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Power of a winch

  1. Apr 17, 2008 #1
    1. The problem statement, all variables and given/known data
    A loaded ore car has a mass of 950kg and rolls on rails with negligible friction. It starts from rest and is pulled up a mine shaft by a cable connected to a winch. The shaft is inclined at 30.0 degrees above the horizontal. The car accelerates uniformly to a speed of 2.2 m/s in 12.0 seconds and then continues at a constant speed.

    a) what power must the winch motor provide when the car is moving at constant speed?

    2. Relevant equations
    Well, Power=Force x Velocity
    Force = T

    3. The attempt at a solution
    Well to find the Tension in the rope, I found the component of G that was opposite the Tension and set it to -Fs. Then I set -Fs + T = 0 => Fs = T. Looking at The triangle under the cart I used sin(30)= Fs/g => Fs= gsin(30) which = 4.9 N

    Since power = F*V I got P= (4.9)(2.2) = 10.78 kW. The back of the book says its 10.2 kW though. Im just wondering where I went wrong
  2. jcsd
  3. Apr 17, 2008 #2
    I can't understand what you do with Fs and T. You do not use the mass of the cart. 4.9 N * 2.2 m/s will give you 10.78 W and not 10.78 kW
  4. Apr 17, 2008 #3
    Oh ok, well then care to give me some advice on how to solve the problem then?
  5. Apr 17, 2008 #4
    The Idea of splitting the force of gravity in components parallel and perpendicular to the ground was ok. As was power = force * speed
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