Question

Your mass is 55 kg. You stand on a bathroom scale in an elevator on Earth. What does the scale read when the elevator moves up at a constant speed?

Answer 1

While stationary - `539N ["down"]`.
While moving - impossible to say. but it has to be `x>539N`.

Explanation:

If the person was not moving, the scale would read `539N ["down"]`:

`F_"g"=mg`

`=55(9.8)`

`=539`

If the elevator is moving up, we can't say for sure what the number would read. What we do know is that the number would be greater than `539`.

I'll explain.

As we all know, mass is not weight. The difference is that weight includes the force of gravity, while mass is used to define how much matter your make up.

When you stand on a scale, the scale measures your force of gravity AKA weight. This measurement is influenced by Earth's gravitational force of `9.8N "[down]`.

However, in certain situations the force of gravity is equal to the net force: `F_"g"=F_"NET"`. This is because `mg=ma`.
=> Where `m` is the mass of the object.
=> Where `g` is the gravitational force; NOT FORCE OF GRAVITY
=> Where `a` is the acceleration of the object.

Both `a` and `g` have a value of `9.8`, the unit varies between `m/s^2` and `N` respectively.

If you are on an elevator (on Earth), your mass is constant.

However, if the elevator is moving (and you're on a scale), you'll notice that your weight changes depending on where the elevator is moving.

The only possible factor that can explain this change is the acceleration of the object - you.

When the elevator (you) moves up - acceleration increases (adding on to the `9.8 m/s^2`) and there is more normal force applied to the floor. This results in a larger number on the scale.

Consequently, when the elevator (you) moves down - acceleration decreases (subtracting from `9.8 m/s^2`), there is less normal force applied to the floor, resulting in a smaller number on the scale.

Keep in mind that your mass is not changing, it's the influence of your acceleration.

This relationship is beautifully illustrated in this image:

As you can see, when the elevator moves up, the weight of the fish increases.

When the elevator moves down, the fish's weight decreases.

The fish did not undergo a change to its physical body - matter was removed/gained. Only its acceleration, which ultimately changed the `F_"g"` - its weight.

Hope this helps :)