# Power

## Power

The quantity work has to do with a force causing a displacement. Work has nothing to do with the amount of time that this force acts to cause the displacement. Sometimes, the work is done very quickly and other times the work is done rather slowly. The quantity that has to do with the rate at which a certain amount of work is done is known as the power. Power is always dependent on work done, so if a person does work at different rates his power also differs at different times.

What is a Power?

Power is the rate of doing work, it is the work done per unit time. The rate at which work is done is called power. If work is defined at uniform rate, average power (P) is defined as,

Power (P) = Work Done (W)/ Time (t)

If the work is done at a variable force, instantaneous power (P) is defined as,

Power (P) = dW/ dt

The SI unit of Power is Watt (W) which is Joules per Second. Sometimes Power of motor vehicles and other machines are given in terms of Horsepower (hp) which is approximately equal to 745.7 Watts.

How to find the Power?

Problem: When doing a chin-up, a physics student lifts her 42kg body a distance of 0.25m in 2 seconds. What is the power delivered by the student’s biceps?

Solution: Given,

Time (t) = 2 sec,

Mass (m) = 42 kg,

Acceleration due to gravity (g) = 9.8 m/ sec²,

Distance (d) = 0.25m,

Power (P) =?

We know that:

Power (P) = Work done (W)/ Time (t)

= [Force (F) x Distance (d)]/ Time (t)

Power (P) = (mg x d)/ t

= [42 Kg x 9.8m/sec² x 0.25m]/ 2 sec

= 51.45 ≈ 51.5 Watts

∴ Power (P) = 51.5 Watts.