Centre of mass test with answers for AP Physics C (free PDF download)

Quick answer: The centre of mass is the mass-weighted average position, xcm = (1/M)∫x dm. This AP Physics C test on centre of mass has 8 questions worth 20 marks, to do in 45 minutes: impulse and momentum, centre of mass of a rod and force–time graph. The mark scheme is on a separate page; free printable PDF.

This test covers impulse and momentum, centre of mass by integration, collisions and the rocket equation. Show all working and give units in final answers. Use g = 9.81 m/s². You have 45 minutes and may use a calculator. Marks are shown in brackets for each part.

Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:M Unit 4

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

Contents

Question 1 Impulse and momentum (2 marks)

Define impulse. (1 mark)
State how impulse is related to the change of momentum. (1 mark)

Question 2 Centre of mass of a rod (3 marks)

A rod of length 0.80 m has linear density λ = 5.0x² kg/m, with x measured from one end.

Calculate its mass by integration. (1 mark)
Calculate ∫xλ dx. (1 mark)
Calculate x_cm. (1 mark)

Question 3 Force–time graph (3 marks)

A racket strikes a 0.057 kg ball initially at rest.

Force on the ball against time.

Calculate the impulse from the area under the graph. (2 marks)
Calculate the speed of the ball after the strike. (1 mark)

Question 4 Sticking collision (3 marks)

A 0.80 kg trolley moving at 1.5 m/s hits a stationary 0.40 kg trolley and they stick together.

Calculate their common speed. (1 mark)
Calculate the initial and final kinetic energies. (1 mark)
Calculate the energy lost. (1 mark)

Question 5 Elastic collision (3 marks)

A 2.0 kg block moving at 3.0 m/s collides elastically with a 1.0 kg block at rest.

State the two quantities that are conserved. (1 mark)
Calculate the final speed of each block. (2 marks)

Question 6 Rocket (2 marks)

A rocket has exhaust speed 2.5 × 10³ m/s. Its mass falls to half its initial mass during the burn. Ignore gravity.

Write the rocket equation. (1 mark)
Calculate the speed gained. (1 mark)

Question 7 Exploding firework (2 marks)

A firework explodes in mid-air into many pieces. Explain what happens to the motion of the centre of mass of the pieces, ignoring air resistance. (2 marks)