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To answer this question first let us know what weight is. When you stand on a bathroom scale there force is acting upon you and is pulling you downwards. This force is mg, where m=your body mass and g=gravity which is +9.8m/s, which is trying to pull you down. Now what prevents you from falling down is the force acting upwards by the bathroom scale that balances mg. Lets take this force as F. Now F can be represented as -

F=mg

Since both are balanced you'll be still on the bathroom scale without falling or being pushed up. The F here is what you call your Body weight and is displayed by the bathroom scale.

Now lets see what happens when you try checking your weight on a bathroom scale in a elevator that is going down. Here while calculating F we need to take in consideration the speed or acceleration at which the elevator is moving down. Lets take this as 'a'. Now if you look at the equation F=mg, mg needs to be greater than F so that you can move down along with the elevator. So now the equation together with 'a' becomes

mg - F = ma (since mg is greater than F as discussed, hence mg - F)

Rearranging this we get F = m (g - a).

Hence in a elevator moving down your weight will be lesser than the weight shown by the scale when you are on a still ground.

Now imagine if the string of the elevator is cut and it free falls on the ground. In this case the acceleration 'a' by the elevator would be almost 9.8 m/s. Substitute a value in the above equation -

F = m (9.8 - 9.8 )

F = 0

This is when the bathroom scale will show your weight as 0 KG or otherwise you will feel weightlessness. This is the scientific reason why you experience weightlessness during a free fall.

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17y ago

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