Momentum Conservation Boundaries

## Question:

If a man stands on a trolley and tries to push it forward, how will it move? Backward or forward? Is the total momentum conserved if we consider the man and the trolley together as one system when the man starts pushing? And is it conserved if we just consider the man as a system? Is the push an external force or an internal one? Moreover, will the motion if trolley be affected if there is friction between the trolley and the ground?

Thanks very much for answering the questions!!!

If a man stands on a trolley and tries to push it forward by pushing some part of the trolley, the forward force applied by the man's hands on the pushed part will be exactly equal and opposite to the backward push of the man's feet on the trolley floor, in accordance with Newton's third law. Therefore the trolley does not move. In this case the push is a force internal to the man-trolley system.

If he stands on the trolley and tries to push it forward by pushing a pole resting on the ground, then the trolley will move forward because the force conveyed from the man's feet to the floor of the trolley will not be balanced by the force of his hands. That force is now applied to the ground through the pole.

In either of these cases momentum is conserved. In the first case the momentum of the man and of the trolley were both zero before the push and after the push. In the second case, the momentum of the man and the trolley were both zero before the push. After the push the momentum of the man-trolley system had some non-zero value. The momentum of the Earth was changed by exactly the same amount in the opposite direction so the total momentum was conserved.

In checking the conservation of momentum we can not choose to ignore any object which participates in the motion, even objects as large as the Earth must follow the laws of nature. Of course because the Earth is so huge compared to the man-trolley system, the change in its motion is undetectable. So your idea of considering the man alone as the system will not give sensible results. Basically you must choose a large enough system that no energy is transferred across the system boundary if you want to apply the conservation laws.

Only in the second case, where the trolley actually moves, will friction come into effect. In that case, the force of friction will oppose the motion, resulting in less acceleration for a given push from the man.

This information is brought to you by M. Casco Associates, a company dedicated to helping humankind reach the stars through understanding how the universe works. My name is James D. Jones. If I can be of more help, please let me know.

JDJ