Power

Rate of Energy Transfer  Power is a quantity that measures the rate at which work is done or energy is transformed. P = W / ∆t power = work ÷ time interval  An alternate equation for power in terms of force and speed is P = Fv power = force  speed

Power  SI unit for power is the watt, W.  Defined as one joule per second.  Horsepower is another commonly used unit, where one horsepower = 746 watts.

Example General: How much power is required to do 100 J of work on an object in a time of 0.5 s? How much power is required to do the same work in 1 s? Advanced: A 193 kg curtian needs to be raised 7.5 m, at constant speed, in as close to 5.0 s as possible. The power ratings for three motors are listed as 1.0 kW, 3.5 kW, and 5.5 kW. Which is best for the job?

Solution Advanced  Given:  m = 193 kg  ∆t = 5.0 s  d = 7.5 m  Unknown:  Power = ?

Solution  Choose an equation:  P = W / ∆t = Fd / ∆t = mgd / ∆t  P = (193 kg)(9.81 m/s 2 )(7.5 m) 5.0 s 5.0 s P = 2.8 x 10 3 W = 2.8 kW

Efficiency:  Efficiency can be expressed as the ratio of useful work output to total work input.  Efficiency=

Example:  An automobile engine is a machine that transforms chemical energy stored into mechanical energy. Of the 100% energy that is available in the fuel, 35% is lost in cooling water, 30% transfers to engine output, and 35% goes into exhaust.

Solution  Efficiency = 30/100 = 30%  The reason it is 30% is that the engine output is the desired energy transfer, therefore, that is the “useful work output”

Your turn:  What is the efficiency of a machine that requires 183 J of input energy to do 48 J of useful work?