Question

If work done by the net force is zero, work done by the individual forces need:
(A) Zero
(B) Not be zero
(C) Can’t be determined
(D) Negative

Answer 1

Hint: Force being a vector quantity has both magnitude and direction. Therefore, two forces having equal magnitude by opposite direction adds up to net force zero. Since the net force applied is zero, work done is also zero although individual forces were non-zero.

Complete Step-By-Step Solution:
We know work is done when an object covers a certain distance on application of a certain force. Therefore, work done is zero, when either net force applied is zero, or when the applied force is not enough to cause a displacement.
Now, we know that force being a vector quantity has both direction and magnitude. Therefore, in our calculations, we need to take both these factors into consideration.
Let us consider the following example to get a better insight to the question.
Let us consider, we apply a force $F$ on the box from the right hand side and another force of the same magnitude $F$ is applied from the Left hand side. Therefore, since the forces are applied from the opposite direction, we can say that the net force is:
$F_{net}=F+(-F)=0$
Thus, we can see from the example the net force is zero, even though individual forces were non-zero.
Therefore, the individual forces need not be zero.

Hence, option (B) is correct.

Note:
As work done mathematically is the dot product of force and displacement, there comes a quantity $\cos \theta$ in the expression of work done, where, $\theta$ is the angle between the applied force and displacement. Therefore, zero or no work is done when$\theta ={90}^o$, that is force and displacement being perpendicular to each other, and maximum work is done when or $\theta ={180}^o$