In this problem a runner must overcome the increase in her gravitational potenti

Question

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 1) . If all the runner’s work output could be collected and sold at the rate of 9 cents per kilowatt-hour, what would be the cash value of the work?

Explanation / Answer

power P = work / time

Work = Power*time = m*g*h = 50*9.81*443= 217291.5 J

1 kilowatt-hour = 1000*(j/s)*3600 s = 3.6*10^6 J

1J = 1/(3.6*10^-6) kwH

work = 217291.5/(3.6*10^6) = 217291.5/(3600*1000) = 0.0603 kwH

1 kwH costs 9 cents

then 0.0603 KwH costs = 0.0603*9 = 0.54 cents

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