# A student is standing on a bathroom scale in an elevator; he weighs 230 lbs when the elevator is...

## Question:

A student is standing on a bathroom scale in an elevator; he weighs 230 lbs when the elevator is stationary,

a) What does the bathroom scale read if the elevator is moving at a constant velocity upward?

b) What does the scale read if the elevator is accelerating downward at 20 {eq}ft/s^2 {/eq}?

c) What does the scale read if the elevator is accelerating upward at 10 {eq}ft/s^2 {/eq}?

## Fictitious Force

In a frame of reference moving with constant velocity Newton's laws will give the correct dynamics. If the frame of reference is accelerating then fictitious forces will have to be incorporated in order to deploy Newton's laws for getting the correct dynamics. If the acceleration of the frame is {eq}\displaystyle {a} {/eq} then an object of mass {eq}\displaystyle {m} {/eq} will experience a fictitious force {eq}\displaystyle {F_f=-ma} {/eq}.

This is the reason why you are thrown forward inside a vehicle that brakes suddenly. The acceleration of the vehicle is backward-directed when the brakes are applied. So the fictitious force acts in the forward direction.

It is given that the student weighs 230 lbs on a bathroom scale when the elevator is stationary. The acceleration due to gravity is {eq}\displaystyle {g=32\ ft/s^2} {/eq}.

a)

The laws of physics have the same form in all inertial frames of reference. There is no way you can distinguish between two inertial frames by observing the same phenomenon in the two inertial frames. Thus when the elevator is moving with a constant velocity the bathroom scales will read the same as in the ground frame.

b)

When the elevator is accelerating downwards at {eq}\displaystyle {20 ft/s^2} {/eq} the person experiences an upward fictitious force of {eq}\displaystyle {F=m\times 20\ lbf} {/eq}.

This will cancel out part of the downward gravity of {eq}\displaystyle {m\times 32\ lbf} {/eq}.

Thus the reading on the scales would correspond to a weight {eq}\displaystyle { m\times 12\ lbf} {/eq}

Or,

Reading in the downward accelerating elevator={eq}\displaystyle { 230\times \frac{12}{32}=86.25\ lbs} {/eq}

c)

When the elevator is accelerating upwards at {eq}\displaystyle {10 ft/s^2} {/eq} the person experiences a downward fictitious force of {eq}\displaystyle {F=m\times 10\ lbf} {/eq}.

This will add with the downward gravity of {eq}\displaystyle {m\times 32\ lbf} {/eq}.

Thus the reading on the scales would correspond to a weight {eq}\displaystyle { m\times 42 \ lbf} {/eq}

Or,

Reading in the downward accelerating elevator={eq}\displaystyle { 230\times \frac{42}{32}=301.875\ lbs} {/eq} 