A 75.0kg person stands on a scale in an elevator. What does the scale read (in kg) when the elevator is (a) at rest, (b) ascending at a constant speed of 3.0m/s, (c) falling at 3.0m/s, (d) accelerating upward at 3.0m/s2, (d) accelerating downward at 3.0m/s2.

Explanation: Scale only reads reaction force so we will find out reaction force of ground in different cases.

a) Let R be the reaction force of floor in the first case.

Net force = R - mg

= mass x acceleration = 0 (body is at rest).

R = mg, scale will read his actual weight.

In the case of b) and c) also acceleration is zero hence

R - mg = 0

R = mg, scale will read his actual weight.

d) In this case there is acceleration of 3 m s⁻² in upward direction so

R - mg = ma

R = m (g+a) = 75 x (9.8 + 3) = 960 N

The reading of scale will be more than his actual weight.

It will read weight as 960/9.8 = 97.96 kg.

e) In this case body is going downwards

mg - R = ma

R = m (g - a)

= 75 (9.8 - 3)

= 435 N

= 435 / 9.8 kg

= 44.38 kg

So scale will read less than his actual weight.