Question

A man of mass 80 kg runs up a flight of stairs 20 m high in 10 s. (a) how much power is used to lift the man? (b) If the man’s body is 25% efficient, how much power does he expend? (c) This man consumes approximately 1.05 × 107 J (2500 food calories) of energy per day while maintaining a constant weight. What is the average power he produces over a day? (d) Compare this with his power production when he runs up the stairs.

Answer is: a) 1.6 kW; (b) 6.3 kW; (c) 122 W; (d) 1.9% of power produced running up stairs

Answer 1

Given is:-

mass of the man m = 80 kg

height of the stairs = 20m

time taken t = 10 seconds

Now,

The work done by the man against the gravity is given by

(here F is the force i.e. weight of the man)

by plugging all the values we get

which gives us

the power required to lift the man is

thus

which gives us

or

Part - b

Efficiency of the man is given by

thus

which gives us

Part - c

Average power produced by the man over a day is

by plugging the values we get

which gives us

Pard - d

BY comparing his all day power to the power produced during running up the stairs is given by

by plugging the values we get

which gives us