Question

A constant force $\left(23,12,32\right)N$acts through a displacement$\left(0.12,0.31,0.24\right)m$. How much work does this force do?

Short answer

Answer

W=-8.64NmWork done by the force is_{.$\mathit{W}\mathbf{}\mathbf{=}\mathbf{-}\mathbf{8}\mathbf{.}\mathbf{64}\mathit{N}\mathit{m}$}

Step-by-step solution

Definition of the work done

Work is said to be done when an object is displaced from its actually position when an external force is applied on it.

The work done as a result of the force is given by $W=\stackrel{\rightharpoonup }{F}$$‐\overrightarrow{∆r}$ or$W=\overrightarrow{F}$$∆\overrightarrow{r}$$\cos \theta$ where $W$is the work done,$\overrightarrow{F}$ is the external force and $∆\overrightarrow{r}$is the displacement.

Finding work done

Substituteand intoto find work done.

The work is negative this indicates that the force in the opposite direction of the displacement.

Therefore, the work done by the force is