Power

Topic Content:

What is Power?

Power is the rate at which work is done, or energy is transferred.

This means that two people may do the same amount of work, but the person who completes the work in less time develops greater power.

The SI unit of power is the watt (W) .

One watt is the power developed when one joule of work is done in one second.

1 W = 1 J/s

Formulae for Power:

Since power is the rate of doing work:

P = \( \frac{W}{t} \)

Where:

• P = power in watts (W)
• W = work done in joulesJoule is the SI (International System of Units) unit of energy and work. It is equal to the amount of work done when a force of 1 newton displaces a mass... More (J)
• t = time taken in seconds (s)

Since work done in the direction of a force is:

W = Fd

Then:

P = \( \frac{Fd}{t} \)

But:

Velocity, v = \( \frac{d}{t} \)

Therefore, when the force acts in the direction of motion:

P = Force (N) × Velocity (m/s)

P = Fv (N m/s)

Units of Power:

• watt (W)
• joule per second (J/s)
• newton metre per second (N m/s)
• kilogram metre squared per second cubed (kg m² /s³ )

Example 8.3.1:

A student lifts