OCR A-Level Physics: Newton's Laws and Momentum
6 exam-style questions with full mark schemes and model answers. Write your own answer and the AI examiner marks it against the mark scheme.
Two trolleys, A and B, collide head-on while moving along a straight, friction-free track. During the collision they push on each other for a short time before separating. No external horizontal forces act on the pair.
Explain how the principle of conservation of linear momentum for this isolated two-trolley system follows from Newton's second and third laws of motion. In your answer you should refer to the force each trolley exerts on the other, the time for which the forces act, and the change of momentum of each trolley.
(6 marks)
During a shunting test, a railway wagon moving along a straight, level track strikes a second, stationary wagon. The two wagons lock together (couple) on impact and move off as one. The data recorded are shown below.
| Quantity | Value |
|---|---|
| Mass of moving wagon, m1 | 1200 kg |
| Velocity of moving wagon before impact, u1 | 4.0 m s⁻¹ |
| Mass of stationary wagon, m2 | 1800 kg |
| Velocity of stationary wagon before impact, u2 | 0 m s⁻¹ |
(a) Calculate the common velocity of the two coupled wagons immediately after the collision. (3 marks)
(b) By comparing the total kinetic energy before and after the impact, determine whether the collision is elastic or inelastic. (3 marks)
A 0.058 kg tennis ball is served. A high-speed sensor records the horizontal force the racket exerts on the ball during the 6.0 ms of contact. The force rises from zero to a peak and falls back to zero, and the recorded values are summarised below. The ball is initially at rest.
| Stage of contact | Description | Impulse contributed / N s |
|---|---|---|
| First half (0 to 3.0 ms) | Force rises 0 → peak | 1.35 |
| Second half (3.0 to 6.0 ms) | Force falls peak → 0 | 1.35 |
The total impulse is the area under the force-time graph, equal to the sum of the two contributions.
(a) State why the impulse is equal to the change in momentum of the ball, and find the change in momentum. (2 marks)
(b) Hence calculate the speed at which the ball leaves the racket. (2 marks)
(c) Estimate the average (mean) force exerted on the ball during the contact. (1 mark)
Two ice skaters stand face to face and stationary on a horizontal ice rink, where friction is negligible. Skater P has a mass of 48 kg and skater Q has a mass of 72 kg. They push hard against each other's hands and then separate, gliding apart in opposite directions. Immediately after they let go, skater Q is moving at 2.0 m s⁻¹.
(a) Calculate the speed of skater P immediately after they separate. (3 marks)
(b) Without further calculation, state and explain which skater has the greater kinetic energy after the push. (2 marks)
A building-site winch lifts a load of bricks of mass 250 kg vertically upwards at a steady speed of 0.80 m s⁻¹. Take g=9.81 m s−2 and assume air resistance is negligible.
(a) Calculate the useful output power of the winch (the rate at which it does work against gravity). (2 marks)
(b) The winch motor draws an electrical input power of 2.6 kW. Calculate its efficiency, and explain in terms of energy conservation why this is less than 100%. (2 marks)
Newton's laws of motion and the concept of momentum underpin all of mechanics.
(a) State Newton's first and third laws of motion. (2 marks)
(b) Define the linear momentum of a body and give its SI unit. (1 mark)