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Skiing away, away the day

  1. Aug 17, 2009 #1
    1. The problem statement, all variables and given/known data

    Physics and Skiers and Rope and Hills?
    A 80 kg skier grips a moving rope that is powered by an engine and is pulled at constant speed to the top of a 24 degrees hill. The skier is pulled a distance x= 200m along the incline and it takes 2.2 min to reach the top of the hill.

    If the coefficient of kinetic friction between the snow and skis is Uk = 0.12, what horsepower engine is required if 30 such skiers (max) are on the rope at one time?


    2. Relevant equations

    F=umgcos(theta)
    P=F(change in x)/t
    HP=746?


    3. The attempt at a solution

    Since the tow rope moves at constant speed, the tension in the rope must equal the force of kinetic friction, which is:

    f = μmgcosθ
    = 0.12(80kg)(9.8m/s²)cos24°
    = 86N (rounded)

    Power is work over time and work is force times distance, so:

    P = FΔx / t
    = 86N(200m) / 132s
    = 130 W

    In horsepower:

    130W = 130W(1.00HP / 746W)
    = 0.175HP

    For 30 skiers then:

    30 x 0.175HP = 5.3HP (rounded)

    I got the wrong answer when I put this in. Everything seems in order. Did I miss something? I've double checked my work so its not a calculator error. Any help=thanks!
     
  2. jcsd
  3. Aug 17, 2009 #2

    kuruman

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    This would be the case if the skiers were on a horizontal surface. You did not include the power required to raise up to a certain height that you can calculate from the slope and the distance along the incline, i.e. Δ(mgh)/Δt.
     
  4. Aug 17, 2009 #3
    So insert that when trying to figure out power?

    P = FΔx / t + Δ(mgh)/Δt??
    or P=Δ(mgh)/Δt??
     
  5. Aug 17, 2009 #4

    kuruman

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    Insert. The engine works against both friction and gravity.
     
  6. Aug 17, 2009 #5
    So...=( 86N(200m) / 132s) + (80*9.8*200cos(24)/132)??
     
  7. Aug 17, 2009 #6

    kuruman

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    Draw yourself a right triangle of hypotenuse 200 m making an angle of 28o with respect to the horizontal. What is the vertical side?
     
  8. Aug 17, 2009 #7
    It's sin24*200=h

    Boom got it
     
    Last edited: Aug 17, 2009
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