Question

How are work and power related?

Answer 1

Hint: We need to understand the physical quantities work and power to understand and analyse the difference between these quantities. They are used in different situations according to the requirement which will lead us to the solution for this problem.

Complete Solution:
We know that the work done and the power are two important physical quantities which we come across in our daily life. Work done is the amount of energy spent on doing something. When we say doing something, we mean that the force applied produces a displacement along the direction of the force. The work done is the scalar quantity which determines how the force on a body or system brought an output.

Usually, in a mechanical system, the work done is given as –
\[\begin{align}
  & W=F.s \\
 & \therefore W=Fs\cos \theta \\
\end{align}\]

Where, W is the work done, F is the force applied on the system, s is the displacement of the system and \[\theta \] is the angle between the force and the displacement. The S.I unit of work done is Joules.

The power is defined as the rate of work done on a system or by the system. It is the rate at which the energy is used or expended on doing a work. It is the ratio of the energy to the
time taken for the work. It is given mathematically as –
\[P=\dfrac{W}{t}\]

We understand that the power of the system is dependent on the work done by the system. The S.I unit of power is Watt.

This is the required solution.

Note:
We are used to noticing the power of devices especially electrical devices instead of the work done. It is because the power of the device is the energy expenditure per unit time which is more easily handleable and therefore used widely.