Power is how fast energy is transferred
Definition
Power
The work done per unit time, which is the same as the energy transferred per unit time.
P=WtandP=ΔEt P = \frac{W}{t} \qquad \text{and} \qquad P = \frac{\Delta E}{t} P=tWandP=tΔEwhere PPP is power in W\text{W}W, WWW is work done in J\text{J}J, ΔE\Delta EΔE is energy transferred in J\text{J}J and ttt is time in s\text{s}s.
- Power says nothing about how much energy is moved. It says how quickly it is moved.
- Two cranes can lift identical loads to identical heights, doing exactly the same work. The one that finishes in half the time has twice the power.
- The unit is the watt, W\text{W}W. One watt is one joule per second, so 1 W=1 J/s1\ \text{W} = 1\ \text{J/s}1 W=1 J/s.
- Larger powers are quoted in kilowatts, where 1 kW=1000 W1\ \text{kW} = 1000\ \text{W}1 kW=1000 W, and in megawatts, where 1 MW=1 000 000 W1\ \text{MW} = 1\,000\,000\ \text{W}1 MW=1000000 W.
- The two equations are the same equation, because work done equals energy transferred. Use P=W/tP = W/tP=W/t when a force and distance are given, and P=ΔE/tP = \Delta E/tP=ΔE/t when the question talks about stores.
- Rearranging gives ΔE=Pt\Delta E = PtΔE=Pt for the energy transferred in a given time, and t=ΔE/Pt = \Delta E / Pt=ΔE/P for how long a transfer takes.
Common Mistake
- Power is not energy. Energy is measured in joules, power in watts. An answer such as "the power is 1800 J1800\ \text{J}1800 J" scores nothing.
- Convert minutes and hours to seconds before substituting. A kettle run for "333 minutes" must go in as 180 s180\ \text{s}180 s.
- Convert kilowatts to watts unless you are deliberately keeping every quantity in kilo units.
- Doing the same job faster does not change the work done, only the power.
Exam technique
- These questions almost always come in two stages: find the work done or energy transferred first, then divide by the time. Set the two steps out on separate lines.
- Decide which force the work is done against. For someone climbing stairs it is their weight, so use W=mgΔhW = mg\Delta hW=mgΔh with the vertical height.
- Look for the words "useful power output", which tell you to ignore energy wasted as internal energy in muscles or bearings.
- Finish with the unit W\text{W}W or kW\text{kW}kW, and say which one you have used.
Self review
- Define power in two different ways, and write the matching equations.
- State the unit of power and express it in terms of joules and seconds.
- A machine does 6000 J6000\ \text{J}6000 J of work in 30 s30\ \text{s}30 s. Calculate its power.
- A 60 W60\ \text{W}60 W lamp is left on for 5.05.05.0 minutes. Calculate the energy it transfers.
- Two cranes lift the same load to the same height, one in 10 s10\ \text{s}10 s and one in 20 s20\ \text{s}20 s. Compare the work done and the power of each.
