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When an elevator suddenly starts decelerating downwards after the cable snaps, why does the person inside the elevator float upwards? In such a scenario why aren't the elevator floor and the person always in contact because the only force that is acting on both objects is gravity so should they not be accelerating at the same rate downwards; therefore, the distance between them should be zero right?

Rohan Rajasekar
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If one had an object such as a steel box in the elevator, it would remain on the floor. In free fall, all objects would fall at the same rate, so the box would fall at the same rate as the elevator, and thus remain at the same location relative to the elevator.

People, however, are a more complicated story. A surprising amount of energy is stored in the tendons of the leg while standing upright. When the elevator falls, and both bodies enter free fall, the energy in those tendons is released. The result is that the person is propelled "upward" with respect to the elevator. If a person was capable of standing upright without loading tendons in this way, they would stay on the floor of the elevator, just like the box did.

Cort Ammon
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Assuming the elevator begins accelerating downwards at acceleration $g$, in the frame of the elevator the person is weightless, i.e. has zero acceleration. This reflects the fact that the person and elevator are accelerating at the same rate. For the remainder of this discussion, let's place ourselves in the frame of the elevator.

In this ideal scenario, in the absence of any other external forces, it's just like a person is in a stationary box floating in outer space. The person won't move relative to the elevator, so they can freely rotate about their center of mass. I suppose if they wanted to they can bring their legs up from the floor of the elevator, or propel themselves by pushing off the walls/floor of the elevator. Note that any contact force with the ground will result in the person accelerating up off the ground, so it's easy for them to start floating upwards.

DanDan面
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