Question

A force of $7\,{\text{N}}$ acts on an object. The displacement is ${\text{8 m}}$, in the direction of the force. Consider force acting on the object through the displacement. What is the work done in this case?
A. ${\text{96 J}}$
B. ${\text{56 J}}$
C. ${\text{76 J}}$
D. ${\text{156 J}}$

Answer 1

We are asked to find the work done on the object. Recall the formula for work done in terms of force applied and displacement of the body, find the angle between the force applied and the displacement of the object. Use these values to calculate the work done on the object.

Complete step by step answer:
Given, force applied, $F = 7\,{\text{N}}$.Displacement of the object, $d = {\text{8 m}}$. Work done can be expressed as the product of the displacement and magnitude of force in the direction of displacement. That is mathematically we can write work done as,
$W = \left( {F\cos \theta } \right)d$ (i)
where $F$ is the force applied on the body, $d$ is the displacement of the body and $\theta$ is the angle between the force and the displacement.
Here, it is said that the displacement is in the direction of force which means the angle between the fore and the displacement is zero.
Now, putting the values of $F$, $d$ and $\theta = 0$ in equation (i), we get
$W = \left( {7\cos 0} \right) \times 8$
$\Rightarrow W = 7 \times 8$
$\therefore W = 56\,{\text{N}}$
Therefore, work done on the object will be $56\,{\text{N}}$.

Hence, the correct answer is option B.

Note: The work done on a body depends upon the displacement and the magnitude of force in the direction of displacement. When the angle between the force and displacement is $\theta = {90^o}$, the work done is minimum and the angle between the force and displacement is $\theta = {0^o}$, the work done is maximum.