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etotheipi

Let [itex]R_{1}[/itex] be the reaction force on the jumper from the ground. Assuming this is larger than the combined mass of the 3 sections of human, if we consider the entire system we will get an upward acceleration (a is labelled as the acceleration of the COM; it will of course vary from the bottom to the top of the system).

For the top block on its own, the force [itex]R_{3}[/itex] evidently does work causing the top block's KE to increase. The same is true for the middle block as the work done by the lower reaction force is greater than the negative work done by the top reaction force (and weight) acting on it.

However, considering the entire system as a whole, the work done by the pair reaction forces should exactly cancel and the only force remaining is the force [itex]R_{1}[/itex] for which the point of application is stationary, so this force does no work. However, the kinetic energy of the system must increase so work has to have been done. Where does this occur?

This stemmed from a related question I had concerning springs; if we stretch a massive spring with one end attached to a wall, and consider the entire spring as accelerating back toward the wall when we release it, the net force acting on the spring is the reaction force from the wall which doesn't move! Please see the following diagram:

The force [itex]F_{1}[/itex] obviously results in an acceleration, yet does no work! How does this work? Thank you very much in advance!