Work done and power

We can link the concept of work done to power!

power usually refers to energy, as we’ll revisit in a minute, but since work done just means energy transferred, we can also link power to work done.

Power and energy

The normal formula for power is:

\text{power} = \frac{\text{Energy transferred}}{\text{Time taken}}

Or, in symbols:

P = \frac{E}{t}

Where:

• P is the power, in watts, W
• E is the energy transferred, in joules, J
• t is the time taken, in seconds, s

Power and work done

Using the knowledge that work done is just the same thing as energy transferred, we can write this as:

\text{power} = \frac{\text{work done}}{\text{Time taken}}

Or in symbols:

P = \frac{W}{t}

Where:

• P is the power, in watts, W
• W is the work done, in joules, J
• t is the time taken, in seconds, s

A machine does 500 J of work in 10 s. What is the power of the machine?

• P = \frac{W}{t}
• W = 500\,J
• t = 10\,s
• P = \frac{500\,J}{10\,s}
• P = 50\,W

A machine does 1000 J of work in 20 s. What is the power of the machine?

• P = \frac{W}{t}
• W = 1000\,J
• t = 20\,s
• P = \frac{1000\,J}{20\,s}
• P = 50\,W

A machine has a power of 200 W and does 400 J of work. How long does it take to do the work?

• P = \frac{W}{t}
• P = 200\,W
• W = 400\,J
• t = \frac{W}{P}
• t = \frac{400\,J}{200\,W}
• t = 2\,s

A machine has a power of 150 W and does 300 J of work. How long does it take to do the work?

• P = \frac{W}{t}
• P = 150\,W
• W = 300\,J
• t = \frac{W}{P}
• t = \frac{300\,J}{150\,W}
• t = 2\,s

A mechanical device does 50 W of power over a period of 5 s. How much work does it do?

• P = \frac{W}{t}
• P = 50\,W
• t = 5\,s
• W = Pt
• W = 50\,W \times 5\,s
• W = 250\,J

A mechanical device does 75 W of power over a period of 8 s. How much work does it do?

• P = \frac{W}{t}
• P = 75\,W
• t = 8\,s
• W = Pt
• W = 75\,W \times 8\,s
• W = 600\,J