Question

What is zero work done?

Answer 1

Hint:Work is said to be done when an object moves in the direction of applied force. It is equal to the
product of the magnitude of displacement and magnitude of the component of the force in the
direction of displacement. Using the formula of work, find out the conditions at which work done
can be zero to find the answer to this question.

Complete step by step answer:
When a force is applied on a body and it moves along the direction of force, work is said to be done
on that object.
Mathematically,
$$\begin{gathered} W=F\mathrm{Cos}\theta \cdot s \\ W=Fs\mathrm{Cos}\theta \\ W=\overrightarrow{F}\cdot \overrightarrow{s} \end{gathered}$$
Where $W=$ work done, $F=$ force applied, $s=$ magnitude of displacement and $\theta =$
the angle between $\overrightarrow{F}$ and $\overrightarrow{s}$ .
Now for work to be zero, any one of the above quantities has to be zero.
For $\cos \theta$ to be zero, $\theta ={90}^{\circ }$ , that is the displacement of the body is
perpendicular to the direction of applied force.
Therefore, work done is zero when force and displacement are perpendicular to each other or when
either the force or displacement is zero.

Additional information:
Force is said to be conservative if work done by it or against it in moving the body from one point to
another depends on the initial and final position of the body and is independent of the path followed
by the body. Also, if the work done in moving a body in a closed path in the field of a force and the
total work done is zero, then the force is said to be conservative.

Note:
Force is a push or pull which –
(a) Moves or tends to move a body kept at rest.
(b) Stops or tends to stop a moving body.
(c) Changes or tends to change the speed of the moving body.
(d) Changes or tends to change the direction of motion of the body.
Work is a scalar quantity as it is the dot product of two vector quantities. The conditions for the dot
product of two vectors to be zero can also lead to the same answer.