Question

Just before class starts in the spring, you take a quick trip to New York City to visit some friends. According to a sign outside the Empire State Building, the most recent winning time for the annual race up all 86 floors to the top was 10 min and 49 s. Let 's say the winner had a mass of 60 kg. If each floor is 3.7 m high, what was his or her change in gravitational energy during this race to the top? If the efficiency of the human body is about 25%, what is the total energy that this person expended? How many food Calories did he/she burn to win the race? Of those Calories, how many were converted to thermal energy?

Answer 1

(a)
m = 60 kg
h = 3.7m
Total floors = 86
Total Heigth gained = 86*3.7 =318.2 m

Gravitational potential energy gained = m*g*h = 60*9.8*3218.2 J
Gravitational potential energy gained = 1892301.6 J

(b)
Let the total energy be x.
0.25 * x = 1892301.6
x = 7569206.4 J

(c)
1 calorie = 4.2 joules
Calories burned = 7569206.4 /4.2 = 1802192 calories
Calories burned = 1802.2 kcal

(d)
Calories converted to thermal energy = 0.75* 1802.2 kcal
Calories converted to thermal energy = 1351.65 kcal