Just before class starts in the spring, you take a quick trip to New York City t
ID: 1998931 • Letter: J
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 has 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?Explanation / Answer
According to the given problem,
A)change in gravitational potential energy is.
h = 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
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