PowerUphillRate of WorkThe WattAverage PowerInstantaneous PowerPower PlantsForce and VelocityPowerPowerUphillUphillYou (You (mm = 60 kg) hike up a 30° hill with a net height = 60 kg) hike up a 30° hill with a net height increase (increase (h h = 50 m). What work is done by gravity?= 50 m). What work is done by gravity?•Distance Distance dd = = hh / sin / sin = (50 m) / sin 30 = (50 m) / sin 30°° = 100 m = 100 m•Work done by gravity Work done by gravity WW = = mg d mg d sinsin = = (60 kg)(9.8 m/s2)(50 m) = (60 kg)(9.8 m/s2)(50 m) = 30 kJ30 kJGravity does negative work on the hikerd = 100 m-mgRate of WorkRate of WorkYou (60 kg) walk up a 30You (60 kg) walk up a 30°° hill hill with a net height increase of with a net height increase of 50 m at 1 m/s.50 m at 1 m/s.•tt = (50 m)/sin30 = (50 m)/sin30°°/(1/ms) /(1/ms) =100 s=100 s•WW = 30 kJ = 30 kJYou run up the same 30You run up the same 30°° hill hill with a net height increase of with a net height increase of 50 m at 4 m/s.50 m at 4 m/s.•tt = 25 s, = 25 s, W W = 30 kJ= 30 kJ•But, running is harder!But, running is harder!The rate of work has The rate of work has increased by 4 times by increased by 4 times by running.running.Hiker does positive work to overcome gravityd = 100 mThe WattThe WattThe rate of work is called power.The rate of work is called power.The SI unit of power is the watt (W).The SI unit of power is the watt (W).•1 watt = 1 J/s = 1 N m/s = 1 kg m1 watt = 1 J/s = 1 N m/s = 1 kg m22 / s / s33Energy can be measured in watt-seconds = joules.Energy can be measured in watt-seconds = joules.tWPtPE Average PowerAverage PowerThe walker had an average The walker had an average power output based on the power output based on the work compared to the time.work compared to the time.•PP = = WW / / tt•PP = 30 kJ / 100 s = 300 W = 30 kJ / 100 s = 300 WThe runner generated the The runner generated the same work in one quarter of same work in one quarter of the time.the time.•PP = 30 kJ / 25 s = 1200 W = 30 kJ / 25 s = 1200 WWhen running seems harder, When running seems harder, it isn’t work, it’s power.it isn’t work, it’s power.Instantaneous PowerInstantaneous PowerWork does not have to be uniform over time.Work does not have to be uniform over time.•Moving over a series of hills and valleys (changing work)Moving over a series of hills and valleys (changing work)•Walking and running (changing rate)Walking and running (changing rate)The power expended at one instant is the limit of The power expended at one instant is the limit of work done over a very small time interval.work done over a very small time interval.tEtWPtt 00limlimPower PlantsPower PlantsElectrical power is measured Electrical power is measured in watts.in watts.•60 W light bulb60 W light bulb•1000 MW power plant1000 MW power plantEnergy used is measured in Energy used is measured in power times time.power times time.If electricity costs $ 0.083 If electricity costs $ 0.083 per kWh, how much does it per kWh, how much does it cost to leave a 1500 W cost to leave a 1500 W floodlamp on all year?floodlamp on all year?•Energy used is Energy used is WW = = PtPt = = (1500 W)(3.2 x 10(1500 W)(3.2 x 1077 s) = s) = 4.8 x 104.8 x 101010 J J•Cost is (4.8 x 10Cost is (4.8 x 101010 W s) * (1 W s) * (1 kW / 1000 W) * (1 h kW / 1000 W) * (1 h / 3600 s)*(0.083 / kWh) = / 3600 s)*(0.083 / kWh) = $1,100$1,100Force and VelocityForce and VelocityPower is work per time.Power is work per time.•Work is force acting over a Work is force acting over a distancedistance•Distance per time is velocityDistance per time is velocityPower is force times velocity.Power is force times
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