Chapter 14.2, Problem 4E

To determine

To find: The work done by the force $F$ in moving an object from $A$ to $B$ .

Answer to Problem 4E

The work done by the force $F$ in moving an object from $A$ to $B$ is $40\text{J}$ .

Explanation of Solution

Given:

The force is $F=5i$ , and points are $A\left(-3,2\right)$ , and $B\left(5,-1\right)$ .

Calculation:

Find the distance.

  $\begin{array}{c}d=\overrightarrow{AB}\\ =\left(5+3\right)i+\left(-1-2\right)j\\ =8i-3j\end{array}$

Find the work done by the force $F$ in moving an object from $A$ to $B$ .

  $\begin{array}{c}W=F\cdot d\\ =\left(5i\right)\cdot \left(8i-3j\right)\\ =5\cdot 8-0\cdot 3\\ =40\text{J}\end{array}$

Therefore, the work done by the force $F$ in moving an object from $A$ to $B$ is $40\text{J}$ .