A ski tow operates on a slope of angle 15.5 of length 320 m . The rope moves at

Question

A ski tow operates on a slope of angle 15.5 of length 320 m . The rope moves at a speed of 12.5 km/h and provides power for 55 riders at one time, with an average mass per rider of 69.0 kg .

Estimate the power required to operate the tow.

I have determined that the total work should be 11.5x10^6 J from W= 37191 x 320 x cos15.5

55 riders at 69 kg each = 3795 kg - converted to Newtons = 37191 N

and 12.5 km/h = 3.47 m/s

And the time for an object to travel 320m at 3.47 m/s should be 92.2 s, therefore:

P should equal (11.5x10^6)/92.2 = 124359 Watts - however this is apparently incorrect. I know that I am on the right track and most likely have made a mistake or false assumption. Please let me know.

Thanks

Explanation / Answer

work done is =mgsin(theta)h = 37191 x 320 x sin(15.5) =3180435.9J

time = 92.2s

P =w/t =34494.96watt

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