Work and Power

Work and power, along with energy, are the three fundamental concepts of Physics. Sometimes, we use them interchangeably, but per Physics, they are all different. While work is defined in terms of energy, power is defined in work, and energy is defined in work or heat. So, for example, energy is needed for certain tasks, and power is the capacity to do work.

Work

In Physics, work is defined as the force exerted on a body to cause motion or displacement in that body in the direction of the force applied. The work done on an object is equal to the amount of force exerted upon that object, multiplied by the displacement or distance that object has moved in the direction of application of force. However, work is a scalar quantity. It means it has no direction, only magnitude.

Work done is the product of force and displacement. Therefore, we can represent work done as:
W = F . d = F (cos θ) d

Where θ is the angle between the direction of applied force and the displacement
F is the force
d is the displacement
The SI unit of work is kg m2 s-2, or Newton-metre. It is also known as joule and represented by J.

When the direction of applied force and displacement is the same, the work done is positive. When the direction of the applied force is opposite to the displacement, then the work done is negative. For example, if we push a block and it moves forwards, we can say the work done is positive in this case. On the other hand, when a rocket goes upwards into space against gravity, we say the work done is negative.

Work done can also be zero. For example, if we lift a suitcase and do not move from our position, work done will be zero in this case. However, we exert force on the suitcase, yet the work done is zero as no displacement occurs.
Work done can also be zero if the force and displacement occur perpendicular to each other. In this case, θ will be 90 degrees, and cos 90 is zero. Therefore, the total work done will be zero according to the formula.

Example: What is the work done by a boy if he pushes his bike with a force of 60N up to a distance of 10 meters?
Solution:

We know, work done = F . d
Therefore, work done by the boy = 60 x 10 = 600 joules.

Power

We use the word power in various meanings. For example, in Physics, the word power is used to denote the capacity of work done. It is the rate at which we do the work. It is also defined as energy that changes with respect to time.

Therefore, power is the rate of change of work or rate of change of energy with time. It means, power is the ratio of work done to time.
Mathematically, power = W / t
Where W = work done and t = time
Power is also a scalar quantity as it does not have direction but only magnitude.
The unit of power is Watt, or J s-1. It is also represented as kg m2 s-3.

Other units of power

Example: What is the power consumed by an electric fan if it works for an hour at 4500 joules?
Solution:

In the SI units of power, we take time in seconds. Therefore, converting 1 hr to seconds we have,
1 hr = 60 x 60 = 3600 seconds
Power = Work / time
= 4500 / 3600 = 1.25 Watt.

Difference between work and power