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

`1.9* 10^5\ J`

`1.8* 10^(2)\ kcal`

`1.3* 10^(2)\ kcal`

`1.2* 10^(3)\ W`

Step-by-step explanation:

m = Mass of person = 60 kg

g = Acceleration due to gravity = 9.81 m/s²

t = Time taken = 10 min and 49 s

Total height

`h=3.7* 86\\\Rightarrow h=318.2\ m`

Potential energy is given by

`U=mgh\\\Rightarrow U=60* 9.81* 318.2\\\Rightarrow U=187292.52\ J`

The gravitational potential energy is
`1.9* 10^5\ J`

The energy in the climb

`(187292.52)/(0.25)=749170.08\ J`

Converting to kcal or Cal

`(749170.08)/(4184)=179.05594\ kcal`

The amount of energy used to climb
`1.8* 10^(2)\ kcal`

Amount gone to heat

`179.05594* 0.75=134.291955\ kcal`

The amount burned
`1.3* 10^(2)\ kcal`

Power is given by

`P=(E)/(t)\\\Rightarrow P=(749170.08)/(10* 60+49)\\\Rightarrow P=1154.34526\ W`

The power is
`1.2* 10^(3)\ W`