Cancel G and m on both sides and rearrange to get d1 = 9d2 Note also that d1 + d2 = distance between the Earth and the Moon = 3.84 × 108 m 9d2 + d2 = distance between the Earth and the Moon = 3.84 × 108 m 10 d2 = 3.84 × 108 d2 = 3.84 × 107 d1 = 3.356 × 108 Height = (3.356 × 108) (6.36 × 106) = 3.39 × 108 m above the earth – The moon orbits the earth every 27.3 days. What is its velocity, expressed in metres per second? = 1022.9 m s-1 v Why is there no atmosphere on the moon? The gravitational force is too weak to sustain an atmosphere. 2009 Question 12 (a) State law. Hooke’s When a string is stretched the restoring force is proportional to the displacement. Calculate the spring constant. Natural length = = 300 mm = 0.3 m l0 Extension = 30 mm = 0.03 m m = 0.5 kg After the mass has been attached it will come to rest at a new equilibrium position where force down = force up Force down = mg = (0.5)(g) Force up = k(extension) = (k)(0.03) Force down = Force up 0.5g = k(0.03)  k = 163.3 N m-1 sphere is then pulled down until the length has increased to 350 mm and is then spring’s released. Describe the motion of the sphere when it is released. It executes simple harmonic motion because the displacement is proportional to the acceleration. What is the maximum acceleration of the sphere? so acceleration will be a maximum when displacement from equilibrium position is a maximum. a = 2 x Displacement is a maximum at the release point, which is a distance of 20 mm or 0.02 m from equilibrium position. So x in this context = 0.02 m However we also need to calculate = To find we use the relationship a = )(0.02) a = 6.532 m s-2 a = 2 x   2008 Question 6
Cancel G and m on both sides and rearrange to get d1 = 9d2 Note also that d1 + d2 = distance between the Earth and the Moon = 3.84 × 108 m 9d2 + d2 = distance between the Earth and the Moon = 3.84 × 108 m 10 d2 = 3.84 × 108 d2 = 3.84 × 107 d1 = 3.356 × 108 Height above the earth = (3.356 × 108) – (6.36 × 106) = 3.39 × 108 m The moon orbits the earth every 27.3 days. What is its velocity, expressed in metres per second? v = 1022.9 m s-1 Why is there no atmosphere on the moon? The gravitational force is too weak to sustain an atmosphere. 2009 Question 12 (a) State Hooke’s law. When a string is stretched the restoring force is proportional to the displacement. Calculate the spring constant. Natural length = l0 = 300 mm = 0.3 m Extension = 30 mm = 0.03 m m = 0.5 kg After the mass has been attached it will come to rest at a new equilibrium position where force down = force up Force down = mg = (0.5)(g) Force up = k(extension) = (k)(0.03) Force down = Force up 0.5g = k(0.03)  k = 163.3 N m-1 sphere is then pulled down until the spring’s length has increased to 350 mm and is then released. Describe the motion of the sphere when it is released. It executes simple harmonic motion because the displacement is proportional to the acceleration. What is the maximum acceleration of the sphere? a = 2 x so acceleration will be a maximum when displacement from equilibrium position is a maximum. Displacement is a maximum at the release point, which is a distance of 20 mm or 0.02 m from equilibrium position. So x in this context = 0.02 m However we also need to calculate To find we use the relationship = a = 2 x  a = )(0.02)  a = 6.532 m s-2 2008 Question 6