Question

A child with a mass of 40Kg is standing on a scale in an elevator. The elevator is accelerating up at 2 m/s2.a) Draw a free body diagram of the situation: b) Calculate the reading on the scale.

Answer 1

Given data:

* The mass of the child is 40 kg.

* The acceleration of the elevator is,

`a=2ms^(-2)`

Solution:

(a). The free body diagram of the given situation is,

(b). The net force acting on the child is,

`F_{\text{net}}=ma`

where m is the mass of the child, and a is the acceleration,

Substituting the known values,

`\begin{gathered} F_(net)=40*2_{} \\ F_{\text{net}}=80\text{ N} \end{gathered}`

The weight of the child is,

`W=mg`

where g is the acceleration due to gravity,

Substituting the known values,

`\begin{gathered} W=40*9.8 \\ W=392\text{ N} \end{gathered}`

The reading on the scale is equal to the normal force acting on the child while the elevator is moving in the upward direction.

Thus, the reading on the scale is,

`\begin{gathered} N-W=F_{\text{net}} \\ N=F_(net)+W \\ N=80+392 \\ N=472\text{ N} \end{gathered}`

Thus, the reading on the scale is 472 N.