Mechanical Power from Work

Mechanical power from work over time

Power tells you how fast work gets done. The formula is P = W / t, measured in watts (W = J/s). When the force stays constant and points along the direction of motion, you can also write P = F · v. Lift a 1 kg mass by 10 cm in 1 s and the work comes to W = m·g·h ≈ 1·9.81·0.10 ≈ 0.98 J, which puts the average power right around 1 W. That makes a handy anchor for picturing the unit.

Horsepower (HP) is an older unit that has stuck around: 1 HP = 745.7 W. So a 100 HP car engine peaks at roughly 74.6 kW. For comparison, a fit cyclist can hold 200–300 W over an hour, while elite sprinters briefly push past 1 500 W.

Applications: motors, treadmills and ergometers

Engineers reach for P = W/t when sizing electric motors, hoists or conveyor belts. Once you know the load, the lift height and the cycle time, the shaft power you need drops right out. Sport uses it too: stationary bikes and rowing ergometers read out power in watts, which measures effort directly and doesn't depend on body mass, so it tells you a lot more than speed does on its own. HVAC sizing, pump duty cycles and elevator specs all run on the same relation.

FAQ

Is power the same as energy? No. Energy (joules) is the total work done. Power (watts) is the speed at which you do it. A 100 W bulb left on for 1 hour burns through 360 000 J = 0.1 kWh.

Why is P = F·v? Take a constant force F that moves a body by dx in a time dt. The bit of work done is F·dx, so the power is F·(dx/dt) = F·v. Think of it as the instantaneous form of W/t.

Watts vs horsepower? Mechanical HP works out to about 745.7 W; the European metric version is closer to 735.5 W. Carmakers tend to quote PS/CV, which is the metric HP.

Does the formula assume constant power? What P = W/t gives you is the average power across the interval. When you want the value at a single instant, switch to F·v or dW/dt.