Question

A 57.6-kg crate is suspended between the floor and the ceiling using two spring scales, one attached to the ceiling and one to the floor. If the lower scale reads 120 N, what is the reading of the upper scale? Ignore the weights of the scales.

Answer 1

Given,

The mass of the crate, m=57.6 kg

The lower scale reading, F₁=120 N

When the crate is balanced between the two springs, the net force on the crate is zero.

The forces acting on the crate are, the weight of the crate, the restoring force of the upper spring, and the restoring force of the lower spring.

The weight of the crate is directed downward. And its weight will be stretching the upper spring. Thus the restoring force of the upper spring will be directed upwards.

The weight of the crate will be pushing the lower spring downward and thus the restoring force of the lower spring will be directed upward.

Thus at equilibrium,

`mg-F_1-F_2=0`

Where F₂ is the reading of the upper scale and g is the acceleration due to gravity.

On substituting the known values,

`\begin{gathered} 57.6*9.8-120-F_2=0 \\ \Rightarrow F_2=57.6*9.8-120 \\ =444.48\text{ N} \end{gathered}`

Thus the reading of the upper scale is 444.48 N.