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I am aware of the classical apparent weight physics but I am confused about what happens when elevator falls with greater acceleration than g say two g or something.if I calculate the normal force it comes out to be - mg what would be the reading on a weight in such an elevator.? I know if it were exactly g the person would feel weightless but now what would be the case?

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Your world would be turned “up side down”.

The ceiling of the elevator would now be the “floor” and you would be standing upright, head downwards, with your feet on the ceiling of the elevator.

If you stood on some weight scales, now on the ceiling/“floor”, which measure the magnitude of the normal reaction on you, the reading would be $mg$.

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  • $\begingroup$ Wow that's pretty cool $\endgroup$ – ben tenyson Sep 15 at 13:25
  • $\begingroup$ I wonder why this scenario is not discussed in most physics books I think it's pretty cool $\endgroup$ – ben tenyson Sep 15 at 13:29
  • $\begingroup$ @bentenyson It would only be cool for a very short time span, until the elevator crashes into the bottom of the shaft. ;) You should calculate how long the ride will last in your 2g elevator if the shaft is 1 km long, and how fast it will be travelling at impact. $\endgroup$ – PM 2Ring Sep 15 at 15:41

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