# How many steps to reach top of empire state building

Asked by wiki @ in Physics viewed by 204 People

A new record for running the stairs of the Empire State Building were set on February 4, 2003. The 86 flights, with a total of 1576 steps, was run in 9 minutes and 33 seconds. If the height gain of each step was 0.20 m, and the mass of the runner was 70.0 kg, what was his average power output during the climb? Give your answer in both watts and horsepower.

Power = 377.35 W or Power = 0.5065 hp

Explanation:

Given:

Number of steps, n = 1576

height of each step, h = 0.20 m

Total height achieved, H = nh = 1576 × 0.20 = 315.2 m

Mass of the runner, M = 70.0 kg

Total time taken, t = 9 minutes 33 seconds = (9 × 60) + 33 = 573 seconds

Now, the potential energy gained by the runner,

E = MgH

where, g is the acceleration due to the gravity

on substituting the values in the above formula, we get

E = 70 × 9.8 × 315.2

or

E = 216227.2 J

also,

Energy = Power × time

therefore,

Power = Energy/time

or

Power = 216227.2 J / 573

or

Power = 377.35 W

Now,

745 watt = 1 hp

or

1 watt = 1/745 hp

thus,

Power = 377.35 W = 337.35 × (1/745) hp

or

Power = 0.5065 hp

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