Estimating the power required to operate a tow.?

Question

A ski tow operates on a slope of angle 14.7 of length 260 . The rope moves at a speed of 11.5 and provides power for 55.0 riders at one time, with an average mass per rider of 75.0 .

Estimate the power required to operate the tow.

Been stuck on this problem for an hour maybe, any ideas?

Answer 1

Is this all the data? Do you have any data about the time it takes to go a certain distance?

You can analyze the horizontal and vertical components. The horizontal is:

cos 14.7*260=251.49

and vertical:

sin 14.7*260=65.98
That is, the ski tow moves a total of 251.49 meters horizontally, and upwards 65.98 meters.

Use the formulas, for kinetic and potential energy.
The KE= 1/2mv^2 where m=mass and v=velocity
PE=mgh, where h=65.98meters.

You are essentially moving a mass horizontally, and also adding potential energy to it. Add KE+PE=Total Energy Input (assuming friction is negligible, which it really isn't but let's assume here it is).

So Total Energy will be in something like Joules, which is based on multiplying a Force in Newtons by length in meters.

When you divide the Total Energy Expenditure by Time, you get the Power here in Watts.

Solve the KE and PE formulas:

KE=1/2(4125)*velocity^2
+PE=4125*10*65.98=2.72 x 10^6Joules
=Total Energy

Total Energy/time to complete 1 cycle=Power

Answer 2

Weight down hill = mgsintheta = 55(75)(9.8)sin(14.7 deg)

Power = Fxd/t = F x v = above*11.5