Question

Work

A constant force $F=(2,8)$moves an object along a straight line from the point $(2,5)$ to the point $(11,13)$. Find the work done if the distance is measured in feet and the force is measured in pounds.

Short answer

Work done in pounds is $W=82\text{ft}-\text{lb}$

Step-by-step solution

Step 1. Given information

Given that a force $F=(2,8)$ moves object along a straight line from the point $(2,5)$ to the point $(11,13)$

Step 2. Concept used

The work done by a force in moving an object in the direction of displacement is

$W=F·d$

The position vector $\overrightarrow{AB}$ is given by $\overrightarrow{AB}=\overrightarrow{B}-\overrightarrow{A}$

To find the work done if the distance is measured in feet and the force is measured in pounds. Calculate the displacement vector from the given points.

Use the formula.

Step 3. Calculation

The displacement vector is as follows

$\begin{array}{l}\overrightarrow{\text{AB}}=(11i+13j)-(2i+5j)\\ \overrightarrow{\text{AB}}=11i+13j-2i-5j\\ \overrightarrow{\text{AB}}=9i+8j\end{array}$

Therefore the work done is as follows-

$\begin{array}{l}W=(2i+8j)\cdot (9i+8j)\\ W=2\left(9\right)+8\left(8\right)\\ W=18+64\\ W=82\text{ft}-\text{lb}\end{array}$