What is the relationship between power and work done?

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

In physics, power and work are closely related concepts. Work is defined as the energy transferred when a force is applied to an object causing it to move. The formula for work is \( \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \), where \( \theta \) is the angle between the force and the direction of movement. Work is measured in joules (J).

Power, on the other hand, measures how quickly this work is done. The formula for power is \( \text{Power} = \frac{\text{Work}}{\text{Time}} \). Power is measured in watts (W), where one watt is equal to one joule per second. This means that if you do a certain amount of work in a shorter period of time, you are using more power.

For example, imagine you are lifting a box. If you lift a 10 kg box to a height of 2 metres, you are doing work against gravity. The work done can be calculated using the formula \( \text{Work} = \text{Force} \times \text{Distance} \). Here, the force is the weight of the box (mass \(\times\) gravitational field strength, \(10 \, \text{kg} \times 9.8 \, \text{m/s}^2\)), and the distance is 2 metres. So, the work done is \( 10 \times 9.8 \times 2 = 196 \, \text{J} \).

If you lift the box in 2 seconds, the power used is \( \frac{196 \, \text{J}}{2 \, \text{s}} = 98 \, \text{W} \). If you lift the same box in 1 second, the power used is \( \frac{196 \, \text{J}}{1 \, \text{s}} = 196 \, \text{W} \). Thus, lifting the box faster requires more power.

Understanding the relationship between power and work helps us analyse how efficiently energy is used in various processes, from everyday tasks to complex machinery.