Question

A boy is moving on a straight road against a frictional force of $ 5 N$. After travelling a distance of $ 1.5 km$ he forgot the correct path at a round about (Fig.) of radius $ 100 m$. However, he moves on the circular path for one and half cycle and then he moves forward up to $ 2.0 km$. Calculate the work done by him.

Answer 1

Step 1: Given data

1. The radius of the circular round is $100m.$
2. The frictional force exerted on the boy is $5N$.
3. Initially, the boy travels $1.5km$ along the road and rounds the circular round one and half times, again he moves $2km$.

Step 2: Work done by force

1. Work done is the product of force and displacement. It is a scalar quantity.
2. $Workdone=force\times displacement$, $W=\overrightarrow{F}.\overrightarrow{ds}$, where $F$ is the force and $ds$ is the displacement due to exerted force.

Step 3: Finding the work done

The total distance travelled by the boy equals to the sum of initial distance travelled along the road $\left(1,500m\right)$, one and a half times travel in circular round (the displacement will be equal to the diameter) $\left(diameter=2\times radius\right)$ and final distance travelled along the road $\left(2,000m\right)$.

So, total distance,

$\begin{array}{rcl}S& =& 1500+2000+\left(2\times 100\right)\\ & =& 3,500m+200m\\ & =& 3,700m\end{array}$

Now, the work done by the boy is

$\begin{array}{rcl}W& =& 5\times 3,700\\ & =& 18,500J\end{array}$

Therefore, work done by the boy is $18,500J$ .