Question

A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.64 of the person's regular weight. Calculate the magnitude of the acceleration of the elevator. Find the direction of the acceleration.

Answer 1

When person is standing on a bathroom scale

then the reading of the scale is the measurement of normal force on the scale

so here we can see that normal force is 0.64 times the weight of the person

This shows that the normal force is less than the weight

It shows that elevator must have to accelerated downward direction

so here we will use the force equation

`mg - F_n = F_(net)`

here we know that

`F_(n) = 0.64 mg`

also we know that

`F_(net) = ma`

now we have

`mg - 0.64 mg = ma`

`a = 0.36g`

`a = 3.53 m/s^2`

so acceleration of elevator will be 3.53 m/s^2 in downward direction