Power

If a force, F,  is doing work on and thereby supplying energy to a system, let dW represent the work done in an infinitesimal period of time dt due to a displacement dr, i.e., dW  = F · dr.  It follows that the instantaneous rate of doing work or transferring energy (power) is given by

P º dW/dt = F · dr/dt = F · v.

The SI unit of power is the watt* (W) º joule/second = N·m/s = kg·m²/s³.  In mechanical systems a commonly used unit of power is the horsepower (hp), where 1 hp = 746 W.  A related and commonly used unit of energy, especially by electrical utility companies, is the kilowatt-hour (kWh):

1 kWh = 1000 W (1 hr) (3600 s/hr) = 3.6 ´ 10⁶ J.

       *The watt is named for the Scottish inventor of the modern steam engine, James Watt (1736-1819).

---

Quiz #5

If you had a perfectly efficient electric motor, to what height could you lift a 100-kg weight ( » 220 lbs) for 1¢, using electricity purchased from Provo City Power (rate » 7¢ / kWh)?