Question

A cyclist comes to a skidding stop in$10m$. During this process, the force on the cycle due to the road is $300N$ and is directly opposed to the motion. How much work does the road do on the cycle?

Answer 1

Step 1: Given data

Skidding displacement, $d=10m$

Force exerted on the cycle by the road, $f=300N$

Angle between the force exerted by the road on the cycle and the displacement of the cycle, $\theta ={180}^0$

Work done by the road on the cycle, $w=?$

Step 2: Formula used

$w=fd\cos \theta$ ………………………(a)

Step 3: Calculation of the work done by the road on the cycle

Substituting the given values in equation (a), we get

$$\begin{gathered} w=300N\times 10m\times \cos {180}^0 \\ w=-3000J \end{gathered}$$

The negative sign indicates that the force and the displacement are opposite to each other

Hence, the magnitude of the work done by the road on the cycle is equal to $3000J$