Question

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

Answer 1

Answer:

Explanation:

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 N

In 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 J

As 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 W

From the above observation we conclude that, the average power P supplied by the woman would be 710 W.