Question

A child pulls a toy bus through a distance of $8m$ on a smooth horizontal floor. The string held in the child’s hand makes an angle of ${{60}^{0}}$ with the horizontal surface. If the force applied by the child is $3N$, calculate the work done by the child in pulling the toy car.

Answer 1

Hint: This problem can be solved by using the direct formula for the work done by a body in terms of the force exerted on another body, the displacement of the second body due to that force and the angle made by the direction of force with the direction of the displacement.

Formula used:
$W=Fs\cos \theta $

Complete answer:
We will use the formula for the work done by a force to solve this problem.
The work done $W$ by a body exerting a force $F$ on another body is given by
$W=Fs\cos \theta $ --(1)
Where $s$ is the displacement of the body and $\theta $ is the angle made by the direction of the force with the direction of the displacement.
Now, let us analyze the question.
The force exerted by the boy on the car is the force with which he pulls the string. It is $F=3N$.
The displacement of the car is $s=8m$. This displacement is in the horizontal direction along the floor.
Now, it is given that the string held in the child’s hand makes an angle of ${{60}^{0}}$. Since, the force applied by the boy will be along the string, hence, the force applied by the boy also makes and angle of ${{60}^{0}}$ with the horizontal.
Now, since the direction of displacement is the horizontal direction, therefore, the angle $\theta $ made by the force with the direction of displacement is nothing but the angle made by the force with the horizontal, that is, $\theta ={{60}^{0}}$.
Let the work done by the boy be $W$.
Therefore, using (1), we get
$W=3\times 8\times \cos {{60}^{0}}=24\times \dfrac{1}{2}=12J$ $\left( \because \cos {{60}^{0}}=\dfrac{1}{2} \right)$
Therefore, the work done by the boy is $12J$.

Note:
By solving this problem, students must have got a feel of the dependence of the work done upon the angle made by the displacement with the force. If the boy would have pulled the string in a horizontal line at the level of the toy car, he would have done more work and made better use of his energy.

This is also the reason why a force perpendicular to the displacement is said to do no work. Therefore, a porter carrying a luggage box and moving forward does not work under the scientific definition of work as the force applied is in the vertical direction while the porter moves with the luggage in a perpendicular direction.