Question

A person of mass 40 kg stands on a bathroom scale in an elevator. What is the reading on the scale if:A. The elevator is stationary?B. The elevator is moving up at a constant speed?C. The elevator accelerates upwards at 5.00 m/s2D. The elevator accelerates downwards at 5.00 m/s2

Answer 1

Given data

*The given mass of the person is m = 40 kg

*The value of the acceleration due to the gravity is g = 9.8 m/s^2

(A)

The reading on the scale is calculated when the elevator is stationary is given as

`\begin{gathered} R=mg \\ =(40)(9.8) \\ =392\text{ N} \end{gathered}`

(B)

The formula for the reading on the scale when the elevator is moving up at constant speed is given as

`\begin{gathered} N=mg \\ =(40)(9.8) \\ =392\text{ N} \end{gathered}`

(C)

The formula for the reading on the scale when the elevator accelerates upwards at 5.00 m/s^2 is given as

`N=m(g+a)_{}`

Substitute the known values in the above expression as

`\begin{gathered} N=(40)(9.8+5) \\ =592\text{ N} \end{gathered}`

(D)

The formula for the reading on the scale when the elevator accelerates downwards at 5.00 m/s^2 is given as

`N=m(g-a)_{}`

Substitute the known values in the above expression as

`\begin{gathered} N=(40)(9.8-5.0) \\ =192\text{ N} \end{gathered}`