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When you stand on a bathroom scale, I know that the force displayed is the normal force. Since it is the normal force, then technically the force displayed would actually be Fg= (mass)(acceleration) right? If this is true, then why is it that your normal force changes in an elevator? (i.e. if you travel down an elevator, why would the normal force decrease?) Please explain this to me, as I am really confused! It would be best if you could relate this to the Newton laws. Thanks!

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Since you accelerate in an elevator, and the force of gravity is constant, then the normal force must be changing such that the net force is equal to $ma$. – Greg Jul 14 '13 at 2:07
I answered a similar question here: – Will Jul 14 '13 at 3:17

The weight shown on the scales does not change while the elevator is travelling up or down at constant speed. It only changes briefly while the elevator is accelerating or decelerating, that is at the beginning and end of the journey in the elevator.

The reason for this is simply that if the elevator is accelerating with some acceleration $a$ then the total acceleration on you is $g + a$ (careful with the sign conventions!) so the weight show on the scales is $m(g + a)$.

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