Question

A person holds a bundle of hay over his head for $30$ minutes and gets tired.Has he done some work or not? Justify your answer.

Answer 1

Hint:We can consider the concept of work done, which is the product of force and displacement applied at a certain angle. It can be positive, negative and zero. It is zero when the applied force and displacement are perpendicular to each other.

Complete step by step answer:
We know that a person is holding a bundle of hay over his head, which can be considered as a load, w. And he holds the hay for a time period of $t = 30\min .$
$W = \overrightarrow {F.} \overrightarrow S= F.S.cos\theta $ . . . (1)
Where $W \to $is the work done
$F \to $ Force applied
$S \to $Displacement
$\theta \to $ Angle between Force$(\overrightarrow {F)} $ and the Displacement $(\overrightarrow {S)}$. Now while performing these operations, he also gets tired and applies a force on the bundle in the upward direction and here we can observe that the displacement of the bundle from one place to another place is zero.
Therefore, mathematically,
$W = \overrightarrow {F.} \overrightarrow S = F.S.cos\theta$
$\Rightarrow W = 0$
Since, $S = 0$
And the person gets tired due to the muscular energy applied on the bundle which gets converted into heat energy, and this heat energy ultimately heats the body of the person.
Hence, the person has not done the work. Therefore, from the above explanation, it is justified that, even though the person got tired, he did not do any work.

Note: From this example we can understand that if we are applying a force on the body but not moving it, then the work done is zero. Also, if we move a body to some distance and then bring it back to the original point, the total work done will be zero.