Table of Contents
Work and Power Relationship
Power is the rate of doing work. A powerful engine does the same work as a weak one but in less time. The watt equals one joule per second. James Watt defined horsepower as 550 ft·lbf/s to compare steam engines to horses.
Understanding work-power-time is essential for sizing motors, estimating energy costs, and analyzing vehicle performance. Same total work can require very different power depending on the timeframe.
Formulas
P is power (W), W is work (J), t is time (s), F is force (N), v is velocity (m/s). The second form gives instantaneous power.
Power Output Examples
| Source | Power |
|---|---|
| Human sustained | 75 W |
| Human sprint | 2,000 W |
| Horse sustained | 746 W (1 hp) |
| Car (200 hp) | 149,000 W |
Frequently Asked Questions
Difference between work and power?
Work = total energy transferred (joules). Power = rate of transfer (watts). A marathoner and sprinter may do the same work, but the sprinter has much higher power.
Human power output?
Sustained: ~75W (0.1 hp). Peak sprint: ~2,000W for seconds. Professional cyclists sustain 300-400W for hours.
Power vs speed?
P = F × v. Drag force increases with v², so power against air resistance increases with v³. Doubling speed requires 8× the power.