Man Jumping from Trolley


For that man and trolley example, it seems that the man pushing on the trolley will have no effect on the whole system with man and trolley as a one part. However, if the floor of the trolley where the man stands on is frictionless, then there will be no 'balancing force' acts on the man. If we consider the man-trolley system again, then it seems that the trolley will move, unless the man only apply a force with one of his hand and a reaction is gained by the other hand. However, if we just consider the trolley but exclude the man as a system, will the trolley move due to no reaction from friction between the floor and the man?

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You are correct that in the man-trolley system, if the man pushes off from the trolley with no friction between them, the man will fly off in the direction in which he pushed and the trolley will move off in the other direction with initial velocity proportional to the ratio of the masses. Since the man in this example transfers energy to the trolley, we must take as a system the man-trolley combination. Otherwise we would observe the trolley to move spontaneously, violating the conservation of momentum. If you ever make a measurement which indicates that the conservation of momentum is violated, you need to look again at the way the system is defined.

It was exactly in this way that the sub-atomic particle the neutrino was discovered. The conservation of momentum in radioactive beta decay appeared to be violated. To prevent this it was necessary to postulate an undiscovered particle.