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NIU PHYS 210 - Power

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PowerUphillRate of WorkThe WattAverage PowerInstantaneous PowerPower PlantsForce and VelocityPowerPowerUphillUphillYou (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 WorkYou (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 kJYou 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 WattThe 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 / s33Energy can be measured in watt-seconds = joules.Energy can be measured in watt-seconds = joules.tWPtPE Average PowerAverage PowerThe 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 WThe 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 WWhen running seems harder, When running seems harder, it isn’t work, it’s power.it isn’t work, it’s power.Instantaneous PowerInstantaneous PowerWork 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 PlantsElectrical power is measured Electrical power is measured in watts.in watts.•60 W light bulb60 W light bulb•1000 MW power plant1000 MW power plantEnergy 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 VelocityPower 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 velocityPower is force times velocity.Power is force times


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