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'.

Suma is swimming in a pond.

Answer 1

Work done

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

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 the force vector and displacement vector.

Finding whether work is done or not

1. In order to swim a force needs to be applied by the hand inside the water, to push the water backward.
2. This causes the water to exert a reaction force on Suma and she can move forward.

$\therefore \theta =180°$

$=FS\cos 180°=-FS$

Hence, the work done is negative.