Question

The winning time for the 2005 annual race up 86 floors of the Empire State Building was 10 min and 49 s. The winner's mass was 60 kg. If each floor was 3.7 m high, what was the winner's change in gravitational potential energy? If the efficiency in climbing stairs is 25 %, what total energy did the winner expend during the race? How many food Calories did the winner "burn" during the race? What was the winner's metabolic power in watts during the race up the stairs? Express your answer using two significant figures.

Answer 1

A is 3.7 m x 86 stories = 318.2 m
GPE = mgh = 60 kg x 9.8 m/s*2 x 318.2 m = 187 kJ

B change efficiency to a decimal (25% = 0.25)
187 kJ/0.25 = 748 kJ

C one calorie = 4.2 kJ so...
748 kJ/4.2 kJ/cal = 178 cal

D since he was only 25% efficient, the remaining energy went straight to heat...
178 x 0.75 = 134 cal

E 10 m 49 s = 649 s
I assume the metabolic power is based on total energy output so...
Power = Energy/Time = 748 000 J/649 s = 1150 W

Hope that helps...

Answer 2

A is 3.7 m x 86 stories = 318.2 m
GPE = mgh = 60 kg x 9.8 m/s*2 x 318.2 m = 187 kJ

B change efficiency to a decimal (25% = 0.25)
187 kJ/0.25 = 748 kJ

C one calorie = 4.2 kJ so...
748 kJ/4.2 kJ/cal = 178 cal

D since he was only 25% efficient, the remaining energy went straight to heat...
178 x 0.75 = 134 cal

E 10 m 49 s = 649 s
I assume the metabolic power is based on total energy output so...
Power = Energy/Time = 748 000 J/649 s = 1150 W