Physics 9702 · AS & A Level · Momentum and Newton's laws of motion

Momentum and Newton's laws of motion — practice question

A ball with mass $0.030\,\text{kg}$ travels along a curved track, as illustrated in Fig. 2.1. At point A, which is $0.31\,\text{m}$ above the reference level, the ball has a speed of $1.3\,\text{m s}^{-1}$. It then rolls down the track and strikes a vertical wall at point B before bouncing back up the track. Frictional forces may be taken as negligible.
(a)[2]

Calculate the change in gravitational potential energy of the ball as it moves from point A to point B.

(b)[3]

Show that the ball strikes the wall at B with a speed of $2.8\,\text{m s}^{-1}$.

(c(i))[2]

The ball’s change in momentum from its collision with the wall is $0.096\,\text{kg m s}^{-1}$. The ball stays in contact with the wall for $20\,\text{ms}$. Determine the speed immediately after the collision.

(c(ii))[2]

Determine the magnitude of the average force on the ball.

(d)[1]

State and explain whether the collision is elastic or inelastic.

(e)[2]

In reality, friction is significant so that the true increase in kinetic energy of the ball in moving from A to B is $76\,\text{mJ}$. The track length between A and B is $0.60\,\text{m}$. Use your answer in (a) to determine the average frictional force acting on the ball as it moves from A to B.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Applies $\Delta E = mg\Delta h$

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