Why does your weight inccrease when an elevator accelerates upward?

Question

but your weight decreases when elevator goes downward ?

say i have mass of 50 kg and elevator accelerates 5m/s^2 , i don't understand how my weight increases if the elevator is accelerating in opposite direction of gravity. shouldn't it decrease?

Answer 1

To counteract the downward acceleration of your body due to gravity, the elevator must apply an upward force equal in magnitude to your weight, or F=mg. Now to achieve the additional acceleration as the elevator moves upward, an addition force of F=ma must be accounted for. Thus, the total force the elevator applies to your body is F=ma + mg, or F=m(a+g), where g is accel due to gravity and a is the additional upward accel.

Technically, your weight does not really increase, but the elevator applies a force to your being that is greater then your weight. Reciprocally (Newton's third law), your body applies a force to the elevator floor that is greater than your weight.

For the case of downward acceleration, since it is negative, F=mg-ma, which is less than mg, your original body weight.