Chapter 9.2, Problem 4E

To determine

To fill: The work done in moving an object along a vector D by a force F.

Answer to Problem 4E

The work done in moving an object along a vector D by a force F is $\text{W}=F\cdot D$.

Explanation of Solution

The formula of work done in moving an object along a straight line is,

$\text{Work}=\text{Force}\times \text{Distance}$

Figure (1)

From the above figure, it can be considered that the force F moves an object from point P to Q, then the component of the force affect the object in the direction $D=\overrightarrow{PQ}$.

The effective magnitude of force on the object is,

${\text{comp}}_{\text{D}}\text{F}=\left|\text{F}\right|\cos \theta$

The work done is,

$\begin{array}{c}W=\left(\left|F\right|\cos \theta \right)\left|D\right|\\ =\left|F\right|\left|D\right|\cos \theta \left[\because \left|u\right|\left|v\right|\cos \theta =u\cdot v\right]\\ =F\cdot D\end{array}$

Thus, the work done in moving an object along a vector D by a force F is $\text{W}=F\cdot D$.