Two trolleys coupling together

9 marks · A-level · original practice case

Write your working and explanations below or on paper. Your responses stay in this page; PhysicsHelp does not submit or save them. Copy anything you want to keep before closing it. Check calculations separately from method marks. Use unrounded working between parts.

The situation

A 0.60 kg trolley moving right collides with a stationary 0.40 kg trolley. They couple together. External horizontal impulse during the collision is negligible. Right is positive. These velocities are model values.

Motion before and after coupling
Stage	0.60 kg trolley / m s⁻¹	0.40 kg trolley / m s⁻¹
Before	2	0
After	u	u

Part (a)

Calculate the common velocity after the collision. [2 marks]

Give the numerical answer to 2 significant figures.

Final value / m s⁻¹

Working

Part (b)

Calculate the decrease in total kinetic energy. [3 marks]

Give the numerical answer to 2 significant figures.

Final value / J

Working

Part (c)

Explain why momentum is conserved although kinetic energy decreases. [3 marks]

Your explanation

Part (d)

Select the change in common speed if both trolley masses are doubled, with initial velocities unchanged. [1 marks]

Choose one answer The common speed doubles. The common speed stays the same. The common speed halves. The common speed becomes zero.

Marking rubric and worked answers

Indicative practice marks. Method marks assess valid working; accuracy marks require the associated valid method. Independent points stand on their own. Tick only points supported by your response. Do not award the same explanation twice. These ticks record your judgement, not an examiner’s result.

Part (a) marking points

Final answer: 1.2 m s⁻¹. Numerical checks assess the final value only; they do not check working or the number of digits typed.

Use 0.60 × 2.0 = (0.60 + 0.40)u. (1 method mark)
Obtain +1.2 m s⁻¹. (1 accuracy mark)

No earlier numerical result is required. Award method credit for valid working and accuracy credit for the stated answer. Accept a defensible equivalent method; wrong physics cannot earn dependent accuracy credit.

Common errors: This leaves the incident velocity unchanged. Include both masses in final momentum.

Part (b) marking points

Final answer: 0.48 J. Numerical checks assess the final value only; they do not check working or the number of digits typed.

Initial kinetic energy is 1.2 J. (1 method mark)
Final kinetic energy is 0.72 J. (1 method mark)
Decrease is 0.48 J. (1 accuracy mark)

Use the common speed from part (a) in Kfinal = ½(1.00)u² and subtract from 1.20 J. Credit a consistent arithmetic error; a negative energy decrease or momentum model excluding a trolley is not defensible.

Common errors: This is the final kinetic energy, not the decrease.

Part (c) marking points

There is negligible external impulse on the two-trolley system. (1 independent mark)
Internal interaction forces cannot change its total momentum. (1 independent mark)
Some kinetic energy becomes internal energy/deformation/sound. (1 independent mark)

Award each distinct physical point once. Equivalent scientifically correct wording is creditable; a contradictory statement cannot earn the same point.

Part (d) marking points

Final answer: The common speed stays the same..

The common speed stays the same. (1 independent mark)

One correct choice earns the mark; no partial credit.

Common errors: Both initial and final momentum double, so the mass factor cancels. The incident momentum doubles as well as the final mass. Doubling mass does not remove the initial momentum.

The common speed doubles. — Both initial and final momentum double, so the mass factor cancels.
The common speed stays the same. — Doubling all masses multiplies both sides of the momentum equation by two.
The common speed halves. — The incident momentum doubles as well as the final mass.
The common speed becomes zero. — Doubling mass does not remove the initial momentum.

Report a problem with this case

Related skills

energy momentum practice

Scope and reference sources

AQA 3.4.1 (selected); OCR A Module 3 (selected). These are shared original exercises; wording, indicative marks and difficulty have not been endorsed by either board.

AQA specification · OCR A specification

Case reference: coupled-trolleys · version 1.1.0 · seed 0. Choose another case