Chapter 13, Problem 15A

Would the gauge inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that accelerated upward? Downward?

To determine

Whether the gauge inside the bathroom scale is more compressed or less compressed if one weighs in an elevator that accelerates upward and downward.

Explanation of Solution

Introduction:

Objects under influence of gravity pull each other and accelerate.

Suppose a man is standing on a bathroom scale on a floor which is at rest, the gravitational force between man and earth pulls him against the floor and scale. The floor and scale also push him in opposite direction with equal force. This pair of forces, compress the gauge.

If elevator is accelerating upward, then floor and scale pushes the man more due to which gauge inside the scale is compressed more and man weighs more.

If elevator is accelerated downward then force by floor is less, so the gauge will be less compressed and man weighs less.

Conclusion:

For upward accelerating elevator, gauge is compressed more and for downward accelerating elevator, gauge is compressed less.