Question

Look at the activity listed here. Reason out whether or not work is done in the light of your understanding of the term 'work'.

A donkey is carrying a load on its back.

Answer 1

Work Done

1. Work done is defined as the force applied to displace a body from its original state.
2. Work done is a scalar quantity.
3. Force and displacement are vector quantities.
4. We know that the dot product of two vectors gives a scalar quantity as its result.
5. Therefore work done is the dot product of force and displacement.

If $\overrightarrow{F}$ is the force applied and $\overrightarrow{S}$ is the displacement of the body, then the work done $W$ can be given as,

$W=\overrightarrow{F}·\overrightarrow{S}$

$=FS\cos \theta$

where, $\theta$ is the angle between the direction of force vector and displacement vector.

Check if work is done

1. When a load is placed on a donkey, its weight acts downwards.
2. To balance this force itself applies a force upwards.
3. When the donkey moves forward, it causes the load to undergo displacement in the forward direction.
4. Therefore the force and the displacement are at an angle perpendicular to each other.
5. Therefore $$\begin{gathered} \theta =90, \\ W=FS\cos \theta \\ W=FS\hspace{0.17em}\cos \left(90\right) \\ W=0as\cos \left(90\right)=0 \end{gathered}$$
6. Hence, the net work done is zero.