Question

You ride on an elevator that is moving with constant downward acceleration while standing on a bathroom scale. The reading on the scale isSelect one:O a. less than your true weight, mg.O b. equal to your true weight, mg.O c. more than your true weight, mg.O d could be more or less than your true weight, mg, depending on the magnitude of the acceleration.

Answer 1

There are two forces acting over you while standing on the scale: your weight and the normal force with the scale.

These two forces balance out when the elevator is at rest, but when the elevator has some acceleration, the value of the normal force with the scale changes. According to Newton's Second Law of Motion:

`\begin{gathered} N-W=ma \\ \Rightarrow N-mg=ma \\ \Rightarrow N=ma+mg \\ \Rightarrow N=m(a+g) \end{gathered}`

If a=0, then N=mg and the reading of the scale matches your weight.

If a<0 (acceleration is downward), then a is a negative number, and the term a+g will be less than g, which means that the normal force with the scale will be lower than your weight.

Therefore, when the elevator accelerates downwards, the reading on the scale is less than your true weight.