Chapter 9.2, Problem 46E

To determine

To find: The work done by the force in moving an object along a straight line if the distance is measured in feet and the force is measured in pounds.

Answer to Problem 46E

The work done by the force in moving an object is 82 ft-lb.

Explanation of Solution

Given:

A constant force F is $\langle 2,8\rangle$ that moves an object along a straight line from the point $\langle 2,5\rangle$ to the point $\langle 11,13\rangle$.

Formula used:

The work done (W) in moving an object along a vector D by a force F is,

$W=F\cdot D$ (1)

Calculation:

The object moves along a straight line from the point $\langle 2,5\rangle$ to the point $\langle 11,13\rangle$.

The displacement vector is,

$\begin{array}{c}D=\langle 11-2,13-5\rangle \\ =\langle 9,8\rangle \end{array}$

Substitute $\langle 2,8\rangle$ for F and $\langle 9,8\rangle$ for D in equation (1) to find work done.

$\begin{array}{c}W=\langle 2,8\rangle \cdot \langle 9,8\rangle \\ =\left(2\right)\left(9\right)+\left(8\right)\left(8\right)\\ =18+64\\ =82\end{array}$

Thus, the work done by the force in moving an object is 82 ft-lb.