decimal place of a centimetre. A reading like 3.675 cm cannot be taken by a metre rule. However, if thereadings 5.6 cm and 6 cm are taken with a metre rule, then they should bewritten as 5.60 cm and 6.00 cm respectively. Example 1What are the readings indicated by arrows P1, P2 and P3 on the metre rule infigure 2.4? Diagram not to scale Fig 2.4SolutionP1 69.50 cmP2 71.00 cmP3 71.50 cmExercise 2.11. What are the readings indicated by the arrows in the figures a to c below? Diagrams not to scale Care should be taken to avoid damage to the ends of metre rules as most of themdo not have the short ungraduated portion at the ends to cater for wear. Tape-MeasureThere are several types of tape-measures, for example, tailor s, carpenter s andsurveyor s types. The choice of a tape-measure is determined by the nature ofthe distance to be measured.
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Diagram not to scale Fig 2.4SolutionP1 69.50 cmP2 71.00 cmP3 71.50 cmExercise 2.11. What are the readings indicated by the arrows in the figures a to c below? Diagrams not to scale Care should be taken to avoid damage to the ends of metre rules as most of themdo not have the short ungraduated portion at the ends to cater for wear. Tape-MeasureThere are several types of tape-measures, for example, tailor s, carpenter s andsurveyor s types. The choice of a tape-measure is determined by the nature ofthe distance to be measured. For example, to measure the length and breadth of aplot of land, or the distance covered by a discus or javelin throw, a surveyor stape-measure would be the most convenient. Always ensure that the tape-measure is taut when measuring. Measurement of Curved LengthCurved lengths such as roads and railway lines on a map or dimensions of somecontainers can be measured using a thread. The thread is placed along therequired lengths and the length is then found by placing the thread on amillimetre scale. For curved surfaces such as a cylinder, a thread is closelywrapped around the surface a number of times. Experiment 2.1: To measure the circumference of a cylinder using a threadApparatusA cylinder, a thread, a metre rule. Fig. 2.5: Estimating the circumference of a cylinderProcedure Closely wrap a thin thread 10 times around a cylinder, as shown in figure 2.5. Mark with ink the beginning and end of the turns. Remove the thread. Measure the length between the ink marks and call it a1.Repeat three times recording the readings as a2 and a3 to ensure accuracy ofyour measurement. Find the average length a:Divide the average length by 10 to find the length of one turn. This gives thecircumference of the cylinder.
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Charo found that the perimeter of his farming plot was approximately 200strides. His stride was 0.9 m long. What was the perimeter of the plot?2. Use the method in Experiment 2.2 to estimate the height of a flag post and agoal post in your school.3. Estimate the width of your desk, classroom door and the classroom bycounting how many of your palm-lengths or foot-lengths and strides thereare in each length.4. Suggest a method you can use to estimate the width of a page of your book. Text-book or notebook .5. Devise a method that should be used to estimate the thickness of a razorblade.6. How would you measure the length of the curve of an athletics field?AreaArea is the quantity that expresses the extent of a given surface on a plane. It is aderived quantity of length.
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By countingthe number of small squares, the area can be estimated. Example 5Estimate the area of the irregular surface shown in figure 2.8 by counting thesmall squares. SolutionThe number of complete squares 39Number of incomplete squares 30These are equal to 15 complete squaresTherefore, the number of complete squares 39 15 54Hence, the estimated area of the surface 54 1 cm2 54 cm2Fig. 2.8: Estimating area of irregular shapesExercise 2.31. Determine the area of each of the following: a The floor of your classroom. B The walls of your classroom. C The top of your desk.2. A Calculate the area of a circle of radius 7.0 cm. B Calculate: i the area of the triangle shown in the figure below: ii the area of the trapezium below: iii the area of the figure below:3. Trace an outline of your palm and foot on a graph paper and estimate thearea of each shape obtained.4. Trace the shape of a leaf on a graph paper and estimate its area.5. The diameter of the bore of capillary tube is 1.0 mm. Calculate the crosssection area of the bore in cm2. Take 3.142 6. A sheet of paper measures 25 cm by 15 cm. Calculate its area in mm2.VolumeVolume is the amount of space occupied by matter. The SI unit of volume is cubic metre m3 .
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A Obtain some plasticine and mould it to form a sphere. Find the radius ofthe sphere and calculate its volume. B Mould the same plasticine into a cylinder. Determine the volume of thecylinder. C Comment on the answers you obtain in a and b above. Measurement of Volume of LiquidsLiquids have no definite shape, but assume the shape of the containers in whichthey are put. One of the methods which can be used to measure the volume of a liquid isto pour the liquid into a container with a uniform cross-section, as shown infigure 2.9.Fig. 2.9: A container with a regular baseThe height of the liquid, h, is measured. The volume of the liquid is thenobtained by applying the formula;V area of cross-section heightV Ah, where A l b and h is the height. Therefore, V l bhExperiment 2.4: To investigate the relationship between volume and heightApparatusRectangular container and a cylinder. Fig. 2.10: Relationship between volume and heightProcedure Take two containers P and Q with rectangular base and cylindrical baserespectively. Container Q is calibrated, see figure 2.10 a and b . Pour some water into P and find its volume V. Transfer the water from P to Q and record the height h of water in Q. Repeat the experiment for different values of volume V, and each time recordthe corresponding value of h as in table 2.5.Table 2.5Draw a graph of V against h.Results and conclusionThe graph of V against h is a straight line, indicating that height increasesuniformly with the increase in volume V.In practice, it is convenient to make measuring vessels in cylindrical form,marked in such a way that volumes can be read off directly. Measuring devices which are marked off like this are called measuringcylinders. They are used to measure the volumes of liquids. Measuring cylinders are made of glass or transparent plastic and graduatedin cm3 or ml. Measuring flasks, pipettes, burettes and beakers figure 2.11 a , b , c , d and e can also be used to measure volumes of liquids. Measuringflasks and pipettes are used to transfer known volumes of liquids. The burettedelivers volumes of up to 50 cm3.Fig.
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Measuring flasks, pipettes, burettes and beakers figure 2.11 a , b , c , d and e can also be used to measure volumes of liquids. Measuringflasks and pipettes are used to transfer known volumes of liquids. The burettedelivers volumes of up to 50 cm3.Fig. 2.11: Instruments for measuring volumes of liquidsNote: i The scale of the burette begins from zero at the top and increasesdownwards to the maximum value. For example, a reading of 31.0 ml onthe burette means that the volume of the liquid poured from the burette is31.0 ml and the volume left in the burette is 50 31 ml, i.e., 19.0 ml. Ii While using the measuring vessels shown in figure 2.11, the reading ofvolume is taken with the eye positioned level with the bottom of themeniscus, see figure 2.12. In the figure, the volume of the liquid is 24.0cm3.Fig. 2.12: Reading the measuring cylinderMeasuring the Volume of an Irregularly-Shaped SolidVolumes of irregular solids are measured using the displacement method. Themethod works with solids that are not soluble in water, do not absorb water, donot react with water or sink in water. Experiment 2.5: To determine the volume of an irregularly-shaped object a Using a measuring cylinderApparatusMeasuring cylinder, stone, thread and Eureka can. Fig. 2.13: Volume of irregular shapesProcedure Partly fill a measuring cylinder with water. Note the volume V1 of the water,see figure 2.13 a . Tie a stone that can be fitted into the measuring cylinder with a thread andlower it gently into the cylinder until it is wholly submerged. Ensure thatthere are no air bubbles surrounding the stone. Record the new volume V2.ResultThe volume of the stoneV V2 V1. B Using a Eureka canA Eureka or displacement can is a container with a spout from the side. Itis used to measure volumes by displacement method. It is also known as anoverflow can. Fig. 2.14: Use of Eureka can for measuring volumeProcedure Fill the Eureka can with water until it flows out of the spout, see figure 2.14 a .
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Itis used to measure volumes by displacement method. It is also known as anoverflow can. Fig. 2.14: Use of Eureka can for measuring volumeProcedure Fill the Eureka can with water until it flows out of the spout, see figure 2.14 a . Once the flow has stopped, place a measuring cylinder under the spout ofthe can. Tie the solid whose volume you want to determine with a thread and lower itgently into the can until it is completely submerged. ResultThe volume of water collected in the measuring cylinder is the volume of theobject. Experiment 2.6: To determine the volume of an object that floats on waterusing the displacement canApparatusEureka can, measuring cylinder, floating object and a sinker small metal block .When finding the volume of an object that floats on water, e.g., a cork,another object that sinks in water is attached to it so that both are totallysubmerged. This object is known as a sinker. Fill the Eureka can with water and allow excess water to flow out through thespout, see figure 2.15 a . After it has ceased to flow, place a measuring cylinder under the spout. Lower the sinker, tied with a thread, gently into the can. Measure the volume V1 of the water that overflows into the measuringcylinder. Remove the sinker and tie it to the cork, see figure 2.15 b . Fig. 2.15: Volume of an object that floats on water Fill the Eureka can again and allow excess water to flow out. When water ceases to flow from the spout, place a clean dry measuringcylinder under the spout. Lower the sinker and cork tied together into the Eureka can gently. Measure the volume V2 that overflows into the measuring cylinder. ResultsThe water collected in the measuring cylinder is the volume of sinker and cork. Call it V2. Therefore, the volume of the corkV V2 V1.Exercise 2.51. Describe how you would measure the volume of a cork using a sinker, athread, a measuring cylinder and water only.2. Describe how you would calibrate the cylinder Q in figure 2.10.3. Describe how you would measure 30 cm3 of a liquid using a burette.4.
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The mass of the object isread on the display. This type of a balance is very accurate. Fig. 2.16: Types of balancesFigure 2.16 b shows a simple form of a beam balance mechanical type .The object whose mass is to be measured is balanced against a known standardmass on an equal arm lever as shown. The beam balances when the mass of theobject is equal to the known standard mass. Figure 2.16 c shows a lever balance in which a combination of leversmoves the pointer around a scale when the mass is placed on the pan. Exercise 2.61. Define mass and state its SI unit.2. Convert each of the following as indicated: a 10 tonnes into kg. B 200 000 mg into kg. C 256 000 g into tonnes. D 0.000342 tonne into mg. E 1.25 g into mg. DensityThe density of a substance is its mass per unit volume. Its symbol is rho andits SI unit is kilogram per cubic metre kgm 3 .Another commonly used unit is gram per cubic centimetre gcm 3 . Fromthe definition, the density of a substance is given by;Example 14The density of water is 1 gcm 3. Express this density in kgm 3.SolutionExample 15The density of a material is 22.5 gcm 3. Express this in SI units. Solution1 gcm 3 1 000 kgm 322.5 gcm 3 22.5 1 000 kgm 3 22 500 kgm 3Example 16A block of glass of mass 187.5 g is 5.0 cm long, 2.0 cm thick and 7.5 cm high. Calculate the density of the glass in kgm 3.SolutionExample 17The density of mercury is 13.6 gcm 3. Find the volume of 2 720 g of mercury inm3.SolutionExample 18The mass of 25 cm3 of ivory was found to be 0.045 kg. Calculate the density ofivory in SI units giving your answer in Kg m3.SolutionExample 19The density of concentrated sulphuric acid is 1.8 gcm 3.
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Solution1 gcm 3 1 000 kgm 322.5 gcm 3 22.5 1 000 kgm 3 22 500 kgm 3Example 16A block of glass of mass 187.5 g is 5.0 cm long, 2.0 cm thick and 7.5 cm high. Calculate the density of the glass in kgm 3.SolutionExample 17The density of mercury is 13.6 gcm 3. Find the volume of 2 720 g of mercury inm3.SolutionExample 18The mass of 25 cm3 of ivory was found to be 0.045 kg. Calculate the density ofivory in SI units giving your answer in Kg m3.SolutionExample 19The density of concentrated sulphuric acid is 1.8 gcm 3. Calculate the volume of3.1 kg of the acid. SolutionDensity 1.8 gcm 3Mass 3 100 gMeasurement of DensityTo Measure the Density of a SolidThe mass and the volume of the object is found by the method described above. The density of the object is then calculated from the formula:Table 2.7: Densities of some common substancesSubstance Density gcm 3kgm 3PlatinumGoldLeadSilverCopperIronAluminiumGlassIceMercurySea waterWaterKeroseneAlcoholCarbon dioxideAirHydrogen21.419.311.310.58.937.862.72.50.9213.61.031.00.800.790.001970.001310.00008921 40019 30011 30010 5008 9307 8602 70013 6001 0307901.971.310.089Experiment 2.7: To find the density of a liquidApparatusClean dry beaker, balance, measuring cylinder, a burette or a pipette. Procedure Find the mass m1 of a clean dry beaker using a balance. Measure a known volume V of the liquid using either a measuring cylinder, aburette or a pipette. Transfer the liquid into the beaker. Find the mass m2 of the beaker with the liquid. ResultMass of the liquid m2 m1Example 20A rectangular tank measures 12.5 m long, 10.0 m wide and 2.0 m high.
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Find the volume of 2 720 g of mercury inm3.SolutionExample 18The mass of 25 cm3 of ivory was found to be 0.045 kg. Calculate the density ofivory in SI units giving your answer in Kg m3.SolutionExample 19The density of concentrated sulphuric acid is 1.8 gcm 3. Calculate the volume of3.1 kg of the acid. SolutionDensity 1.8 gcm 3Mass 3 100 gMeasurement of DensityTo Measure the Density of a SolidThe mass and the volume of the object is found by the method described above. The density of the object is then calculated from the formula:Table 2.7: Densities of some common substancesSubstance Density gcm 3kgm 3PlatinumGoldLeadSilverCopperIronAluminiumGlassIceMercurySea waterWaterKeroseneAlcoholCarbon dioxideAirHydrogen21.419.311.310.58.937.862.72.50.9213.61.031.00.800.790.001970.001310.00008921 40019 30011 30010 5008 9307 8602 70013 6001 0307901.971.310.089Experiment 2.7: To find the density of a liquidApparatusClean dry beaker, balance, measuring cylinder, a burette or a pipette. Procedure Find the mass m1 of a clean dry beaker using a balance. Measure a known volume V of the liquid using either a measuring cylinder, aburette or a pipette. Transfer the liquid into the beaker. Find the mass m2 of the beaker with the liquid. ResultMass of the liquid m2 m1Example 20A rectangular tank measures 12.5 m long, 10.0 m wide and 2.0 m high. Calculatethe mass of water in the tank when it is full.
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This is because whenheld in the hands, it may expand due to body warmth. Ii The outside of the bottle must be wiped carefully. Iii It must be ensured that there are no air bubbles when the bottle is filledwith liquid. Experiment 2.9: To measure the density of a solid using a density bottleThis method is used for solids in form of grains, beads or turnings. ApparatusDensity bottle and lead shot, beam balance. Procedure Measure the mass m1 of a clean dry empty density bottle, see figure 2.18 a . Fill the bottle partly with lead shot and measure the mass m2. Fill up the bottle with water up to the neck and measure its mass m3, seefigure 2.18 c . Empty the bottle and rinse it. Fill it with water and replace the stopper. Wipe the outside dry and measurethe mass m4 of the bottle filled with water, see figure 2.18 d . Fig. 2.18: Use of density bottleResultsMass of water m4 m1 gVolume of water m4 m1 since density of water is 1 gcm 3 Therefore, volume of bottle m4 m1 cm3Mass of lead shot m2 m1 gMass of water present when bottle is filled with lead shot and water m3 m2 gVolume of water m3 m2 cm3Volume of lead shot m4 m1 m3 m2 Therefore, density of lead shotIt should be noted that this method is unsuitable for solids which are eithersoluble in water or react with it. Example 21The mass of a density bottle is 20 g when empty and 45 g when full of water. When full of mercury, its mass is 360 g. Calculate the density of mercury. SolutionMass of water 45 20 25 gVolume of water 25 cm3 density of water is 1 gcm 3 Therefore, volume of bottle 25 cm3Mass of mercury 360 20 340 gVolume of mercury 25cm3 volume of the density bottle 13.6 gcm 3 13 600 kgm 3Example 22The mass of an empty density bottle is 20 g.
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Fig. 2.18: Use of density bottleResultsMass of water m4 m1 gVolume of water m4 m1 since density of water is 1 gcm 3 Therefore, volume of bottle m4 m1 cm3Mass of lead shot m2 m1 gMass of water present when bottle is filled with lead shot and water m3 m2 gVolume of water m3 m2 cm3Volume of lead shot m4 m1 m3 m2 Therefore, density of lead shotIt should be noted that this method is unsuitable for solids which are eithersoluble in water or react with it. Example 21The mass of a density bottle is 20 g when empty and 45 g when full of water. When full of mercury, its mass is 360 g. Calculate the density of mercury. SolutionMass of water 45 20 25 gVolume of water 25 cm3 density of water is 1 gcm 3 Therefore, volume of bottle 25 cm3Mass of mercury 360 20 340 gVolume of mercury 25cm3 volume of the density bottle 13.6 gcm 3 13 600 kgm 3Example 22The mass of an empty density bottle is 20 g. Its mass when filled with water is40.0 g and 50.0 g when filled with liquid X. Calculate the density of liquid X ifthe density of water is 1 000 kgm 3.SolutionDensities of MixturesA mixture is obtained by putting together two or more substances such that theydo not react with one another. The density of the mixture lies between thedensities of its constituent substances and depends on their proportions. It isassumed that the volume of the mixture is equal to the sum of the volumes of theindividual constituents. Density of the mixtureExample 23100 cm3 of fresh water of density 1 000 kgm 3 is mixed with 100 cm3 of seawater of density 1 030 kgm 3.
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Calculate the density of liquid X ifthe density of water is 1 000 kgm 3.SolutionDensities of MixturesA mixture is obtained by putting together two or more substances such that theydo not react with one another. The density of the mixture lies between thedensities of its constituent substances and depends on their proportions. It isassumed that the volume of the mixture is equal to the sum of the volumes of theindividual constituents. Density of the mixtureExample 23100 cm3 of fresh water of density 1 000 kgm 3 is mixed with 100 cm3 of seawater of density 1 030 kgm 3. Calculate the density of the mixture. SolutionMass of fresh water density volumeMass of sea waterMass of the mixture mass of fresh water mass of sea water 0.1 0.103 kg 0.203 kgVolume of mixture volume of fresh water volume of sea water 100 cm3 100 cm3 200 cm3Therefore, density of mixtureExample 24Bronze is made by mixing molten copper and tin. If 100 kg of the mixturecontains 80 by mass of copper and 20 by mass of tin, calculate the density ofbronze. Density of copper is 8 900 kgm 3 and density of tin 7 000 kgm 3 SolutionExercise 2.71. Explain how you would determine the density of solid common salt.2. Fill the following table:3. A density bottle has a mass of 17.5 g when empty. When full of water, itsmass is 37.5 g. When full of liquid X, its mass is 35 g. If the density of wateris 1 000 kgm 3, find the density of liquid X.4. Describe the experiment to find the density of air. TimeTime is a measure of duration of an event. Some ancient time-measuringinstruments were the sundial and the hourglass. In modern measurement of time, it has been found necessary to obtainreference of time from an atomic clock. The SI unit to time is second s .
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Water has a density of 1 000 kgm 3. What does this mean? What is itsdensity in gcm 3?10. In finding the density of liquid, why is the method of using a density bottlemore accurate than the one of using a measuring cylinder?11. What mass of lead has the same volume as 1 600 kg of alcohol? Use thevalues of densities given in table 2.7 12. An empty density bottle has a mass of 25 g. Its mass is 50 g when full ofwater and 45 g when full of another liquid. What is the density of the liquidin kgm 3?13. Describe an experiment to find the density of copper turnings using a densitybottle and kerosene.14. The mass of a density bottle is 20.0 g when empty, 70.0 g when full of waterand 55.0 g when full of a second liquid. Calculate the density of the liquid.15. The mass of a density bottle of volume 50 cm3 is 10.0 g when empty. Aluminium turnings are poured into the bottle and the total mass is 60.0 g.Water is then added into the turnings till the bottle is full. If the total mass ofthe bottle and its contents is 90.0 g, calculate the density of the aluminiumturnings.16. 1 800 cm3 of fresh water of density 1000 kgm 3 is mixed with 2 200 kgm 3of sea water of density 1 025 kgm 3. Calculate the density of the mixture. ForceYou may have observed a person kicking a ball in the field or a group of peopleparticipating in a tug of war. You may also have seen a mason lifting a stone at aconstruction site or people pushing a car stuck in mud. These activities, some ofwhich are shown in figure 3.1, involve either pushing or pulling. Fig. 3.1: Pull and pushA force is a push or pull. The SI unit of force is the newton N . A force acts in aparticular direction and may have any of the following effects on an object: i Make a stationary object start moving or increase the speed of a movingobject. Ii Slow down or stop a moving object.
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3.1: Pull and pushA force is a push or pull. The SI unit of force is the newton N . A force acts in aparticular direction and may have any of the following effects on an object: i Make a stationary object start moving or increase the speed of a movingobject. Ii Slow down or stop a moving object. Iii Change the direction of a moving object. Iv Distort change the shape of an object. Force is, therefore, that which changes a body s state of motion or shape. Someforces are small while others are large. Forces, therefore, have size magnitude .A force is represented by a line with an arrow showing the direction in which itacts, thus:Types of ForcesThere are many types of forces some of which are listed below: Gravitational force. Tension. Upthrust force. Frictional force. Magnetic force. Centripetal force. Cohesive and adhesive forces. Surface tension. Molecular force. Electric force. Nuclear force. Electrostatic force. Gravitational ForceThis is the force of attraction between two bodies of given masses m1 and m2 ,see figure 3.2. Fig. 3.2: Force of attraction between two bodiesWhen two objects are thrown up from or near the earth s surface, they alwaysfall downwards towards the ground. This is because of the force of attractionwhich the earth exerts on any body near its surface. This force which pulls thebody towards the centre of the earth is called the gravitational force of theearth. An object near or on the surface of the moon also experiences thegravitational force of the moon. Each planet exerts its own gravitational pull onan object on it. On the earth s surface, gravitational force is the force of attraction betweena body and the earth. The pull of gravity on the body towards the centre of theearth is called weight. The weight of an object varies on different planetsbecause planets have different gravitational pull. TensionTension is the quantity of the pulling force exerted by a string, spring or cable onan object. Some materials can withstand greater tension than others. Steel canwithstand very high tension and is difficult to break. Similarly, nylon canwithstand more tension than cotton. Tension is as a result of two opposing forcesapplied, one at each end of a body, see figure 3.3.Fig. 3.3: Tension on a springFig.
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Similarly, nylon canwithstand more tension than cotton. Tension is as a result of two opposing forcesapplied, one at each end of a body, see figure 3.3.Fig. 3.3: Tension on a springFig. 3.4: A loaded steel springExperiment 3.1: To study the relationship between mass and extension of aspringApparatusSpring with a pointer, metre rule, two retort stands and six 50 g masses. Procedure Set up the apparatus as shown in figure 3.4. Record the position of the pointer when there is no mass. P0 cm Add 50 g masses, one at a time, and record the position of the pointer P everytime a 50 g mass is added. Do not overstretch the spring. Obtain the extension, e P P0. Record the results as in table 3.1.Table 3.1Mass added g Pointer position cm when loadingExtension250300What happens to the spring each time a load is added? Draw a graph of extension y-axis against mass added x-axis .ConclusionThe length of a spring increases when loaded since the weight of the load acts onthe spring, forcing it to stretch. The graph of extension against mass is a straightline, see figure 3.5.Fig. 3.5Stretch resulting from tension is made using bows and catapults as shown infigure 3.6. Fig. 3.6: Application of stretching forcesSome forces compress bodies and are called compressive forces. A compressedor stretched object will tend to regain its original shape when the stretching orcompressing force is removed. Materials that can be compressed or extendedwithout breaking are called elastic materials. UpthrustThere is always an upward force acting on an object immersed in a fluid liquidor gas . This upward force is called upthrust. An object in a vacuum will notexperience upthrust. Experiment 3.2: To illustrate upthrust in liquidsApparatusSpring balance, metal cube, water, paraffin, beaker. Fig. 3.7: Upthrust in liquidsProcedure Set up the apparatus as shown in figure 3.7 a .
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An object in a vacuum will notexperience upthrust. Experiment 3.2: To illustrate upthrust in liquidsApparatusSpring balance, metal cube, water, paraffin, beaker. Fig. 3.7: Upthrust in liquidsProcedure Set up the apparatus as shown in figure 3.7 a . Record the reading of thespring balance. Lower the metal cube into the beaker of water as in figure 3.7 b and recordthe reading on the spring balance. Remove the metal cube from the water and dry it. Repeat with paraffin andother liquids. Compare the readings. ExplanationThe reading of the spring balance is determined by the medium in which theobject is. If the medium is air, the reading is larger than when the medium is aliquid. The reading also varies from one liquid to another. The reading of thebalance is highest when the object is in air and lowest when the object iscompletely submerged in water. The difference in the readings when the object is immersed in liquid andwhen the object is in air is due to upthrust force. Example 1A body weighs 100 N in air and 80 N when submerged in water. Calculate theupthrust acting on the body. SolutionWeight in air 100 NWeight in water 80 NUpthrust weight in air weight in water 100 80 N 20 NCohesive and Adhesive ForcesThe force of attraction between molecules of the same kind is known ascohesive force, e.g., between a water molecule and another water molecule,while force of attraction between molecules of different kinds is called adhesiveforces, e.g., between water molecules and glass molecules. Experiment 3.3: To investigate the behaviour of water on different surfacesApparatusClean glass slide, waxed glass slide, dropper, water. Fig. 3.8: Water drops on glass slidesProcedure Using a dropper, place a few drops of water onto a clean glass slide. Similarly, place a few drops of water on the waxed glass slide. Observe the shapes of the drops on the glass slides. What do you notice?ObservationWater on the clean glass slide spreads on the glass surface wets the surface .However, small drops of water collect into small spherical balls on the waxedsurface. If mercury is used, small mercury drops in a clean glass dish surface collectinto spherical balls.
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Fig. 3.8: Water drops on glass slidesProcedure Using a dropper, place a few drops of water onto a clean glass slide. Similarly, place a few drops of water on the waxed glass slide. Observe the shapes of the drops on the glass slides. What do you notice?ObservationWater on the clean glass slide spreads on the glass surface wets the surface .However, small drops of water collect into small spherical balls on the waxedsurface. If mercury is used, small mercury drops in a clean glass dish surface collectinto spherical balls. Larger mercury drops form oval balls as in figure 3.9.Fig. 3.9: Mercury drops on a glass slideNote:Mercury is poisonous and should not be handled in an ordinary laboratory. ExplanationWater wets the glass surface because the adhesive forces between the watermolecules and the glass molecules are greater than the cohesive forces betweenwater molecules. Water does not wet the waxed glass surface because thecohesive force is greater than the adhesive force. The stronger cohesive forces inmercury form spherical drops of mercury even on clean glass surface. The weakadhesive force between mercury and glass makes mercury not to wet the glass. Experiment 3.4: To demonstrate cohesive and adhesive forces of liquids innarrow tubesApparatusNarrow tubes with different sizes of bore, beaker, water, glycerol, kerosene andmethylated spirit. Fig. 3.10: Cohesion and adhesion in mercury and waterProcedure Dip the length of clean narrow tube into water. Look at the shape of water inside the narrow tube. Compare the water level inside the tube with that outside it. Try another narrow tube with a different bore, i.e., a different diameter, seefigure 3.10. Repeat the experiment with other liquids, e.g., glycerol, kerosene ormethylated spirit. ObservationThe level of water inside the tubes is higher than outside the tubes. A meniscus is formed at top of water level. The water curves upwards fromthe reading level a concave meniscus . The rise in the tube with a smaller boreis higher than in the tube with a larger bore. Different liquids rise by different heights, depending on the diameter of the glasstube. If mercury is used, the level of mercury inside the tubes goes lower thanthat outside the tubes.
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The water curves upwards fromthe reading level a concave meniscus . The rise in the tube with a smaller boreis higher than in the tube with a larger bore. Different liquids rise by different heights, depending on the diameter of the glasstube. If mercury is used, the level of mercury inside the tubes goes lower thanthat outside the tubes. The surface of the mercury in the tubes will curvedownwards, i.e., the meniscus curves downwards from the reading level aconvex meniscus .The level of mercury in the tube with the smaller bore will be lower thanthat in the tube with a larger bore. ExplanationSince the adhesive force between the water and glass molecules is greater thanthe cohesive force between the water molecules, the water rises up the tube sothat more water molecules can be in contact with the glass. This wets the glass. Liquids such as glycerol, kerosene and methylated spirit wet the glass or thevessel and will rise in a narrow tube. On the other hand, the force of cohesion within the mercury is greater thanthe force of adhesion between the mercury and glass. The mercury, therefore,sinks down the tube to enable mercury molecules to keep together. Liquidswhich do not wet the container will be depressed inside the tube. Frictional ForceFriction is a force that opposes relative motion between two surfaces in contact. Practical applications of friction in our daily lives include walking and braking. Friction is caused by the interlocking of the surfaces and attractive forcebetween the surface molecules. Experiment 3.5: To investigate frictional forceApparatusWooden block, spring balance, rollers. Fig. 3.11Procedure Place a wooden block on a horizontal surface, such as a bench. Using a spring balance, pull the block gently as shown in the figure 3.11 a ,gradually increasing the force. What finally happens to the block? Repeat the experiment, this time with the block resting on rollers as shown infigure 3.11 b . In which case do you require less force for the block to startmoving?
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3.11Procedure Place a wooden block on a horizontal surface, such as a bench. Using a spring balance, pull the block gently as shown in the figure 3.11 a ,gradually increasing the force. What finally happens to the block? Repeat the experiment, this time with the block resting on rollers as shown infigure 3.11 b . In which case do you require less force for the block to startmoving? How else, apart from using rollers, can you reduce the force neededto make the block start moving?ConclusionIn figure 3.11 a , the wooden block starts moving when the applied force is justgreater than a frictional force between the block and the surface of the bench. Frictional force can be reduced by using rollers, oiling or smoothening. Experiment 3.6: To investigate friction in liquidsApparatusTwo measuring cylinders, two ball bearings, water, glycerine. Fig. 3.12: Frictional force in liquidsProcedure Fill two glass jars or measuring cylinders, one with water and the other withglycerine, to the same level. Hold two small identical ball bearings, just above the jar. Release them at the same time and observe their motion through the liquids,see figure 3.12. Which ball bearing reaches the bottom of the jar first?ConclusionWhen the ball bearing is introduced into the liquid, a layer of the liquid forms onthe surface of the bearing. As it moves through the liquid, it rubs against theliquid molecules. Due to the movement of the body, there is an opposing forcebetween the layer of the liquid molecules on the body and the layer of the liquidmolecules in the measuring cylinder. The opposing force frictional force involving a fluid is called viscous drag viscosity . Viscous drag limits thespeed with which a body can move in a liquid. Magnetic ForceThe force which causes attraction or repulsion by a magnet is called magneticforce. A magnet has two types of poles, a north pole and a south pole. Like polesrepel while unlike poles attract. Some materials are attracted by a magnet whileothers are not.
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A magnet has two types of poles, a north pole and a south pole. Like polesrepel while unlike poles attract. Some materials are attracted by a magnet whileothers are not. Those which are attracted are called magnetic materials whilethose not attracted are called non-magnetic materials. Experiment 3.7: To investigate magnetic forceApparatusTwo pieces of magnet, string, iron bar, iron fillings. Procedure Suspend a bar magnet as shown in figure 3.13.Fig. 3.13 a : Attraction and repulsion forces of a magnet Bring one end of another magnet near the poles of the suspended magnet inturns. Observe what happens in both cases. Bring the unsuspended magnet near an iron bar or iron fillings and observeagain what happens. Fig. 3.13 b : Iron fillings concentrate more at the ends of a bar magnetObservationThere is attraction on one end and repulsion on the other. The iron fillings oriron bar are attracted by magnetic force. Electrostatic ForceA plastic pen or ruler rubbed on dry hair or fur picks up small pieces of paperlying on a table when it is brought near them. The same pen or ruler attracts athin stream of water from a tap. The rubbing creates static charges. The force of attraction or repulsion dueto these changes is called electrostatic force. When a glass window is wiped with a dry cloth on a dry day, dust particlesare attracted on it. Also, when shoes are brushed, they tend to attract dustparticles. This is because electrostatic charges formed on the rubbed surfaceattract dust. Centripetal ForceCentripetal Force is a force which constrains a body to move in a circular path ororbit. This force is directed towards the centre of the orbit. Examples of wherecentripetal forces is applied include a stone tied on a string sling , separation ofghee from milk and the merry-go-round, see figure 3.14. Fig.
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This force is directed towards the centre of the orbit. Examples of wherecentripetal forces is applied include a stone tied on a string sling , separation ofghee from milk and the merry-go-round, see figure 3.14. Fig. 3.14: Children enjoying a merry-go-roundSurface TensionIt is commonly observed that liquids form drops, water wets some surfaces butruns off others, some insects like the pond skater manage to rest on the surfaceof the water without sinking, water rises up a narrow glass tube but mercury ispushed down to a lower level in the same tube and a steel razor blade floats onwater, even though steel is denser than water. The above observations will be explained by the following experiment. Experiment 3.8: To investigate the behaviour of a liquid surfaceApparatusBeaker, steel needle or razor blade, water, kerosene or soap solution. Procedure Fill a beaker with clean water to the brim. Fig. 3.15: Surface tension Place a dry steel needle or razor blade at the edge of the beaker and carefullyintroduce it on the surface of the water. Take care not to break the surface ofthe water. Observe what happens to the needle. Put a few drops of kerosene or soap solution on the surface of the water nearthe needle not directly on the needle . Note what happens. Depress the tip of the needle into the water and note what happens. ObservationThe needle floats on the surface of the water and remains floating so long as thewater surface is not broken, see figure 3.15. When the surface of the water wherethe needle lies is observed carefully a magnifying lens would help , the watersurface is found to be slightly depressed and stretched like an elastic skin. When drops of paraffin or soap solution are put on the surface of the wateraround the needle, the needle sinks on its own after a few seconds. If,alternatively, the tip of the needle is depressed lightly into the water, the needlesinks very quickly to the bottom of the water. ExplanationThe steel needle or the razor blade floats because the surface of the waterbehaves like a fully stretched, thin, elastic skin. This skin always has a tendencyto shrink, i.e., to have a minimum surface area or elastic membrane. The forcewhich causes the surface of a liquid to behave like a stretched elastic skin iscalled surface tension.
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If,alternatively, the tip of the needle is depressed lightly into the water, the needlesinks very quickly to the bottom of the water. ExplanationThe steel needle or the razor blade floats because the surface of the waterbehaves like a fully stretched, thin, elastic skin. This skin always has a tendencyto shrink, i.e., to have a minimum surface area or elastic membrane. The forcewhich causes the surface of a liquid to behave like a stretched elastic skin iscalled surface tension. This force is due to the force of attraction betweenindividual molecules of the liquid cohesion .The needle or the blade sinks when a drop of kerosene or soap solution isput in the liquid near the needle because the kerosene or soap solution reducesthe surface tension of the water. When the tip of the needle is pressed into thewater, it pierces the surface skin and sinks. Molecular Explanation of Surface TensionFig. 3.16: Molecular force in liquidA molecule, say C, deep in the liquid is surrounded by molecules on all sides sothat the net force on it is zero. However, molecules of the surface, say A and B,will have fewer molecules on the vapour side and hence will experience aresultant inward force, causing the surface of the liquid to be in tension. Experiment 3.9: To study the behaviour of soap bubblesApparatusGlass funnel, soap or detergent solution. Fig. 3.17Procedure Take a glass funnel and dip it in liquid soap or detergent solution. Take it out and blow a soap bubble to the wide end, see figure 3.17 a . Hold the funnel with the bubble downward and leave the top open. Observewhat happens. ObservationThe bubble flattens to a film and the film slowly rises up the funnel. ExplanationThe soap bubble behaves as if its surface is tightly stretched. As it tries to makeits surface as small as possible, it rises up the funnel.
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3.17Procedure Take a glass funnel and dip it in liquid soap or detergent solution. Take it out and blow a soap bubble to the wide end, see figure 3.17 a . Hold the funnel with the bubble downward and leave the top open. Observewhat happens. ObservationThe bubble flattens to a film and the film slowly rises up the funnel. ExplanationThe soap bubble behaves as if its surface is tightly stretched. As it tries to makeits surface as small as possible, it rises up the funnel. Experiment 3.10: To study the behaviour of soap filmsApparatusCopper wire, thread, soap solution and needle. Procedure Make a rectangular loop of copper wire. Tie a thread loosely across it, as in figure 3.18 a . Dip the loop in a soap solution and bring it out so that the loop is filled with asoap film, see figure 3.18 b . Break the soap film on one side of the thread by touching it with a hot needle. Note the new shape of the thread. ObservationWhen the film is broken on one side, the thread assumes a perfect curve, seefigure 3.18 c . Fig. 3.18ExplanationIn figure 3.18 b , the thread lies in any position in the soap film because thethread is being pulled on both sides by equal forces of surface tension. However,when one side of the film is broken, the surface tension acts only on one side ofthe thread. As the water tries to make its surface as small as possible, it pulls thethread in such a way that it forms a perfect curve. The soap film exhibits surfacetension. Experiment 3.11: To examine the appearance of water drops coming out ofa tubeApparatusBurette, clamp, stand. Fig. 3.19Procedure Fill a burette with water. Clamp it on a stand and turn the tap slowly so that a drop of water forms onits mouth.
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As the water tries to make its surface as small as possible, it pulls thethread in such a way that it forms a perfect curve. The soap film exhibits surfacetension. Experiment 3.11: To examine the appearance of water drops coming out ofa tubeApparatusBurette, clamp, stand. Fig. 3.19Procedure Fill a burette with water. Clamp it on a stand and turn the tap slowly so that a drop of water forms onits mouth. Observe how each drop grows and eventually drops. ObservationThe growth of the water drop appears as if the mouth of the burette is coveredwith an elastic membrane which stretches as more and more water gets into it. When it can hold no more water, it falls. The following observations are also due to surface tension of water: i A glass tumbler can be filled with water above the brim, see figure 3.20 a . Ii When a soft brush such as an artists brush is placed in water, the bristlesspread out but when it is taken out, they cling together, see figure 3.20 b . Fig. 3.20: Effects of surface tensionSurface Tension of Different LiquidsThe difference in surface tension of different liquids can be visualised in thefollowing demonstrations. The surface tension of soap is less than that of waterA match stick or a small toy boat rubbed at one end with soap and placed on thesurface of water starts moving immediately. It moves in one direction only andin such a way that the end that is not rubbed with soap is always in front. Anyattempt to make it move in the opposite direction will fail, see figure 3.21 a . Fig. 3.21: Effects of surface tensionExplanationThe soap at the end of the stick immediately dissolves in water, thereby loweringthe surface tension at the end of the stick. The surface tension at the other endwhich is now greater pulls the stick and makes it move in that direction. Themovement gradually weakens and ultimately ceases. This happens when thewhole surface of water is covered with soap solution. The camphor has the same effect as that of soap. Oil Spreads on WaterA few drops of oil from a fine tube form a circular patch when they fall on aclean water surface. ExplanationThe forces along the surface of oil are weaker than those of the water surface. The oil is thus pulled outwards into a thin film. Factors Affecting Surface Tension1.
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The surface tension at the other endwhich is now greater pulls the stick and makes it move in that direction. Themovement gradually weakens and ultimately ceases. This happens when thewhole surface of water is covered with soap solution. The camphor has the same effect as that of soap. Oil Spreads on WaterA few drops of oil from a fine tube form a circular patch when they fall on aclean water surface. ExplanationThe forces along the surface of oil are weaker than those of the water surface. The oil is thus pulled outwards into a thin film. Factors Affecting Surface Tension1. ImpuritiesImpurities reduce the surface tension of a liquid. Detergents, for instance,weaken the cohesive forces between liquid molecules. 2. TemperatureWith rise in temperature, the kinetic energy of the molecules of a liquid isincreased. The inter-molecular distance increases and the force of cohesion isdecreased. Hence, the surface tension is lowered. Consequences of Surface Tension1. Water insects can rest on the surface of water without breaking the surface. The insects also skate across the surface of water at high speed.2. Mosquito larvae float on water surface. Oiling the water surface usingkerosene lowers surface tension, thus making the larvae sink. Oiling stillwater, therefore, controls the breeding of mosquitoes. Action and ReactionExamine carefully the following cases in which forces are applied:1. When a block of wood is placed on a table, its weight action acts on thetable. It is pressed on the surface downwards. The reaction force in theopposite direction of the table acts on the block, see figure 3.22 a .2. When you hold a hose-pipe which is projecting a powerful jet of water, younotice that there is a steady force of reaction from the jet. This is the forcewhich is harnessed in some garden sprinklers, see figure 3.22 b .In both cases, there are two forces acting in opposite directions. One of the forces is called action and the other reaction. Action andreaction are equal and opposite, i.e., when one force acts on a body, an equal andopposite force acts on the body. Fig. 3.22: Action and reactionExercise 3.1Table 3.2 shows types of forces and the nature of work to be done.
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Action andreaction are equal and opposite, i.e., when one force acts on a body, an equal andopposite force acts on the body. Fig. 3.22: Action and reactionExercise 3.1Table 3.2 shows types of forces and the nature of work to be done. Match thetype of force with the type of work it can do. Table 3.2Work to be doneType of forceSeparate a mixture of ironfillings and sand. Elastic tension. Fire a gun. Magnetic force. Cause tides in the seas oceans .Gravitational force of attraction between theearth and the moon. Absorb shock in vehicles. Upthrust force. Swim. Action and reaction. Water rising a narrow tube. Centripetal force. Toy boat moving on watersurface. Cohesive and adhesive force. Mass and WeightMass and WeightWhile mass is the quantity of matter present in an object, weight is a measure ofthe pull of gravity on the object. This pull of gravity is always directed towardsthe centre of the earth. Thus, weight has both direction and size. The SI unit of weight is the newton symbol N . Weight is measured by a springbalance calibrated in newtons. Due to the shape and rotation of the earth, the weight of an object variesfrom place to place. The earth is not a perfect sphere, it is flattened at the polessuch that the distance between the centre of the earth and the poles is shorterthan that between the centre of the earth and the equator. Thus, a body weighsmore at the poles than at the equator. Relationship between Mass and WeightExperiment 3.12: To determine the gravitational field strength g of a placeApparatusSix 20 g masses, spring balance calibrated in newtons, retort stand. Procedure Take a 20 g mass and obtain the corresponding weight by use of the springbalance. Repeat each time adding a 20 g mass. Tabulate the results as in table 3.2.Table 3.3: To determine the gravitational strength g Plot a graph of weight in newtons y-axis against mass in kilograms x-axis . Find the slope of the graph. The value of the slope is called the gravitational field strength intensity . Thisis the gravitational force on a unit mass at that place on the earth.
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A mass of 7.5 kg has weight of 30 N on a certain planet. Calculate theacceleration due to gravity on this planet.12. Define the following terms, giving examples: a Vector quantity. B Scalar quantity.13. A Define a resultant vector. B Find the resultant of a force of 4 N and a force of 8 N acting on the samepoint on an object if: i the forces act in the same direction in the same straight line. Ii the forces act in opposite directions but in the same straight line.14. Show diagramatically how forces of 7 N and 9 N can be combined to give aresultant force of: a 16 N b 2 NPressureThe term pressure is used in day-to-day life. To understand its meaning, considerthe following examples of experiences with force on solids. I A person makes deeper marks while walking on soft ground in high-heeledshoes than in flat shoes. Fig. 4.1: High and flat-heeled shoes ii It is easier to push a sharp pin through a cardboard than it is to push ablunt one through the same material using the same force, see figure 4.2 a and b . Fig. 4.2: Effect of force on an areaIn all the above cases, a given force acting on an area causes a penetration,depression or distortion. The effect is greater when the force acts on a smallerarea than when it acts on a larger area. In general, when a force is applied on a given area, pressure is exerted onthe surface. Pressure is defined as the force acting normally perpendicularly perunit area. Units of PressureFrom the definition,Therefore, the SI unit of pressureThe SI unit of pressure is thus newton per square metre Nm 2 , which is alsocalled the Pascal Pa .1 Nm 2 1 PaOther units include the mmHg, the cmHg and an atmosphere atm .Example 1A man of mass 84 kg stands upright on a floor.
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Fig. 4.2: Effect of force on an areaIn all the above cases, a given force acting on an area causes a penetration,depression or distortion. The effect is greater when the force acts on a smallerarea than when it acts on a larger area. In general, when a force is applied on a given area, pressure is exerted onthe surface. Pressure is defined as the force acting normally perpendicularly perunit area. Units of PressureFrom the definition,Therefore, the SI unit of pressureThe SI unit of pressure is thus newton per square metre Nm 2 , which is alsocalled the Pascal Pa .1 Nm 2 1 PaOther units include the mmHg, the cmHg and an atmosphere atm .Example 1A man of mass 84 kg stands upright on a floor. If the area of contact of his shoesand floor is 420 cm2, determine the average pressure he exerts on the floor. Take g 10 Nkg 1 SolutionExample 2A metallic block of mass 40 kg exerts a pressure of 20 Nm 2 on a flat surface. Determine the area of contact between the block and the surface. Take g 10 Nkg 1 SolutionExample 3A brick 20 cm long, 10 cm wide and 5 cm thick has a mass of 500 g. Determinethe: a greatest pressure that can be exerted by the brick on a flat surface. B least pressure that can be exerted by the brick on a flat surface. Take g 10Nkg 1 Solution a Dimensions of the brick are 0.20 m, 0.10 m and 0.05 m.P is greatest when area A is smallest. Area of the smallest face of the brick 0.10 0.05 0.005 m2 b Pressure is least when area A is greatest. From the above examples, it is clear that: i If area is held constant, the higher the force, the higher the pressure and thelower the force, the lower the pressure. Ii If force is kept constant, the smaller the area, the greater the pressure andthe larger the area, the smaller the pressure. Exercise 4.11. A force of 100 N is applied to an area of 100 mm2.
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The water will settle in the tube with the levels on both arms being the same, seefigure 4.6 a .Fig. 4.6: Effect of pressure on liquid levelsWhen one arm of the U-tube is blown into with the mouth, the level movesdownwards, while in the other arm it rises, see figure between 4.6 b . This iscaused by the pressure difference between the two arms. The pressure increaseson the arm that is blown into and causes water to rise on the other arm. Experiment 4.2 a : To investigate the variation of liquid pressure withdepth and densityApparatusA tall jar, liquids of different densities, thistle funnel, U-tube, rubber tubing. Fig. 4.7: Pressure variation in a liquidProcedure Fill the glass vessel with water. Connect the thistle funnel to a U-tube filled to some level with water. Lower the funnel to different depths from the surface and notice thedifference in levels, h, of water in the U-tube, see figure 4.7. Replace the water in the glass vessel with a denser liquid, such as sodiumchloride solution brine . Lower the funnels to the same depths as above and compare the heightsobtained. Observations i The deeper the funnel goes below the surface, the greater the difference inlevels, h. ii The differences in levels, h, obtained with brine at a particular depth isgreater than that obtained with water at that depth. ConclusionPressure in a liquid increases with the density of the liquid and with depth. Experiment 4.2 b : To show the distribution of pressure at a point in aliquidApparatusA tall jar, water, thistle funnels, U-tube, rubber tubing. Fig. 4.8: Pressure distributionProcedure Fill the glass vessel with water. Connect one of the thistle funnels to a U-tube filled to some level with water. Lower the funnel P to a depth from the surface of the water and notice thedifference in levels, h, of the water in the U-tube. Replace the funnel with Q whose mouth is pointing in a different direction. Lower the funnel Q into the water so that the mouth of the funnel is at thesame point as the straight one P.
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Fig. 4.7: Pressure variation in a liquidProcedure Fill the glass vessel with water. Connect the thistle funnel to a U-tube filled to some level with water. Lower the funnel to different depths from the surface and notice thedifference in levels, h, of water in the U-tube, see figure 4.7. Replace the water in the glass vessel with a denser liquid, such as sodiumchloride solution brine . Lower the funnels to the same depths as above and compare the heightsobtained. Observations i The deeper the funnel goes below the surface, the greater the difference inlevels, h. ii The differences in levels, h, obtained with brine at a particular depth isgreater than that obtained with water at that depth. ConclusionPressure in a liquid increases with the density of the liquid and with depth. Experiment 4.2 b : To show the distribution of pressure at a point in aliquidApparatusA tall jar, water, thistle funnels, U-tube, rubber tubing. Fig. 4.8: Pressure distributionProcedure Fill the glass vessel with water. Connect one of the thistle funnels to a U-tube filled to some level with water. Lower the funnel P to a depth from the surface of the water and notice thedifference in levels, h, of the water in the U-tube. Replace the funnel with Q whose mouth is pointing in a different direction. Lower the funnel Q into the water so that the mouth of the funnel is at thesame point as the straight one P. Observe the difference in the levels of thewater in the U-tube. ObservationsAt the same depth in a given liquid, difference in levels obtained is the sameregardless of the direction which the funnel faces. ConclusionPressure in liquids increases with density and depth. In summary: i pressure in a liquid increases with depth below its surface. Ii pressure in a liquid increases with the density of the liquid. Iii the distribution of pressure in a liquid at a particular depth is the same inall directions. Derivation of Fluid Pressure Formula P h gFig.
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4.8: Pressure distributionProcedure Fill the glass vessel with water. Connect one of the thistle funnels to a U-tube filled to some level with water. Lower the funnel P to a depth from the surface of the water and notice thedifference in levels, h, of the water in the U-tube. Replace the funnel with Q whose mouth is pointing in a different direction. Lower the funnel Q into the water so that the mouth of the funnel is at thesame point as the straight one P. Observe the difference in the levels of thewater in the U-tube. ObservationsAt the same depth in a given liquid, difference in levels obtained is the sameregardless of the direction which the funnel faces. ConclusionPressure in liquids increases with density and depth. In summary: i pressure in a liquid increases with depth below its surface. Ii pressure in a liquid increases with the density of the liquid. Iii the distribution of pressure in a liquid at a particular depth is the same inall directions. Derivation of Fluid Pressure Formula P h gFig. 4.9: Liquid columnIf A is the cross-section area of the column, h the height of the column and thedensity of the liquid, then;Volume of the liquid cross-section height AhMass of the liquid volume of the liquid density Ah Therefore, weight of the liquid column mass of the liquid gravitational force per unit mass Ah gTherefore, pressure P exerted by the column on A is given by, p h gFrom the formula P h g, it can be seen that the pressure due to a liquid columnis directly proportional to: i height h of the column. Ii the density of the liquid. Pressure does not depend on the cross-section area of the container which holdsthe liquid. The formula is also used to determine pressure due to a column of gas. Example 4A diver is 10 m below the surface of the water in a dam. If the density of water is1 000 kgm 3, determine the pressure due to the water on the diver. Take g 10Nkg 1 SolutionPressure on the diver is given by;P h g 10 1 000 10 100 000 Nm 2Example 5The density of mercury is 13 600 kgm 3.
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4.9: Liquid columnIf A is the cross-section area of the column, h the height of the column and thedensity of the liquid, then;Volume of the liquid cross-section height AhMass of the liquid volume of the liquid density Ah Therefore, weight of the liquid column mass of the liquid gravitational force per unit mass Ah gTherefore, pressure P exerted by the column on A is given by, p h gFrom the formula P h g, it can be seen that the pressure due to a liquid columnis directly proportional to: i height h of the column. Ii the density of the liquid. Pressure does not depend on the cross-section area of the container which holdsthe liquid. The formula is also used to determine pressure due to a column of gas. Example 4A diver is 10 m below the surface of the water in a dam. If the density of water is1 000 kgm 3, determine the pressure due to the water on the diver. Take g 10Nkg 1 SolutionPressure on the diver is given by;P h g 10 1 000 10 100 000 Nm 2Example 5The density of mercury is 13 600 kgm 3. Determine the liquid pressure at a point76 cm below the surface of mercury. Take g 10 Nkg 1 SolutionPressure is given by P h g 0.76 13 600 10 103 360 Nm 2Transmission of Pressure in LiquidsConsider:Fig. 4.10 shows a round bottomed flask fitted with a piston and holes of samediameter drilled along the same level. Fig. 4.10Initially, the water squirts out at the same rate with some force. When theplunger is pushed in, the liquid squirts out at the same rate but with increasedforce.
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Fig. 4.10Initially, the water squirts out at the same rate with some force. When theplunger is pushed in, the liquid squirts out at the same rate but with increasedforce. If the plunger exerts a force F and the piston area is A, then the additionalpressure P , developed is transmitted equally to all parts of the liquid forcingthe liquid out of the holes with the same increased force. Experiment 4.3: To investigate how pressure is transmitted in liquids Pascal s principle Using Identical SyringesApparatusTwo identical syringes, rubber tubing, water, pairs of different masses, twostands and clamps. Fig. 4.11: Transmission of pressure in liquidsProcedure Set up the apparatus as shown in figure 4.11. Place a mass m on one of the plungers and observe what happens. Place an identical mass on the other plunger and observe what happens. Repeat with the other pairs of identical masses. Observation i When the first mass is placed on the plunger, the plunger movesdownwards and the second plunger moves up. Ii When an identical mass is placed on the second plunger, the first plungerwith the mass on it moves upwards and stops when their levels are thesame. The pressure in the two syringes is the same. This is because the masses and thediameters of the syringes are the same. Using Syringes of Different DiametersApparatusSyringes of different diameters, two stands and clamps, different masses, water,rubber tubing. Fig. 4.12: Effects of transmitted pressureProcedure Replace one of the syringes in Experiment 4.3 a with syringe of differentdiameter, and set up the apparatus as shown in figure 4.12. Starting with a large mass on syringe Q, put masses on syringe P until Q juststarts to move upwards. Note the mass on P and Q as in table 4.1.Table 4.1 Syringe PSyringe QArea A of piston m2 Weight F on piston N From the table, compare the value of in P and Q.ConclusionAt balance, the pressure due to the mass in P is equal to the pressure due to theother mass in Q.From the foregoing experiment, pressure applied at one part of an enclosedliquid is transmitted equally to all other parts of the enclosed liquid.
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This is because the masses and thediameters of the syringes are the same. Using Syringes of Different DiametersApparatusSyringes of different diameters, two stands and clamps, different masses, water,rubber tubing. Fig. 4.12: Effects of transmitted pressureProcedure Replace one of the syringes in Experiment 4.3 a with syringe of differentdiameter, and set up the apparatus as shown in figure 4.12. Starting with a large mass on syringe Q, put masses on syringe P until Q juststarts to move upwards. Note the mass on P and Q as in table 4.1.Table 4.1 Syringe PSyringe QArea A of piston m2 Weight F on piston N From the table, compare the value of in P and Q.ConclusionAt balance, the pressure due to the mass in P is equal to the pressure due to theother mass in Q.From the foregoing experiment, pressure applied at one part of an enclosedliquid is transmitted equally to all other parts of the enclosed liquid. This iscalled the principle of transmission of pressure in liquids Pascal sPrinciple . Gases may transmit pressure in a similar way when they are confinedand incompressible. Hydraulic MachinesThe principle of transmission of pressure in liquids is made use of in hydraulicmachines where a small force applied at one point of a liquid produces a muchlarger force at some other point of the liquid. Hydraulic LiftThe hydraulic lift consists of a small piston S of cross-section area A1 and alarge piston L of cross-section area A2. When a force is applied on piston S, thepressure generated by the force is transmitted throughout the liquid to piston L,see figure 4.13.Fig. 4.13: Hydraulic liftConsider a force F1 applied on the small piston of cross-section area A1. Then,pressure P1 generated on the liquid by the piston S due to F1 is given by;This pressure is transmitted by the liquid to the larger piston L. Therefore,pressure of liquid acting on the area A2 of the large piston is equal to P1. Thus,the force F2 produced on the large piston is given by;F2 pressure area P1 A2Hydraulic lifts are used to hoist cars in garages.
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Then,pressure P1 generated on the liquid by the piston S due to F1 is given by;This pressure is transmitted by the liquid to the larger piston L. Therefore,pressure of liquid acting on the area A2 of the large piston is equal to P1. Thus,the force F2 produced on the large piston is given by;F2 pressure area P1 A2Hydraulic lifts are used to hoist cars in garages. Hydraulic presses on the otherhand are used to compress certain materials such as cotton bales into therequired shapes and sizes. Example 6A small force of 100 N applied on the small piston of area A1 equal to 0.25 m2produces a bigger force F2 on a larger piston of area A2 equal to 10 m2. Seefigure 4.14 below. Calculate F2.Fig.4.14Note:A small force applied on the small piston produces a much bigger force on thelarger piston. Hydraulic Brake SystemFig. 4.15: Vehicle hydraulic brake systemA vehicle hydraulic brake system is shown in figure 4.15.The force applied on the brake pedal exerts pressure on the master cylinder. The pressure is transmitted by the brake fluid to the slave cylinder. This causesthe pistons of slave cylinder to open the brake shoe and hence the brake liningpresses on the drum. The rotation of the wheel is thus resisted. When the force on the foot pedal is withdrawn, the return spring pulls backthe brake shoe which then pushes the slave cylinder piston back. The advantage of this system is that the pressure exerted in master cylinderis transmitted equally to all the four wheel cylinders. Hence, the braking forceobtained is uniform. The liquid to be used as a brake fluid should have the following properties: i Be incompressible, to ensure pressure exerted at one point is transmittedequally to all other parts in the liquid. Ii Have low freezing point and high boiling point. Iii Should not corrode the parts of the brake system. Exercise 4.21. Calculate the pressure due to water experienced by a diver working 15 mbelow the surface of the sea. Take g 10 Nkg 1 and density of sea water 1.03 gcm 3 2.
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The atmosphere thins outwards,indicating the density of air decreases with the distance from the surface of theearth. Consider a column of air as in figure 4.16 b , extending vertically intospace to the end of the atmosphere. This column of air stands on the earth ssurface like a liquid in a tube and exerts pressure on the surface of the earth. Thepressure exerted on the surface of the earth by the weight of the air column iscalled atmospheric pressure. The existence of atmospheric pressure is demonstrated by the experimentbelow. Experiment 4.4: To demonstrate the existence of the atmospheric pressureApparatusTin container with a tight-fitting cork, water, tripod stand, Bunsen burner. Fig. 4.17: Crushing can experimentProcedure Remove the cork from the container and pour in some little water. Boil the water for several minutes. Replace the cork and allow the container to cool. You may pour cold water onit to cool it faster. Observe what happens to the container. ObservationDuring cooling, the container is crushed in. ExplanationSteam from boiling water drives out most of the air inside the container, seefigure 4.17 a . When the cork is first replaced, the steam pressure inside thecontainer balances the atmospheric pressure outside. On cooling, the steamcondenses. A partial vacuum is therefore created in the container. Since pressure insidethe container is less than atmospheric pressure outside, the container is crushed,see figure 4.17 b .Maximum Column of Liquid that can be Supported by AtmosphericPressureWhen water is sucked up a straw as in figure 4.18, the air pressure inside thestraw reduces. Fig. 4.18: The working of the drinking strawThe atmospheric pressure acting on the water surface is now greater thanthe pressure inside the straw. Water is thus pushed up the straw by theatmospheric pressure. If the straw was long enough and sealed at the top, it would be possible toestimate the height of water in the straw that would be supported by atmosphericpressure. A more convenient method is to use a glass tube sealed at one end, as infigure 4.19 a . Fig. 4.19: Water and mercury columns supported by atmospheric pressureFill glass tubes of different lengths completely with water and invert them in awater reservoir.
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Water is thus pushed up the straw by theatmospheric pressure. If the straw was long enough and sealed at the top, it would be possible toestimate the height of water in the straw that would be supported by atmosphericpressure. A more convenient method is to use a glass tube sealed at one end, as infigure 4.19 a . Fig. 4.19: Water and mercury columns supported by atmospheric pressureFill glass tubes of different lengths completely with water and invert them in awater reservoir. You will realise that the water column can be very large, in facttoo large for your available apparatus to accommodate. However, if mercury, which is much denser than water is used, the columnsupported is found to be much shorter, see figure 4.19 b . In this figure, themercury column in the tube exerts pressure at point B. For the height of thiscolumn to remain constant, there must be a counter pressure to hold it up. Thiscounter pressure is provided by the atmosphere. At sea level, the atmosphericpressure supports approximately 76 cm of mercury column or approximately 10m of water column. Example 7A girl in a school situated in the coast region sea level plans to make abarometer using sea-water of density 1 030 kgm 3. If the atmospheric pressure is103 000 Nm 2, Determine the minimum length of the tube that she will require. SolutionPressure in liquid is given by P h gBut P atmospheric pressureTherefore, h g atmospheric pressureh 1 030 10 103 000Example 8A sea diver is 35 m below the surface of sea-water. If density of the sea-water is1.03 g cm3 and g is 10 Nkg 1, determine the total pressure on him. Takeatmospheric pressure to be 103,00 N m 2SolutionPressure in liquid is given by P h gBut total pressure atmospheric pressure, Pa liquid pressure Pa h g 103 000 35 1 030 10 Nm 2 463 500 Nm 2Example 9The air pressure at the base of a mountain is 75.0 cm of mercury while at the topit is 60.0 cm of mercury.
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It is then inverted into adish filled with mercury and supported upright with a stand and clamp, seefigure 4.21. The tightly closed end is then opened while under the surface of themercury. The column of mercury in the tube drops to create a vacuum in thespace above the column. Fig. 4.21: Simple mercury barometerThe height h of the column barometric height is a measure of the atmosphericpressure. At sea level, h 76 cmHg. Since density of mercury is 13 600 kgm 3,Pa h g 0.76 13 600 10 103 360 Nm 2This is the standard atmospheric pressure, and is sometimes referred to asone atmosphere. Testing the Vacuum BarometerIf the barometer has air at the top, then it is faulty. The value of pressureindicated by such a barometer is less than the actual value since the trapped airalso exerts pressure on the mercury column. To test for the vacuum, the tube is tilted as shown in figure 4.22 a so that thetopmost part of the tube is below the height that is supported by atmosphericpressure. Fig. 4.22If there is air in the tube, the mercury will not fill the tube completely. However,if the space is a vacuum, the mercury fills the tube completely. The space above the mercury in the tube when upright is called Toricellianvacuum and contains a little mercury vapour. Fortin BarometerThe simple mercury barometer cannot be used for accurate measurements ofatmospheric pressure. An improved version called the Fortin barometer is usedwhere high precision is required. It was designed by Fortin, a French instrument maker. Figure 4.23 showsmain parts of the barometer. Fig. 4.23: Fortin barometerThe Fortin barometer has a: i vertical glass tube containing mercury. Ii leather bag as the reservoir of mercury. Iii short fixed main scale and a movable vernier scale which facilitatesaccurate reading of the mercury height. Iv fixed ivory index with a sharp point at the bottom, which acts as the zero mark of the main scale. Before taking the reading, the level of mercury surface in the reservoir isadjusted by turning the adjusting screw until the surface of the mercury justtouches the tip of the ivory index.
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| 1,750,280,446.985062 |
Figure 4.23 showsmain parts of the barometer. Fig. 4.23: Fortin barometerThe Fortin barometer has a: i vertical glass tube containing mercury. Ii leather bag as the reservoir of mercury. Iii short fixed main scale and a movable vernier scale which facilitatesaccurate reading of the mercury height. Iv fixed ivory index with a sharp point at the bottom, which acts as the zero mark of the main scale. Before taking the reading, the level of mercury surface in the reservoir isadjusted by turning the adjusting screw until the surface of the mercury justtouches the tip of the ivory index. The mirror-like mercury surface produces animage of the tip which helps to make the adjustment very accurate. The height ofmercury is then read from the main scale and the vernier scale. Any change in airpressure makes the surface of mercury in the reservoir move up and down andtherefore this adjustment is necessary before the barometer is read. The height ofmercury is read from the top part of the meniscus. The readings obtained from the barometer are in terms of the height ofmercury column and are written as mmHg or cmHg Hg is the chemical symbolfor mercury . Therefore, the atmospheric pressure at sea level is expressed as760 mmHg. It is important however to note that pressure is force per unit area,but not a length. The atmospheric pressure Pa when the mercury column is 760 mm long isgiven by;Pa h g 0.76 13 600 10 density of mercury is 13 600 kgm 3 and g is 10 Nkg-1 103 360 Nm 2Aneroid BarometerThe mercury barometer is the most reliable type of barometer, but is not readilyportable. Fig. 4.24: Aneroid barometerThe aneroid barometer is a portable type of barometer consisting of asealed, corrugated metal box, as shown in figure 4.24. This metal box expands alittle if pressure outside is reduced, and reduces in volume a little if subjected tohigher pressure from outside.
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It is important however to note that pressure is force per unit area,but not a length. The atmospheric pressure Pa when the mercury column is 760 mm long isgiven by;Pa h g 0.76 13 600 10 density of mercury is 13 600 kgm 3 and g is 10 Nkg-1 103 360 Nm 2Aneroid BarometerThe mercury barometer is the most reliable type of barometer, but is not readilyportable. Fig. 4.24: Aneroid barometerThe aneroid barometer is a portable type of barometer consisting of asealed, corrugated metal box, as shown in figure 4.24. This metal box expands alittle if pressure outside is reduced, and reduces in volume a little if subjected tohigher pressure from outside. The motion due to the changes in shape of themetal box is magnified by the corresponding movements of the spring strips,lever arm, chain and finally the pointer on the scale. Normally, the pointer would indicate a particular value of the atmosphericpressure of the surrounding so that any changes in pressure would be noticeableby the movement of the pointer to either side of this atmospheric value on thescale. The aneroid barometer movements make it adaptable to measure heights. Altimeters are basically aneroid barometers, and are used in aircrafts to measureheights. The aneroid barometer is normally calibrated in millibars. 1 bar is apressure of 100 000 Nm 2 standard atmospheric pressure 1 millibar mbar 100 Nm 2Pressure GaugesPressure gauges are portable and are used mostly for measuring gas pressure,tyre pressure, pressure of compressed air in compressors and steam pressure. They are basically made of coiled flexible metal tubes which uncoil whenthe pressure inside increases. The movement of the tube is made to drive apointer across a scale, through a combined system of levers and gears, see figure4.25.Fig.
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The motion due to the changes in shape of themetal box is magnified by the corresponding movements of the spring strips,lever arm, chain and finally the pointer on the scale. Normally, the pointer would indicate a particular value of the atmosphericpressure of the surrounding so that any changes in pressure would be noticeableby the movement of the pointer to either side of this atmospheric value on thescale. The aneroid barometer movements make it adaptable to measure heights. Altimeters are basically aneroid barometers, and are used in aircrafts to measureheights. The aneroid barometer is normally calibrated in millibars. 1 bar is apressure of 100 000 Nm 2 standard atmospheric pressure 1 millibar mbar 100 Nm 2Pressure GaugesPressure gauges are portable and are used mostly for measuring gas pressure,tyre pressure, pressure of compressed air in compressors and steam pressure. They are basically made of coiled flexible metal tubes which uncoil whenthe pressure inside increases. The movement of the tube is made to drive apointer across a scale, through a combined system of levers and gears, see figure4.25.Fig. 4.25: Pressure gaugeExample 10The pressure of a car tyre, measured with a pressure gauge, is 40 N cm2.Determine the total pressure of the tyre in Nm 2 given that atmospheric pressureis 103 360 N m2.SolutionTotal pressure atmospheric pressure gauge pressure 103 360 40 10 000 103 360 400 000 503 360 N m2Applications of Pressure in Gases and LiquidsThe Bicycle PumpA bicycle pump is a simple form of a compression pump. Figure 4.26 shows themain parts of the pump. Fig. 4.26: Bicycle pumpIt has a flexible leather washer which works both as a valve and a piston insidethe pump barrel. Before the pump is used, it is connected to the tyre which has arubber valve in it. When the pump handle is drawn out as shown, the volume of air below thewasher increases and its pressure is reduced below the atmospheric pressure. Airfrom outside the pump then flows past the leather washer into the barrel. At thesame time, the higher air pressure in the tube closes the tyre valve. When the pump handle is pushed in, the air in the pump barrel iscompressed.
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Before the pump is used, it is connected to the tyre which has arubber valve in it. When the pump handle is drawn out as shown, the volume of air below thewasher increases and its pressure is reduced below the atmospheric pressure. Airfrom outside the pump then flows past the leather washer into the barrel. At thesame time, the higher air pressure in the tube closes the tyre valve. When the pump handle is pushed in, the air in the pump barrel iscompressed. The high pressure in the barrel presses the leather washer againstthe sides of the barrel. When the pressure of the compressed air becomes greaterthan that of air in the tyre, air is forced into the tyre through the tyre valve whichnow opens. Note that there is an increase in temperature of the pump barrel duringpumping. This is because of the work done in compressing air. The Lift PumpA lift pump is used to raise water from wells. It consists of a cylindrical metalbarrel with a spout. It has two valves, P and Q, as shown in figure 4.27.To start the pump, water is poured on top of the piston priming so that agood air-tight seal is made round the piston and valve P. The pump is operatedby means of a lever as shown in the figure. UpstrokeWhen the plunger moves up during the upstroke, valve P closes due to its weightand pressure of water above it. At the same time, air above valve Q expands andits pressure reduces below atmospheric pressure. The atmospheric pressure onwater in the well below thus pushes water up past valve Q into the barrel, asshown in figure 4.27 a .The plunger is moved up and down until the space between P and Q isfilled with water. Lever Reduced air pressureWater level P Upstroke b DownstrokeFig.
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At the same time, air above valve Q expands andits pressure reduces below atmospheric pressure. The atmospheric pressure onwater in the well below thus pushes water up past valve Q into the barrel, asshown in figure 4.27 a .The plunger is moved up and down until the space between P and Q isfilled with water. Lever Reduced air pressureWater level P Upstroke b DownstrokeFig. 4.27: Lift pumpDownstrokeDuring downstroke, valve Q closes due to its weight and pressure of waterabove, see figure 4.27 b .Water is forced out through valve P and thus flows out of the spout. Limitations of this pumpThe atmospheric pressure can only support a column of water of about 10 m.This is, therefore, the theoretical maximum height to which water can be raisedby the pump at normal atmospheric pressure. In practice, the possible height of water can be raised by this pump is lessthan 10 m because of: i reduced atmospheric pressure in places high above sea level. Ii leakages at the valves and pistons. The Force PumpThis pump can be used to raise water to heights of more than 10 m.UpstrokeDuring upstroke, air above the valve S expands and its pressure reduces belowatmospheric pressure. The atmospheric pressure on the water in the well belowpushes water up valve S into the barrel. Note that pressure above valve T isatmospheric. Hence, this valve does not open in this stroke, see figure 4.28 a .DownstrokeDuring the downstroke, the valve S closes, see figure 4.28 b . Increase inpressure in the water in the barrel opens valve T and forces water into chamberC so that as water fills the chamber, air is trapped and compressed at the upperpart. UpstrokeFig.
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Hence, this valve does not open in this stroke, see figure 4.28 a .DownstrokeDuring the downstroke, the valve S closes, see figure 4.28 b . Increase inpressure in the water in the barrel opens valve T and forces water into chamberC so that as water fills the chamber, air is trapped and compressed at the upperpart. UpstrokeFig. 4.28: Force pumpDuring the next upstroke, valve T closes and the compressed air expands,ensuring a continuous flow through P.This pump has an advantage over the lift pump in that it enables acontinuous flow of water and the height to which water can be raised by thispump does not depend on atmospheric pressure, but on the following: i Amount of force applied during the downstroke. Ii Ability of the pump and its working parts to withstand pressure of the longcolumn of water in chamber C.The SiphonA tube usually plastic or rubber can be used to empty tanks or draw petrol frompetrol tanks of cars, as in figure 4.29. When used in this way, it is referred to as asiphon. Fig. 4.29: The siphonThe pressure at the surface of the liquid is atmospheric. The tube is first filledwith the liquid and end C held below the surface. Pressure at C is greater thanthat at the surface by an amount h g.The liquid will continue to run out so long as the end C is below the liquidsurface. Pressure at A and B is atmospheric pressure since they are at the samehorizontal level. Pressure at C is equal to atmospheric pressure plus pressure dueto column h of the liquid. That is;Pressure at CPc Pa h g, where Pa is atmospheric pressure and the density of water. Theexcess presure h g thus causes the liquid to flow out of the tube at C. The siphon will only work if: i the end C of the tube is below the surface of A of the liquid to be emptied. Ii the tube is first filled with the liquid, without any bubbles in it. Iii the tube does not rise above the height of the liquid surface A. iv one end of the tube is inside the liquid to be emptied. Note:A siphon can operate in a vacuum.
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| 1,750,280,447.080057 |
That is;Pressure at CPc Pa h g, where Pa is atmospheric pressure and the density of water. Theexcess presure h g thus causes the liquid to flow out of the tube at C. The siphon will only work if: i the end C of the tube is below the surface of A of the liquid to be emptied. Ii the tube is first filled with the liquid, without any bubbles in it. Iii the tube does not rise above the height of the liquid surface A. iv one end of the tube is inside the liquid to be emptied. Note:A siphon can operate in a vacuum. To understand this, consider a chain or thickrope coiled into a bucket, raised above the ground and one end of it over apulley, see figure 4.30. The loose end A, when it is below the bucket will have anet weight on it. This net weight resulting from the pull of gravity pulls down thechain completely out of the bucket. Fig. 4.30This is how the siphon works in a vacuum. An application of the siphon is the automatic flushing unit, shown in figure 4.31. Fig. 4.31: An automatic water flushing unitIt is used where constant cleaning is necessary, like urinals. When the water inthe tank fills above the top of the inverted U-tube, a pressure difference betweenthe two arms is created. This causes the water to flow out of the tank. The tapcan be adjusted to enable the flushing unit to flush at pre-determined intervals. The ordinary lavatory flusher is set to work by mechanically filling the tube withwater to create the necessary pressure difference. Revision Exercise 41. Define pressure and state its SI unit.2. Explain how a fountain pen is filled up with ink.3. The atmospheric pressure on a particular day was measured as 750 mmHg. Express this in Nm 2. Assume density of mercury is 13 600 kgm 3 and g 10 Nkg 1 4. In a hydraulic press, a force of 200 N is applied to a master piston of area 25cm2. If the press is designed to produce a force of 5 000 N, determine: a the area of the slave piston. B the radius of the slave piston.5. The barometric height of a town is 70 cmHg.
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| 1,750,280,447.123411 |
In a hydraulic press, a force of 200 N is applied to a master piston of area 25cm2. If the press is designed to produce a force of 5 000 N, determine: a the area of the slave piston. B the radius of the slave piston.5. The barometric height of a town is 70 cmHg. Given that the standardatmospheric pressure is 76 cmHg and the density of mercury is 13 600 kgm 3, determine the altitude of the town. Density of air is 125 kgm 3 6. The height h of a water manometer is 20 cm when used to measure thepressure of a gas. Calculate the height of a manometer whose liquid isglycerine of density 1.26 g cm3 Take g 10 Nkg 1 7. Explain how the pressure of a gas can be examined using the apparatusshown in the figure below:8. The figure below shows how to empty water from a large tank into a lowlying container using rubber tubing: a Explain why the tube must be filled with water before the emptyingprocess starts. B Soon after the tank begins to empty, the lower end is momentarilyblocked by placing a finger at end D. Determine the pressure differencebetween points A and D. Take density of water to be 1000 kgm 3 9. The diagram below shows a mercury manometer. Some dry gas is present inthe closed space in limb A, while limb B is open. If atmospheric pressure Pa 100 000 Nm 2, h 20 mm and density of mercury is 13 600 kgm 3,determine pressure Pg of the gas in mmHg. Take g 10 Nkg 1 10. A Explain briefly the working of a simple mercury barometer. B Explain the test that would be made to find out whether such abarometer has any gas in the space above the mercury. C Figure i below shows a simple mercury barometer, while figure ii shows the same barometer with the tube tilted from the vertical:Mark the level of mercury in tube ii .11. The figure below shows a U-tube filled with water, mercury and anotherliquid: a Determine the density of the liquid. B State a possible reason why mercury is used.12.
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| 1,750,280,447.100713 |
Take g 10 Nkg 1 10. A Explain briefly the working of a simple mercury barometer. B Explain the test that would be made to find out whether such abarometer has any gas in the space above the mercury. C Figure i below shows a simple mercury barometer, while figure ii shows the same barometer with the tube tilted from the vertical:Mark the level of mercury in tube ii .11. The figure below shows a U-tube filled with water, mercury and anotherliquid: a Determine the density of the liquid. B State a possible reason why mercury is used.12. The figure below shows a liquid in a pail. A If the liquid has a density of 1.20 gcm 3, determine the pressure exertedat the bottom of the container by the liquid. B Suggest a reason why pail manufacturers prefer the shape shown toother shapes. 13. The figure below shows columns of different liquids in a tube. Determine theheight of liquid A if its density is 1.20 g cm3.14. A roof has a surface area of 20 000 cm2. If the atmospheric pressure exertedon the roof is 100 000 Pa, determine the force on it. Take g 10 Nkg 1 15. Explain how a syringe draws; a injectable drug from a bottle. B blood from a patient s body. The Particulate Natureof MatterMatter is anything that occupies space and has mass. Matter commonly exists assolid, liquid or gas. The physical objects and materials around us like glass,water and the air manifest the existence of matter in its three states. The process of subdividing matter into smaller and smaller units continuesindefinitely, suggesting that matter is not continuous, but is made up of evensmaller parts. Investigating MatterThere are several experiments that can be performed to show that matter is madeup of tiny particles. Some are considered below. Experiment 5.1: To demonstrate that matter is made of tiny particlesApparatusA sheet of paper and a pair of scissors. Procedure Cut the piece of paper into two parts. Take one part and cut it again into two parts and continue the process. Figure 5.1 shows that the piece of paper can be cut into very many tiny pieces. Fig.
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Matter commonly exists assolid, liquid or gas. The physical objects and materials around us like glass,water and the air manifest the existence of matter in its three states. The process of subdividing matter into smaller and smaller units continuesindefinitely, suggesting that matter is not continuous, but is made up of evensmaller parts. Investigating MatterThere are several experiments that can be performed to show that matter is madeup of tiny particles. Some are considered below. Experiment 5.1: To demonstrate that matter is made of tiny particlesApparatusA sheet of paper and a pair of scissors. Procedure Cut the piece of paper into two parts. Take one part and cut it again into two parts and continue the process. Figure 5.1 shows that the piece of paper can be cut into very many tiny pieces. Fig. 5.1: Paper cut into smaller piecesObservationThe process of cutting can continue until further subdivision becomesimpracticable. ConclusionThe fact that the piece of paper can be subdivided into tiny pieces suggests thatmatter is made up of tiny particles. Experiment 5.2: To demonstrate dilutionApparatusBeaker, potassium permanganate crystals, water. Procedure Pour water into the beaker till it is a quarter full. Dissolve a few crystals of potassium permanganate in the water until thecolour is deep purple. Add water to top up the volume to about half full as you observe the changein colour intensity. Gradually add more water as you observe the change in colour intensity. Continue the process until the beaker is full. Fig. 5.2ObservationThe process of dilution can continue until the solution appears colourless. Thissuggests that the particles of potassium permanganate are spread out evenly onthe water. Through each dilution process, the particles spread out further.
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