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Power/Work-Energy HW

  1. Jun 8, 2012 #1
    1. The problem statement, all variables and given/known data
    The motor of a ski boat generates an average power of 7.50 * 10^4 W when the boat is moving at a constant speed of 12 m/s. When the boat is pulling the skier at the same speed, the engine must generate an average power of 8.30 * 10^4 W. What is the tension in the tow rope that is pulling on the skier?


    2. Relevant equations
    Average power = force * average speed
    Average power = change in energy/time
    Average power = Work/time


    3. The attempt at a solution

    I tried setting up an equation:

    8.30 * 10^4 W = F*12 m/s
    F = 83,000/12 N

    = 7 * 10^3 N which is wrong.
     
  2. jcsd
  3. Jun 9, 2012 #2

    ehild

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    The motor needs to move both the boat and the skier. The boat is pulled with 7.50 * 10^4 W. What is the power of the force that moves the skier then?

    ehild
     
  4. Jun 9, 2012 #3
    Another useful equation that would work in your case is

    P=Fv

    This comes from the fact that

    P = ΔW/Δt = FΔx/Δt = Fv
     
    Last edited: Jun 9, 2012
  5. Jun 9, 2012 #4
    Is it 83000 - 75000 = 1.2 * 10^4?
     
  6. Jun 9, 2012 #5

    ehild

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    It is 83000 - 75000, but not 1.2 * 10^4. Check the subtraction.

    ehild
     
  7. Jun 9, 2012 #6
    Fail. So 8.0 * 10^4?
     
  8. Jun 9, 2012 #7
    interesting derivation
     
  9. Jun 9, 2012 #8
    Its not 8*10^4 either. That's, 80,000.

    And.. thanks?
     
  10. Jun 9, 2012 #9

    Fail. 8*10^3. Why thanks?
     
  11. Jun 9, 2012 #10

    ehild

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    The skier is pulled at v=12 m/s speed by 8000 W power. What is the pulling force then?

    ehild
     
  12. Jun 9, 2012 #11
    deleting my post
     
  13. Jun 10, 2012 #12

    So: 8000/12 N is the answer. Significant digits yield 6.7*10^2, which is correct!
     
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