# Gaining and losing weight in an elevator

1. Oct 14, 2009

1. The problem statement, all variables and given/known data

Person with mass m = 80 kg stands on a scale during a ride in an elevator. How much weight shows on the scale, when the elevator is being moved evenly upwards (downwards) with velocity (speed) v = 1 m/s. How much weight shows on the scale when the elevator starts to move upwards (downwards) or when moving upwards (downwards) starts to stop; if we suppose that at this time the absolute value of acceleration or deceleration is equal to 1 m/s²?

2. Relevant equations

W= mg

3. The attempt at a solution

Moving with constant velocity of 1 m/s:

Elevator is stopped: a= 0, g= 9.8, W= mg= 80 kg * 9.8 m/s²= 784 N
Elevator is moving up: a= g, W= 2mg= 2 * 80 kg * 9.8 m/s²= 1568 N
Elevator in moving down: a= -g, W= 0

Moving with an acceleration of 1 m/s²:

Elevator is moving up: W= m (g + a)= 864 N
Elevator is moving down: W= m(g - a)= 704 N
Elevator is going down and stopping: W= m(g- (-a))= 864 N
Elevator is going up and stopping: W= m( g+ (-a))= 704 N

Are my conclusions correct?

2. Oct 14, 2009

### Delphi51

These don't make sense! You don't feel double your weight when going steadily upward and you don't float around like an astronaut when going steadily downward. Use the same formula you had for the last bet W= m (g + a) with a=0 and you'll get the correct answer.

The 864 and 704 look good!

3. Oct 14, 2009

So, calculation when elevator is stopped: a= 0, g= 9.8, W= mg= 80 kg * 9.8 m/s²= 784 N is correct?
Elevator is moving up: W= m(g + a)= 80 kg (9.8 m/s² + 0)= 784 N
Elevator in moving down: W= m(g - a)= 784 N.
So, in this cases I get the same result, or one has to positive and the other negative?

Last edited: Oct 14, 2009
4. Oct 14, 2009

### Delphi51

Those look good. When the acceleration is zero, you always get 784.
You can't tell by your weight whether you are stopped or moving any direction at constant speed. Only acceleration changes your weight.

Unless you leave the Earth and go somewhere where gravity varies.

5. Oct 14, 2009

Thank you for explaining!
I always wondered how life would be with no gravity!

6. Oct 14, 2009

### Delphi51

Most welcome.
No gravity - like being in an elevator when the cable breaks. Not for me.

7. Oct 15, 2009