Question

Estimate the power you produce in running up a flight of stairs. Give your answer in horsepower (1 hp = 746 W). Suppose you climb one flight of stairs (3 m) in 10 seconds (you run up the stairs quickly). Estimate your mass to be 71 kg .

Answer 1

The first thing you should do is calculate the work done when climbing the stairs. This work by definition will be given by:
 W = F * d
 W = (m * g) * (d)
 W = ((71) * (9.8)) * (3) = 2087.4J
 Then, you can calculate the power that in this case is given by
 P = W / t
 P = (2087.4) / (10) = 208.74W
 To have the result in HP we use the fact that 1HP = 746W
 P = (208.74) / (746)
 P = 0.28 HP
 answer
 the power you produce in running up a flight of stairs is 0.28 HP

Answer 2

If we call the time it took for you to climb the stairs in seconds, T, the height of the stairs in meters, h, your weight in newtons, W, then to find the power you developed in watts, P, the following formula restates what we said above: Power = W x h/t, W= 71kg x 9.81m/sec sq.= 696.51 N, Height h= 3m, time t= 10 sec, Power P=( 696.51 x3) 10= 208.953 watts = 0.28 hp.