Question

Write an expression for the work done when a force acts on an object in the direction of its displacement.

Answer 1

Work Done, Force, and Displacement.

1. Work done-Work is said to be done when a force causes an object to move.
2. Force- It is an external influence on a body to change its state or direction of motion.
3. Displacement: It is the shortest distance between two positions or points.

Step 1: Given

1. The angle between force and displacement, $\theta =0°$

Step 2: Formula Used

1. $W=F·d\Rightarrow W=Fd\cos \theta$

• Where $W$ is work done, $F$ is force, $d$ is displacement and $\theta$ is the angle between force and displacement.

Step 2: Expression

$W=F·d$,

$W=Fd\cos \theta$ ---- (i)

When the direction of force is the same as the direction of displacement then, $\theta =0°$.

Putting $\theta =0°$ in eq (i)

$W=Fd\cos 0°$

$W=Fd\left(1\right)$

$W=Fd$

Expression for the work done when a force acts on an object in the direction of its displacement is $W=Fd$.