You are standing on a bathroom scale inside an elevator. The elevator slows down while moving.

Question

What is true about the scale reading compared to your actual weight?

A) The scale reading is the same as your actual weight.

B) The scale reading is greater than your actual weight.

C) The scale reading is less than your actual weight.

D) Cannot be determined.

Answer 1

Hi Robert C.,

Tricky question! You don't know if the elevator was ascending or descending, as it starts to slow down. Hence, you don't know if the acceleration of the elevator during the slowdown decreased or increased the apparent force of gravity. Either way, an analog scale would misread.

So, necessarily the scale won't read your correct weight. Or will it? If it's a digital scale, which locks the reading once it detects stability, you might have climbed on and triggered the readout freeze before the elevator velocity change began. Did you?

Or, maybe you triggered the tare weight detection (scale reads 0.0 before you climb on) before the velocity change began, then climbed on and got a reading during the velocity change period. In that case, the change in scale tare will only exacerbate your misperceived mass readout.

However, it's not exactly correct to say that the relationship between your true mass and the indicated mass cannot be determined. It is simply that enough information was not provided for you to detemine it. There's a subtle difference there, though I suppose that "official" (= grade only the letter choice, disregard any comments!) result would be "D."

There may be additional caveats based on piezoelectric device operation moving across a magnetic field (such as obtains on Earth), but that's quite advanced engineering, and nobody is going to quiz you on that in your secondary school curriculum. I hope.