MOMENTUM

5 marks · Hard

Two identical trolleys, A and B, each of mass 1.2 kg, move along a smooth, straight track. Trolley A is moving at 1.6 m/s towards stationary trolley B. The trolleys collide and stick together.

(a)

Calculate the total momentum of the two trolleys before the collision.

[2 marks]

(b)

Calculate the velocity of the combined trolleys immediately after the collision.

[2 marks]

(c)

Explain why the principle of conservation of momentum can be applied in this situation.

[1 mark]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

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(a) 1.92 kg m/s · must show p = m × v, only A has initial momentum

(b) 0.80 m/s · must show momentum conserved, combined mass 2.4 kg, correct substitution

(c) There are negligible external forces (the track is smooth) · must show no significant external forces, mention of momentum conservation

Common mistakes: Omitting that both trolleys move together after collision; Ignoring that B was stationary

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Correctly substitutes mass and velocity for A to find its momentum.

A1 (a) · 1 mark · Correct calculation and value: 1.92 kg m/s.

M2 (b) · 1 mark · Applies conservation of momentum and substitutes correct total mass. (follow-through)

A2 (b) · 1 mark · Correct calculation and value: 0.80 m/s. (follow-through)

B1 (c) · 1 mark · States that no significant external forces act or the track is smooth.

Worked solution

(a) Only trolley A has initial velocity; B is stationary.

(b) Total momentum before = momentum after (conservation of momentum):

(c) The principle of conservation of momentum applies because the track is smooth, so there is negligible external force acting on the system.