A-LevelPhysicsMotion in a circle9702/42 · Oct/Nov 2021 · Q18 Marks
State what is meant by centripetal acceleration.
- (a)State what is meant by centripetal acceleration.[1]
- (b)(i)State what happens to the magnitude of the centripetal acceleration of the car as it moves around the loop from X to Y.[1]
- (b)(ii)Explain, if the car remains in contact with the track, why the centripetal acceleration of the car at point Y must be greater than 9.8ms-2.[2]
- (c)The initial speed at which the car in (b) moves along the track is 3.8ms-1. Determine whether the car is in contact with the track at point Y. Show your working.[3]
- (d)Suggest, with a reason but without calculation, whether your conclusion in (c) would be different for a car of mass 460 g moving with the same initial speed.[1]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- acceleration perpendicular to velocity
- decreases
- (acceleration of) 9.8 ms-2 is caused by weight of car
- or centripetal force must be greater than weight of car
- (acceleration > 9.8 ms¯²) requires contact force from track
- or (centripetal force > weight) requires contact force from track
- 1/2mvy2 = 1/2mvx² – mgh
- a = v² / r
- vy2 = 3.82-2 × 9.81 × 0.62 so vy = 1.5ms-1
- a = 1.52 / 0.31 = 7.3 ms-2 (which is less than 9.8 ms-2) so no
- or vy = √(9.81 × 0.31) = 1.74 m s¯¹ so vx2 = 1.742 + 2 × 9.81 × 0.62
- vx = 3.9 m s-1 (which is greater than 3.8 m s-¹) so no
- acceleration is independent of mass so makes no difference
- or mass cancels in the equation so makes no difference
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