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28: Power

Last updated

Aug 8, 2024
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- 27: Conservative Forces
- 28.1: Energy Conversion of a Falling Body

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Simply put, power is the rate of change of energy (or work) with time:

$\mathcal{P}=\frac{d E}{d t}$

In SI units, power is measured in units of watts (W), named for the Scottish engineer James Watt:

$1 \mathrm{~W}=1 \frac{\mathrm{J}}{\mathrm{s}}=1 \frac{\mathrm{kg} \mathrm{m}^{2}}{\mathrm{~s}^{3}}$

In CGS units, power is measured in units of statwatts:

$1 \text { statwatt }=1 \frac{\mathrm{erg}}{\mathrm{s}}=1 \frac{\mathrm{g} \mathrm{cm}^{2}}{\mathrm{~s}^{3}}$

The British engineering unit of power has no special name; it is simply a foot-pound per second (ft-lbf/sec).

Another common unit that is not part of the British engineering system is the horsepower (hp): $1 \mathrm{hp}=$ $550 \mathrm{ft}-\mathrm{lbf} / \mathrm{sec}$ , or about 745.7 watts. The power produced by an automobile engine is traditionally measured in horsepower. A few examples:

Lawn mower: $5 \mathrm{hp}$
Smart car: $90 \mathrm{hp}$
Typical modern automobile engine: about $200 \mathrm{hp}$
1967 Pontiac GTO “muscle car”: $360 \mathrm{hp}$
Semi truck (tractor): $500 \mathrm{hp}$
Modern farm tractor: $500 \mathrm{hp}$
Formula One engine used in a modern Indianapolis 500 race car: $700 \mathrm{hp}$ or more
"Monster truck" (as seen at county fairs): $1500 \mathrm{hp}$

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