An race is held each year to see who can be the first person

An race is held each year to see who can be the first person to climb the 86 floors of the Empire State Building. If a 60.0 kg person runs the race in 10 minutes and 59 seconds , answer the questions below.

Part A) If each floor was 3.70 m high, what was the racer\'s change in gravitational potential energy? Give your answer in kJ.

Part B) If the efficiency in climbing stairs is 30 % , what total energy did the racer expend during the race? Give your answer in kJ.

Part C) How many food Calories did the racer \"burn\" during the race?

PART D) Of those Calories, how many were converted to thermal energy? (in Cal units)

Part E) What was the racer\'s metabolic power in watts during the race up the stairs? (in W)

Solution

a)

Total height of building

h=86*3.7 =318.2 m

change in gravitational potential energy is

dPE =mgh =60*9.8*318.2

dPE=187.1 KJ

b)

Total energy the racer expend during the race

TE =187.1/0.3 =623.7 KJ

c)

1 KJ = 0.239 Kcal

TE =0.239*623.7 =149.1 Kcal or 149100 calories

d)

Energy converted into thermal energy is

E =(1-0.3)*149.1 =104.4 KCal or 104400 cal

e)

time to climb the 86 floors

t=10 min 59 sec =659 sec

Metablolic power in watts is

P=TE/t =623.7*1000/650

P=959.5 Watts