PowerPower

Rate of Energy TransferRate of Energy Transfer PowerPower is a quantity that measures the rate at is a quantity that measures the rate at

which work is done or energy is transformed.which work is done or energy is transformed.P = W P = W / ∆/ ∆tt

power = work ÷ time intervalpower = work ÷ time interval

An alternate equation for power in terms of An alternate equation for power in terms of force and speed isforce and speed is

PP = = FvFvpower = force power = force speed speed

PowerPower SI unit for power is the watt, W.SI unit for power is the watt, W. Defined as one joule per second.Defined as one joule per second. Horsepower is another commonly used Horsepower is another commonly used

unit, where one horsepower = 746 watts.unit, where one horsepower = 746 watts.

ExampleExampleGeneral:General:How much power is required to do 100 J of work on 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 an object in a time of 0.5 s? How much power is required to do the same work in 1 s?required to do the same work in 1 s?

Advanced:Advanced:A 193 kg curtian needs to be raised 7.5 m, at constant 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 speed, in as close to 5.0 s as possible. The power ratings for three motors are listed as 1.0 kW, 3.5 ratings for three motors are listed as 1.0 kW, 3.5 kW, and 5.5 kW. Which is best for the job?kW, and 5.5 kW. Which is best for the job?

SolutionSolution

AdvancedAdvanced Given:Given:

m = 193 kgm = 193 kg ∆∆t = 5.0 st = 5.0 s d = 7.5 md = 7.5 m

Unknown:Unknown: Power = ?Power = ?

SolutionSolution Choose an equation:Choose an equation:

P = W / ∆t = Fd / ∆t = mgd / ∆t P = W / ∆t = Fd / ∆t = mgd / ∆t P = P = (193 kg)(9.81 m/s(193 kg)(9.81 m/s22)(7.5 m))(7.5 m)

5.0 s5.0 sP = 2.8 x 10P = 2.8 x 1033 W = 2.8 kW W = 2.8 kW

Efficiency:Efficiency: Efficiency can be expressed as the ratio Efficiency can be expressed as the ratio

of useful work output to total work input.of useful work output to total work input.

Efficiency=Efficiency=

Example:Example: An automobile engine is a machine that An automobile engine is a machine that

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

SolutionSolution

Efficiency = 30/100 = 30%Efficiency = 30/100 = 30%

The reason it is 30% is that the engine The reason it is 30% is that the engine output is the desired energy transfer, output is the desired energy transfer, therefore, that is the “useful work output”therefore, that is the “useful work output”

Your turn:Your turn: What is the efficiency of a machine that What is the efficiency of a machine that

requires 183 J of input energy to do 48 J requires 183 J of input energy to do 48 J of useful work?of useful work?