Question

In the Empire State Building Run-up, participants compete to see who can run up the 320 m Empire State Building the fastest. The current record holder, Paul Crake, who has a mass of 64 kg, covered this distance in 9 min and 33 s. What is the minimum average output power that his body produced while doing this?

Answer 1

Wow ! I'll betcha his mass was not still 64 kg when he got to the top.

In raising the mass of 64 Kg to 320 m above the street,
the mass gained gravitational potential energy equal to

m G h = (64 kg) (9.8 m/s²) (320 m)

= 200,704 joules .


9 minutes 33 seconds is equivalent to

(9 min x 60 sec/min) + (33 sec)

= 540 sec + 33 sec = 573 seconds .


Power = (energy) / (time) = (200,704 joules) / (573 sec) = 350.3 watts

That's pretty nearly 1/2 horsepower (0.47), and he kept it up for almost 10 minutes.
Wotta guy !

Answer 2

Power can be calculated using the following rule:
Power = work / time

So, first we need to calculate the work done. Work can be calculated using the following rule:
W = mass * gravity = 64 * 9.8 * 320 = 200704 joules

We are given that the time is 9 minutes and 33 seconds. That is equal to 9(60)+33 = 573 seconds

Substitute with the work and time in the equation of power to get the value of the power as follows:
P = (200704) / (573) = 350.2687609 watt