Chapter 5, Problem 101A

To determine

Net force read by scale.

Answer to Problem 101A

The net force read by scale is $283.6\text{N}$ .

Explanation of Solution

Given:

The given figure is,

  

  $\begin{array}{l}{F}_{\text{left}}=75\text{N, }{F}_{\text{right}}=75\text{N},F_{\text{middle}}=150\text{N}\\ \theta =27°\end{array}$

Formula Used:

Component of force in the direction of $\theta$ is given as $F\cos \theta$ .

Calculation:

From the given figure the two side forces are resolved into x and y components.

The y component of the side force is,

  $\begin{array}{c}{F}_y=F\cos \theta \\ =75\times \cos 27°\\ =66.8\text{N}\end{array}$

Now, the scale will read the total force in the y direction.

So,

  $\begin{array}{c}{F}_{y\text{total}}=F_{y\text{left}}+F_{y\text{middle}}+F_{y\text{right}}\\ =66.8\text{N}+150\text{N+66}\text{.8}\text{N}\\ F_{y\text{total}}=283.6\text{N}\end{array}$

Conclusion:

The net force read by scale is $F_{y\text{total}}=283.6\text{N}$ .