Rebound from wall or barrier

A particle hits a fixed wall and rebounds; find impulse from wall or subsequent motion, possibly with friction on the surface after rebound.

9 questions · Moderate -0.6

Sort by: Default | Easiest first | Hardest first
Edexcel M1 2016 June Q3
7 marks Standard +0.3
3. A particle \(P\) of mass 0.4 kg is moving on rough horizontal ground when it hits a fixed vertical plane wall. Immediately before hitting the wall, \(P\) is moving with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in a direction perpendicular to the wall. The particle rebounds from the wall and comes to rest at a distance of 5 m from the wall. The coefficient of friction between \(P\) and the ground is \(\frac { 1 } { 8 }\). Find the magnitude of the impulse exerted on \(P\) by the wall.
Edexcel M1 2018 June Q4
13 marks Standard +0.3
4. A ball of mass 0.2 kg is projected vertically downwards with speed \(U \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point A which is 2.5 m above horizontal ground. The ball hits the ground. Immediately after hitting the ground, the ball rebounds vertically with a speed of \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The ball receives an impulse of magnitude 7 Ns in its impact with the ground. By modelling the ball as a particle and ignoring air resistance, find
  1. the value of \(U\). After hitting the ground, the ball moves vertically upwards and passes through a point \(B\) which is 1 m above the ground.
  2. Find the time between the instant when the ball hits the ground and the instant when the ball first passes through \(B\).
  3. Sketch a velocity-time graph for the motion of the ball from when it was projected from \(A\) to when it first passes through \(B\). (You need not make any further calculations to draw this sketch.)
Edexcel M1 2017 June Q4
8 marks Moderate -0.8
  1. A small ball of mass 0.2 kg is moving vertically downwards when it hits a horizontal floor. Immediately before hitting the floor the ball has speed \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Immediately after hitting the floor the ball rebounds vertically with speed \(7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
    1. Find the magnitude of the impulse exerted by the floor on the ball.
    By modelling the motion of the ball as that of a particle moving freely under gravity,
  2. find the maximum height above the floor reached by the ball after it has rebounded from the floor,
  3. find the time between the instant when the ball first hits the floor and the instant when the ball is first 1 m above the floor and moving upwards.
Edexcel M1 2005 January Q6
13 marks Moderate -0.3
  1. A stone \(S\) is sliding on ice. The stone is moving along a straight horizontal line \(A B C\), where \(A B = 24 \mathrm {~m}\) and \(A C = 30 \mathrm {~m}\). The stone is subject to a constant resistance to motion of magnitude 0.3 N . At \(A\) the speed of \(S\) is \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and at \(B\) the speed of \(S\) is \(16 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Calculate
    1. the deceleration of \(S\),
    2. the speed of \(S\) at \(C\).
    3. Show that the mass of \(S\) is 0.1 kg .
    At \(C\), the stone \(S\) hits a vertical wall, rebounds from the wall and then slides back along the line \(C A\). The magnitude of the impulse of the wall on \(S\) is 2.4 Ns and the stone continues to move against a constant resistance of 0.3 N .
  2. Calculate the time between the instant that \(S\) rebounds from the wall and the instant that \(S\) comes to rest.
Edexcel M1 Q1
6 marks Moderate -0.8
  1. A tennis ball, moving horizontally, hits a wall at \(25 \mathrm {~ms} ^ { - 1 }\) and rebounds along the same straight line at \(15 \mathrm {~ms} ^ { - 1 }\). The impulse exerted by the wall on the ball has magnitude 12 Ns .
    1. Calculate the mass of the ball.
    2. State any modelling assumptions that you have made.
    \includegraphics[max width=\textwidth, alt={}]{977c24cc-8280-4881-8a62-65b7efd336ac-1_278_337_751_434}
    Forces of magnitude \(4 \mathrm {~N} , 5 \mathrm {~N}\) and 8 N act on a particle in directions whose bearings are \(000 ^ { \circ } , 090 ^ { \circ }\) and \(210 ^ { \circ }\) respectively. Find the magnitude of the resultant force and the bearing of the direction in which it acts.
OCR MEI Further Mechanics Major 2022 June Q3
6 marks Moderate -0.3
3 A particle, of mass 2 kg , is placed at a point A on a rough horizontal surface. There is a straight vertical wall on the surface and the point on the wall nearest to \(A\) is \(B\). The distance \(A B\) is 5 m . The particle is projected with speed \(4.2 \mathrm {~ms} ^ { - 1 }\) along the surface from A towards B . The particle hits the wall directly and rebounds. The coefficient of friction between the particle and the surface is 0.1 .
  1. Determine the speed of the particle immediately before impact with the wall. The magnitude of the impulse that the wall exerts on the particle is 9.8 Ns .
  2. Find the speed of the particle immediately after impact with the wall.
OCR MEI Further Mechanics Major 2021 November Q1
3 marks Moderate -0.3
1 A small ball of mass 0.25 kg is held above a horizontal floor. The ball is released from rest and hits the floor with a speed of \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). It rebounds from the floor with a speed of \(4.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The situation is modelled by assuming that the ball is in contact with the floor for 0.02 s and during this time the normal contact force the floor exerts on the ball is constant. Determine the magnitude of the normal contact force that the floor exerts on the ball.
AQA Further Paper 3 Mechanics Specimen Q1
1 marks Easy -1.8
1 A ball of mass 0.2 kg is travelling horizontally at \(7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it hits a vertical wall.
It rebounds horizontally at \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
Find the magnitude of the impulse exerted on the ball by the wall.
Circle your answer.
[0pt] [1 mark]
0.4 N s
1.4 N s
Edexcel M1 2002 January Q1
3 marks Easy -1.3
  1. A ball of mass 0.3 kg is moving vertically downwards with speed \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it hits the floor which is smooth and horizontal. It rebounds vertically from the floor with speed \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find the magnitude of the impulse exerted by the floor on the ball.
    (3)
  2. A railway truck \(A\) of mass 1800 kg is moving along a straight horizontal track with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). It collides directly with a stationary truck \(B\) of mass 1200 kg on the same track. In the collision, \(A\) and \(B\) are coupled and move off together.
    1. Find the speed of the trucks immediately after the collision.
      (3)
    After the collision, the trucks experience a constant resistive force of magnitude \(R\) newtons. They come to rest 8 s after the collision.
  3. Find \(R\).
    (3)