Question

A particle moves from A to D in $FIGUREEX10.35$while experiencing force$\overrightarrow{F}=(6\hat{i}+8\hat{j})N$. How much work does the force do if the particle follows path (a) ABD, (b) ACD, and (c) AD? Is this a conservative force? Explain.

Short answer

If particle followed path ABD then work done =$50J$.

If particle followed path ACD then work done =$50J$.

If particle followed path AD then work done =$50J$.

Step-by-step solution

Given information

Force, $\overrightarrow{F}=(6\hat{i}+8\hat{j})N$

Curve followed path,

Explanation : 

The force exerted on a mass item that causes it to alter velocity.

When particle follows the path ABD, the work done is

$$\begin{gathered} W_{ABD}=\left(6\times 3+8\times 0\right)+\left(6\times 0+8\times 4\right) \\ =50J \end{gathered}$$

When particle follows the path ACD, the work done is

$$\begin{gathered} W_{ACD}=\left(6\times 0+8\times 4\right)+\left(6\times 3+8\times 0\right) \\ =50J \end{gathered}$$

When particle follows the path AD, the work done is

$$\begin{gathered} W_{AD}=\left(6\times 3+8\times 4\right) \\ =50J \end{gathered}$$

Hence, in all the conditions the work done is same. So, the force is a conservative force.