State the law of conservation of momentum.

Far from any massive object, a space rocket is moving with constant velocity. The engines of the space rocket are turned on and it accelerates by burning fuel and ejecting gases. Discuss how the law of conservation of momentum relates to this situation.

Jane and Joe are two ice skaters initially at rest on a horizontal skating rink. They are facing each other and Jane is holding a ball. Jane throws the ball to Joe who catches it. The speed at which the ball leaves Jane, measured relative to the ground, is 8.0 m s^–1.
The following data are available.
                                                                                         Mass of Jane = 52 kg
                                                                                         Mass of Joe = 74 kg
                                                                                         Mass of ball = 1.3 kg

Use the data to calculate the

(i) speed v of Jane relative to the ground immediately after she throws the ball.

(ii) speed V of Joe relative to the ground immediately after he catches the ball.

if the net external force acting on a system is zero;
the momentum of the system remains constant/unchanged/the same;

or

for a closed system;
the momentum remains constant/unchanged/the same;
Award [1] for “momentum before collision equals momentum after collision”.
Do not accept “momentum is conserved”.

identifies the system as rocket + exhaust gases / total momentum of rocket and gas is equal before and after; (it must be clear that this is the system, a mention of rocket and gases is not enough)

no external forces act on this system / closed system;

increase/change in momentum of the gases is equal and opposite to the increase/change of momentum of the rocket;

(i) attempts to use conservation of momentum, eg 8.0×1.3=52×v;
v=0.20(ms^-1);
Award [2] for a bald correct answer.

(ii) identifies new mass as 75.3(kg);
V=0.14(ms^-1); 

A common error re-emerged in this examination. If asked to state a law of conservation a candidate must not simply say that the “quantity is conserved”. This tells the examiner nothing (other than that the candidate has read the question) and will never attract marks. This is a simple examination skill that many candidates continue to fail to learn.

Few were able to give adequate discussions of the how momentum conservation applies to one of the most common cases discussed in teaching at this level, that of a rocket in free space. There was no clear recognition that the system is closed or even what the system is or that the important factor is the change in momentum of the fuel and therefore the rocket. These are difficult ideas for candidates to grasp but examiners expected better attempts from the most able.

(i) This was well done.

(ii) About one-third of candidates failed to recognise that the mass of Joe needs to have the mass of the ball added to it for a correct solution of the problem