Chapter 8, Problem 90A

To determine

The distance she can walk before the beam begins to tip.

Answer to Problem 90A

The distance she can walk before the beam begins to tip is $0.848\text{ m}$ from the end.

Explanation of Solution

Given:

The length of the steel beam is $6.5\text{ m}$ .

The weight of the steel beam is $325\text{ N}$ .

The weight of Suki is $575\text{ N}$ .

Formula used:

The expression for the torque is,

  $T=Fl$

Here, $F$ is the applied force and $l$ is the length.

Calculation:

Consider each support is $1.75\text{ m}$ from the end of the beam.

Consider the point of rotation to be the support which is closer to Suki.

The center of mass of the beam is $1.5\text{ m}$ from the support which is closer to Suki.

The beam tips when the torque due to Suki’s weight equal to the torque due to the center of mass.

The distance can she walk before the beam begins to tip as follows:

  $\begin{array}{l}{\tau }_{\text{S}}={\tau }_{\text{cm}}\\ F_{\text{S}}{r}_{\text{S}}=F_{\text{cm}}{r}_{\text{cm}}\\ r_{\text{S}}=\frac{\left(\text{325 N}\times 1.5\text{ m}\right)}{575\text{ N}}\\ r_{\text{S}}=0.848\text{ m}\end{array}$

Conclusion:

Thus, the distance she can walk before the beam begins to tip is $0.848\text{ m}$ from the end.