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Why must a water skier at constant velocity lean back?

  1. Jan 18, 2015 #1
    1. The problem statement, all variables and given/known data
    Why must a water skier moving with constant velocity lean backward? What determines how far back she must lean? Draw a free-body diagram for the water skier to justify your answers.

    2. Relevant equations
    Equilibrium: Fnet=0 and Torquenet=0
    rcenter of mass=(m1r1+m2r2+m3r3...)/(m1+m2+m3...)

    This chapter also discusses stress, strain, elasticity etc. but I don't think it's applicable to this problem.

    3. The attempt at a solution

    In my free body diagram, the forces acting on the skier are air resistance and water resistance in the negative direction, and the tension in the rope she's holding in the positive direction.

    The net force will always be zero because the tension will match resistance. The torque needs to be kept at 0 so she doesn't flip. I think she leans back to keep the torque at 0, but I'm not sure why that would work.
     
  2. jcsd
  3. Jan 18, 2015 #2

    Bystander

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    Just where are these forces acting on the skier.
     
  4. Jan 18, 2015 #3
    Air resistance acts across the front of the skier (equivalent to being concentrated at the center of mass), and water resistance, which exerts more force, acts along the skis. The tension acts along her arms, probably near the center of mass.
     
  5. Jan 18, 2015 #4

    Bystander

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    And, how does she accomplish zero torque?
     
  6. Jan 18, 2015 #5

    NascentOxygen

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    Don't overlook gravity! Gravity acts vertically downwards; you can often picture it being concentrated at about waist height, when standing.
     
  7. Jan 18, 2015 #6
    by leaning back, apparently. is it because she shifts her center of gravity?
     
  8. Jan 18, 2015 #7
    Oh yeah, completely forgot about gravity in the free body diagram...
     
  9. Jan 18, 2015 #8

    NascentOxygen

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    So, can you show on a stick figure how gravity can counter the tendency of the tow line to produce a face plant (i.e., a rotation about the ankle straps)?
     
  10. Jan 19, 2015 #9

    CWatters

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    Show us the free body diagram. Did you include the normal force at the feet/lift force due to the skies?
     
  11. Jan 19, 2015 #10
    I can't show the free body diagram but i have the tension of the cable, gravity, air resistance, water resistance (friction?), normal force (buoyancy?). Is it because leaning back causes gravity to have a torque that counters the water resistance?
     
  12. Jan 19, 2015 #11
    ok it might be sideways but the top one is without leaning and the bottom one is with leaning
     

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  13. Jan 19, 2015 #12

    NascentOxygen

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    That looks like the right idea, but .... If skiing at constant speed, fa whatever it is won't be there. I would keep the skis flat, and water resistance and bouyancy shouldn't change to act at an angle.
     
  14. Jan 19, 2015 #13
    Fa is air resistance... I guess it's not necessary to include it. I think i have it figured out- thank you for your help!
     
  15. Jan 20, 2015 #14

    CWatters

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    Ski's aren't very bouyant. FB would be due to lift caused by the skis being at an angle to the water.

    When you show the man leaning back I would leave the FB pointing vertically. You already have FW due to friction (drag) and I would suggest that FB and FW should be orthogonal (at 90 degrees to each other).
     
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