Collisions test with answers for AP Physics 1 (free PDF download)

Quick answer: In a collision, the total momentum of the colliding objects is the same before and after, provided no outside net force acts. This AP Physics 1 test on collisions has 8 questions worth 20 marks, to do in 45 minutes: core ideas, classify the events and trolleys that couple. The mark scheme is on a separate page; free printable PDF.

First, this test lasts 45 minutes and counts for 20 points. Next, show every substitution, give units, and write the sign of each velocity. No data sheet is given beyond the formulae you learned in the lesson; write clearly so that the marker can follow your reasoning.

Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 4

Time: 45 minutes · 8 questions · Total: 20 marks · Calculator allowed

Contents

Question 1 Core ideas (2 marks)

First, state the condition for the total momentum of a system to be conserved. (1 mark)
Then, define the centre of mass of a two-object system and give its velocity formula. (1 mark)

Question 2 Classify the events (2 marks)

Answer both parts.

For example, a ball of putty hits a wall and stays on it. (1 mark)
Then, two air-track gliders with spring bumpers rebound with no loss of kinetic energy. (1 mark)

Question 3 Trolleys that couple (3 marks)

For example, a 0.60 kg lab cart moves at 2.0 m/s towards a 0.90 kg cart moving the same way at 0.50 m/s. They couple.

First, calculate the speed after coupling. (2 marks)
Then, calculate the kinetic energy transformed. (1 mark)

Question 4 An elastic collision (3 marks)

Next, a 0.30 kg block at 4.0 m/s collides elastically and head-on with a stationary 0.10 kg block on a frictionless surface.

First, calculate the velocity of each block afterwards. (2 marks)
Then, show that kinetic energy is conserved. (1 mark)

Question 5 Centre of mass (3 marks)

First, two masses are on a metre rule.

Masses on a rule, positions measured from the left end.

First, calculate the position of the centre of mass. (2 marks)
Then, calculate the velocity of the centre of mass. (1 mark)

Question 6 Third law and conservation (2 marks)

Finally, explain, using Newton’s third law, why the momentum gained by one object in a collision equals the momentum lost by the other.

Question 7 Identify the collision (3 marks)

For example, in a collision a 1.5 kg cart at +2.0 m/s hits a 1.0 kg cart at −1.0 m/s. Also, afterwards the 1.5 kg cart moves at +0.20 m/s.

First, calculate the velocity of the 1.0 kg cart afterwards. (1 mark)
Then, calculate the kinetic energy before and after. (1 mark)
Classify the collision. (1 mark)

Question 8 Paragraph argument (2 marks)

Also, a student states that kinetic energy lost in a collision means that momentum was not conserved. Then, write a short argument that evaluates this statement.

Condition for conserved total momentum? — Zero net external force on the system.

What is conserved in an elastic collision? — Both momentum and kinetic energy.

What is conserved in an inelastic collision? — Momentum only; kinetic energy decreases.

Final velocity when two objects stick together? — v = (m₁u₁ + m₂u₂) ÷ (m₁ + m₂).

Elastic collision speed shortcut? — Speed of approach equals speed of separation.

Centre of mass position formula? — x_cm = Σmx ÷ Σm.

Centre of mass velocity formula? — v_cm = total momentum ÷ total mass.

Why does v_cm stay constant in a collision? — Internal forces cancel; net external force is zero.

Equal masses, elastic, one at rest? — They exchange velocities.

Unit of momentum? — kg m/s (same as N s).