Chapter 8, Problem 89A

To determine

The force exerted by each person.

Answer to Problem 89A

The force exerted by each person on each side is $F_{\text{L}}=154.3\text{ N}$ and $F_{\text{R}}=595.7\text{ N}$ .

Explanation of Solution

Given:

The weight of a bag of topsoil is $75\text{ N}$ .

The length of the sheet of wood is $2.43\text{ m}$ .

Formula used:

The expression for the torque as follows:

  $T=Fr$

Here, $F$ is the applied force and $r$ is the radial distance.

Calculation:

Consider the weight of the topsoil bags as $F_{\text{Soil}}$ and the two persons on each side as $F_{\text{R}}$ and $F_{\text{L}}$ .

The weight of the topsoil bags as follows:

  $\begin{array}{c}{F}_{\text{Soil}}=10\times 75\text{ N}\\ =750\text{ N}\end{array}$

Show the situation as shown in Figure below.

  

Consider the location of $F_{\text{R}}$ as the axis of rotation to make that torque zero.

Apply the total torque on the system is zero.

  $\begin{array}{l}{\tau }_{\text{R}}+{\tau }_{\text{Soil}}+{\tau }_{\text{L}}=0\\ 0+F_{\text{Soil}}{r}_{\text{Soil}}+F_{\text{L}}{r}_{\text{L}}=0\\ F_{\text{L}}\times 2.43\text{ m}=\left(750\text{ N}\times 0.50\text{ m}\right)\\ F_{\text{L}}=154.3\text{ N}\end{array}$

The total force on the system is zero.

  $\begin{array}{l}{F}_{\text{R}}-F_{\text{Soil}}+F_{\text{L}}=0\\ F_{\text{R}}-750+154.3=0\\ F_{\text{R}}=595.7\text{ N}\end{array}$

Conclusion:

Therefore, the force exerted by each person on each side is $F_{\text{L}}=154.3\text{ N}$ and $F_{\text{R}}=595.7\text{ N}$ .