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A 57-kg woman runs up a flight of stairs having a rise of 4.5 m in 3.5 s. what average power must she supply?
A 57-kg woman runs up a flight of stairs having a rise of 4.5 m in 3.5 s. what average power must she supply?

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5 years ago

Deepak Patra
471 Points
```							As the woman runs up a flight of stairs, there are two forces will act on the woman. One is the gravitational force which is in the downward direction and other one is the normal force N of the floor which balances the weight of the body (gravitational force) and the direction is just opposite to the direction of gravitational force.So, F = N = weight of the body = mg (Since, weight of the body = mg)Here m is the mass of the body and g is the acceleration due to gravity.To obtain the force F exerted by the woman to propel herself up the stairs, substitute 57 kg for m and 9.8 m/s2 for g in the equation F = mg,F = mg = (57 kg) (9.8 m/s2) = (560 kg.m/s2) (1 N/1 kg.m/s2) = 560 NIn accordance to the reference of woman the stairs are moving down. Thus the woman will exert a force in the down ward direction.To obtain the work done W by the woman, substitute 560 N for F and 4.5 m for s in the equation W = Fs,W = Fs = (560 N) (4.5 m) = (2500 N.m) (1 J/1 N.m) = 2500 JAs the direction of force is in the direction of displacement, thus the work done is positive here.To obtain the average power P supplied by the woman, substitute 2500 J for W and 3.5 s for t in the equation P = W/t,P = W/t = 2500 J/3.5 s = (710 J/s) (1 W/ 1 J/s) = 710 WFrom the above observation we conclude that, the average power P supplied by the woman would be 710 W.
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5 years ago
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• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions