Connected particle problems (previously covered in AS Mathematics Mechanics content, see SoW Unit – 8b) can now be extended so at least one of the particles is placed on a rough or smooth inclined plane and/or a rough horizontal plane. This introduces the resolving and frictional concepts from the previous unit. For and caravan’ type questions, the tow rope or tow-bar can now be modelled at an rather than ‘car horizontally. OPPORTUNITIES FOR PROBLEM SOLVING/MODELLING To make this dynamics topic more real, you could set up experiments, involving connected particles for example, and video the motions. You can then see that when one particle hits the ground, the second particle continuing to move up and the string become slack. COMMON MISCONCEPTIONS/EXAMINER REPORT QUOTES Common errors candidates make include: confusing the terms and incorrectly ‘resultant’ ‘reaction’; treated the scenario as a statics problem and assuming the forces are in equilibrium; omitting from the g weight term; and, more rarely, including in the term. g ‘ma’ NOTES The guidance on the specification document states particle problems include problems ‘Connected with particles in contact e.g. lift problems.’ Students may be required to resolve a vector into two components or use a vector diagram, e.g. problems involving two or more forces, given in magnitude–direction form. UNIT 8: Further kinematics SPECIFICATION REFERENCES 7.3 Extend the constant acceleration formulae of motion to 2 dimensions using vectors. 7.4 Use calculus in kinematics for (variable acceleration) motion in a straight line. Extend to 2 dimensions using vectors. PRIOR KNOWLEDGE Basic trigonometry, Pythagoras and vectors Find the magnitude and direction of vectors AS Mathematics Mechanics content –
Connected particle problems (previously covered in AS Mathematics – Mechanics content, see SoW Unit 8b) can now be extended so at least one of the particles is placed on a rough or smooth inclined plane and/or a rough horizontal plane. This introduces the resolving and frictional concepts from the previous unit. For ‘car and caravan’ type questions, the tow rope or tow-bar can now be modelled at an rather than horizontally. OPPORTUNITIES FOR PROBLEM SOLVING/MODELLING To make this dynamics topic more real, you could set up experiments, involving connected particles for example, and video the motions. You can then see that when one particle hits the ground, the second particle continuing to move up and the string become slack. COMMON MISCONCEPTIONS/EXAMINER REPORT QUOTES Common errors candidates make include: confusing the terms ‘resultant’ and ‘reaction’; incorrectly treated the scenario as a statics problem and assuming the forces are in equilibrium; omitting g from the weight term; and, more rarely, including g in the ‘ma’ term. NOTES The guidance on the specification document states ‘Connected particle problems include problems with particles in contact e.g. lift problems.’ Students may be required to resolve a vector into two components or use a vector diagram, e.g. problems involving two or more forces, given in magnitude–direction form. UNIT 8: Further kinematics SPECIFICATION REFERENCES 7.3 Extend the constant acceleration formulae of motion to 2 dimensions using vectors. 7.4 Use calculus in kinematics for (variable acceleration) motion in a straight line. Extend to 2 dimensions using vectors. PRIOR KNOWLEDGE Basic trigonometry, Pythagoras and vectors Find the magnitude and direction of vectors AS Mathematics – Mechanics content