Chapter 7, Problem 13CT

To determine

To find: What force is needed when you increase the distance to $15ft$ from the pivot point? Justify.

Answer to Problem 13CT

  $F=40lbs$

Explanation of Solution

Given: You can use a simple lever to lift a $300$ pound rock. The force $F$ in foot pounds needed to lift the rock is inversely related to the distance $d$ (in feet) from the pivot point of the lever. To lift the rock you need $60$ pounds of force applied to a lever with a distance of $10ft$ from the pivot point.

  

Since

The force $F$ in foot pounds needed to lift the rock is inversely related to the distance $d$ (in feet) from the pivot point of the lever.

i.e.

  $F=\frac{a}{d}$

Here

  $\begin{array}{l}F=10\\ d=60\\ then\\ F=\frac{a}{d}\\ 10=\frac{a}{60}\\ a=600\end{array}$

Substitute $a=600$ in $F=\frac{a}{d}$

We get

  $F=\frac{600}{d}$

Now

Substitute $d=15ft$

We get

  $\begin{array}{l}F=\frac{600}{15}\\ F=40lbs\end{array}$

Hence, $F=40lbs$