Question

Find the total work done by forces and if the object undergoes the displacement $\mathit{C}$ . Hint: Can you add the two forces first?

Short answer

The required work done is, $\mathrm{W}=‐5$.

Step-by-step solution

Definition of work done

By substituting the force with the equation of

$\mathbf{W}\mathbf{=}\mathbf{F}\mathbf{.}\mathbf{d}$$\mathbf{W}\mathbf{=}\mathbf{F}\mathbf{.}\mathbf{d}$

Where $\mathbf{F}$is the force and$\mathbf{d}$ is the displacement and$\mathbf{W}$ is equal to the work.

Simplify

Let us know if work done can be calculated as,

$\mathrm{W}=\mathrm{F}.\mathrm{d}$

To find $\mathrm{F}$

role="math" localid="1659153886346" $$\begin{gathered} \mathrm{F}=\mathrm{A}+\mathrm{B}, \\ \mathrm{d}=\mathrm{C} \end{gathered}$$

Substitute the values in the equation

$$\begin{gathered} \mathrm{W}=\left(\mathrm{A}+\mathrm{B}\right)\times \mathrm{C} \\ =\left(\left(\mathrm{i}+\mathrm{j}-2\mathrm{k}\right)+\left(2\mathrm{i}-\mathrm{j}+3\mathrm{k}\right)\right)\times \left(\mathrm{j}-5\mathrm{k}\right) \\ =\left(3\mathrm{i}+\mathrm{k}\right)+\left(\mathrm{j}-5\mathrm{k}\right) \\ =-5 \end{gathered}$$

Therefore, the work done is $\mathrm{W}=‐5$