A man whose mass is 70 kg walks up to the third floor of the building which is 12m above the ground in 20s. Find his Power in watts and hp. (P = 411.6 watt = 0.55 hp) 



Given:

Mass of the man = m = 70 kg
Height of the building = h = 12 m
Time = t = 20 s 
Value of g = 9.8 ms⁻²

To Find:

Power of man = P = ? (both in watt and horsepower)


Solution:

Power is defined as the rate with respect to the time at which work is done. The mathematical formula of power is given by:

P = Work/Time

P = `\ frac{W}{t}`  ------------(1)

but here all the work is done is stored as potential energy so,

W = Gain in P.E. = mgh, therefore equation (1) will be

P = `\ frac{mgh}{t}` 

by putting values

P = `\ frac{70 kg ｘ 9.8 ms⁻²ï½˜ 12 m}{20 s}` 

P = 411.6 kg m² s⁻³           [kg m² s⁻³ = W (watt)]

or

P = 411.6 W ------------------Ans

In Horse Power Unit:

We know that 

1 horse power = 746 watts

or 

1 W = `\ frac{1}{746}`  hp

then 

P = 411.6 W = `\ frac{1}{746}` ｘ 411.6 hp

P = 0.55 hp ---------------Ans. 2

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