Answer to Question #247993 in Mechanics | Relativity for gel an

Question

When a student steps on a bathroom scale inside an elevator that is at rest, the scale reads 490 N. When the elevator starts to move, the scale reads 425 N. Is the elevator moving up or down? What is its acceleration?

Answer 1

When the elevator is at rest, the only force F acting is the person’s weight w. We know that the weight w of a body is the product of its mass m and acceleration due to gravity g.

w = mg

The net force F is hence

F = w = mg.

a) It is given that the reading on the scale in the elevator is reduced from 490 N to 425 N. This means that the net force when the elevator was at rest has been reduced. When the elevator is moving, the forces acting are the force due to acceleration ma, and the force due to gravity mg. Thus, the net force F becomes

F = mg – ma.

From this, we get F = m(g – a)

Thus, the acceleration of gravity g is reduced by an amount a.

Therefore, the lift is moving downwards.

b) Rearrange the equation, F = mg, to get for m.

$m=\frac{F}{g}$

Substitute 600 N for F, and $9.8 m/s^2$ for g.

$m=\frac{425}{9.8}=43.36 kg$

The net force while moving downwards is given by F = mg – ma.

Rearrange the equation for a.

$a=\frac{mg-F}{m}$

Substitute 425 N for F, 490 N for mg, and 43.36 kg for m.

$a=\frac{490N-425N}{43.36kg} \\ =\frac{65}{43.36}\\ =1.499 \frac{m}{s^2}$

Thus, the elevator is accelerated by $1.499 \;m/s^2$