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?

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.