Question

A 50 kg person is standing on a bathroom scale in an elevator moving upward.

a.) if the scale reads 56 kg, what is the magnitude of upward acceleration of the elevator (m/s^2)?
b.) Now the elevator is traveling up while slowing down. If the magnitude of deceleration is the same as that in part (a), what is reading given by the scale?

Answer 1

The scale reads the Normal (reaction) force.

a) Upward acceleration

Balance of forces on the scale: Normal - Weight = ma

Normal = 56kg*g
Weight =50*g
ma = 50*a

56*g - 50*g =50*a => a =[ 56*g* - 50*g ] / 50 = 0.12*g =0.12*9.8m/s^2 =

a = 1.176 m/s^2

b) Downward acceleration

Weight - Normal = ma

=> Normal = Weight - m.a

Normal = 50*9.8m/s^2 - 50*1.176m/s^2 = 431.2 N

Scale reading: 431.2 N/ 9.8 N/m = 44 kg.