# Gravitational force in a building

Suppose that a person is standing on the top of a multi storey building and at an instant earth's gravitational pull becomes zero.What will happen in the next instant?

(Consider only earth's gravity and contact force to answer the question)

My Reasoning: He should remain standing at the same spot because for him to move an unbalanced force must act on him and that very instant contact force will become zero,so, no unbalanced force. But the trouble is that what happens to the potential energy of the person because if we consider an example of a spring which bounces back on being pressed against a surface because of PE.

The person would be accelerated upwards briefly, then continue to float upwards at constant speed until his head hits the ceiling.

When standing on a floor, the ground is pushing up on you with a force equal to your weight. Your shoes and your feet aren't perfectly rigid. They are compressed by this force and will act a bit like a spring if this force were suddenly released. It is this spring action that will accelerate you upwards a little when gravity suddenly magically vanishes.

As for what happens to the potential energy, that can't be answered because this is your magical made-up world. In the scenario that you seem to be imagining, the potential energy would just vanish. That's a violation of conservation of energy, but then again, gravity suddenly poofing away makes no sense either, so this whole part of the question is pointless.

Here's another angle to this: it depends on your latitude. If you are standing somewhere near the equator, you're also experiencing circular motion around the Earth's axis of rotation with an angular frequency of 2*Pi/86400 and a velocity around 463 m/s. In the rotating frame of reference you'll suddenly find a centrifugal force

$$|\vec a| = \omega^2 R = \omega v = 0.0336 m/s^2$$

and in the absence of gravity to hold you back you'll be slowly accelerating upwards in the frame of reference relative to the rotating Earth. This approximation will be good enough for 20 minutes or so when you'll find yourself almost 40 kilometers above the surface and dead, so what happens further doesn't really matter.

And that's notwithstanding the probable crumbling of the Earth in the absence of a Roche limit and the lightning-fast dissipation of our atmosphere into outer space ]:>