Problem 1: A 70 kg man runs up a long flight of stairs in 4.0 seconds. The vertical height of the stair is 4.5 m. Calculate his power.
Solution
Theory: When the man goes up stairs, he is doing work by lifting his own weight to a vertical height. This work is equal to the gain in the potential energy of his body. Power is the rate of doing work (P = W/t). Hence, the gain in potential energy will be calculated which is equal to the work done and then divided by the time he takes will give us the power of the man.
Given Mass of the man = 70 kg OR weight of the man = 70 × 9.8 = 686 N
Vertical height = 4.5 m, Time taken = 4.0 s
Required Power of the man
Now gain in the P.E = mgh = 686 × 4.5 = 3087 J = the work done the man do going upstairs.
Power = work done/time = P = 3087/4.0 = 771.75 = 772 = 7.7 × 102 watts
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