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 windmill is lifting water from a well.

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. A windmill is a device that lifts water upwards.
2. Hence it works against gravity.
3. Therefore a force is applied to the water to lift it upwards.
4. So, the force applied and the displacement occur in the same direction.
5. Hence, the work is done by a windmill is lifting water from a well.