Physics / Unit 5: Work, Energy and Power
5.5 Power
Notes
Power is the rate of doing work or transferring energy: $\displaystyle P = \frac{W}{t}$.
- Unit: the watt (W). $1 \text{ W} = 1 \text{ J/s}$. One horsepower is about $746 \text{ W}$.
- For a force pushing at constant speed: $P = Fv$.
- Doing the same work in less time takes more power.
- Example: a 60 kg student climbs 3 m of stairs in 4 s. $W = 60 \times 9.8 \times 3 = 1764 \text{ J}$; $\displaystyle P = \frac{1764}{4} = 441 \text{ W}$.
Practice
A motor does 1,200 J of work in 6 s. What is its power?
$\displaystyle P = \frac{1200}{6} = 200 \text{ W}$.
Two students of equal mass climb the same stairs. One runs up in 5 s; the other walks up in 10 s. Which is true?
Work $= mgh$ is the same; power $\displaystyle = \frac{W}{t}$ is larger for the shorter time.
A tow truck pulls a car with a 2,000 N force at a steady $5 \text{ m/s}$. What power does it deliver?
$P = Fv = 2000 \times 5 = 10000 \text{ W}$.
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