Natalie M.

asked • 10/22/15

I am confused as to how to solve this, given that there are multiple skiers on the rope

At a ski resort, a tow rope powered by an engine can tow a 60-kg skier (at a constant speed) up a 300-m hill that is inclinded at angle of 24? in 2.7 minutes. If the coefficient of kinetic friction between the skiers and the snow is 0.12, how much power does the engine produce if there are 30 such skiers on the rope at one time?

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Bill K. answered • 10/22/15

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Tow rope does work increasing potential energy of the skier PE = mgh
(where m = 60 and g = 9.8 and h = 300sin24° is the height each skier is lifted)
and work against the friction f = μN
where N is the normal force and can be found by setting N = mgcos24° 
W = f*300 = μmgcos24°
total work to tow one person is W =  μmgcos24° + 300mgsin24°
total power = 30W/t, where t is the time to tow one person or 2.7 min or 2.7*60 = 162 seconds
 
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Natalie M.

Thanks, I'm still a little confused. In the distance used for work, why are we not using the distance that the tow is following. I assumed since 300m is the height of the mountain that the rope would be going farther since it is at a 24 degree angle from the ground. Also at the end am I just going to multiply by 60?
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10/22/15

Bill K.

I am solving the problem by using energy relationships but you can also just consider the work done on each person as the sum of work done against the frictional and work done against gravity.  The second part can be viewed as increase in potential energy or as work done against gravity.  The gravitational force along the tangent is mgsin24°. The work is then this force multipled by the distance of 300, or 300mgsin24°. 
 
Multiplying by 60 at the end of the paragraph is just to make sure everything is in SI untis that is time is in seconds.
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10/22/15

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