Video Tutor Solution A jet airplane engine develops a thrust (a forward force on

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Video Tutor Solution A jet airplane engine develops a thrust (a forward force on the plane) of 15,000 N (roughly 3000 lb). When the plane is flying at 300 m/s (roughly 670 mi/h), what horsepower does the engine develop? SOLUTION REFLECT This power is comparable to the power developed by a diesel railroad locomotive. The airplane travels 10 times as fast as the locomotive, with a much smaller cargo weight SET UP AND SOLVE From Equation 7.20, Practice Problem: Suppose the airplane carries 150 passengers with an average mass of 55 kg each. After disembarking, all these passengers get on a freight elevator, which itself has a mass of 750 kg. How fast can the elevator's 6000 hp motor lift the loaded elevator? (That is, at what speed is 6000 hp just enough to keep the elevator rising?) Answer: 51 m/s P- Fv (1.50 x 104N) (300 m/s)-4.50 x 106 w or w)(71%)-6030 hp EXAMPLE 7.16 A marathon stair climb In this problem a runner must overcome the increase in her gravitational potential energy as she climbs the stairs of a tall building. The rate at which she does this is directly related to her average power output. As part of a charity fund-raising drive, a Chicago marathon runner with mass 50.0 kg runs up the stairs to the top of the Willis Tower, the tallest building in Chicago (443 m), in 15.0 min (Figure 7.36). What is her aver- O age power output in watts? In kilowatts? In horsepower? Video Tutor Solution REFLECT A horse can supply considerably more than 1 hp for short periods of time Practice Problem: If all the runner's work output could be collected and sold at the rate of 10 cents per kilowatt-hour, what would be the cash value of the work? Answer: 0.603 cent SOLUTION SET UP AND SOLVE The runner's total work W is her weight mg multiplied by the height h she climbs Wmgh (50.0 kg) (9.80 m/s2) (443 m) 2.17 x 105J The time is 15 min 900 s, so the average power is 2.17 × 105 J - 241 W -0.241 kW- 0.323 hp 900 s Alternative Solution: The average vertical component of velocity is (443 m)/(900 )0.492 m/s, so the average power is -(50.0 kg) (9.80 m/s2)(0.492 m/s) 241 W FIGURE 7.36 Climbing the Willis Tower.

Explanation / Answer

Given

there are 150 passengers , with mass each is of 55 kg

mass of elevator is is 750 kg ,

the total mass is (150*55+750) kg = 9000 kg

the power of the motor, is P = F*v = 9000*9.8*V

V = 6000hp/(9000*9.8)

V = 6000*746 /(9000*9.8) m/s

V = 50.75 m/s

V = 51 m/s

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here the power is P = 2.17*10^5 J

we know that 1 kWh = 1000*3600 J = 3600000 J

so

2.17*10^5 J = 2.17*10^5 /3600000 kWh = 0.06027778 kWh

1 kWh = 10 cents

0.0602777777778 *10 = 0.602777777778 cents

so the cost is 0.602777777778 cents= 0.603 cents

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