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?

Question

Physics

Lincoln Cochran

10 December, 06:25

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?

+1

Answers (2)

Know the Answer?

Moriah Little · 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!

Trystan May · 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