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Force applied on cable attached to car and tree

  1. May 20, 2016 #1
    1. The problem statement, all variables and given/known data
    your car is stuck in the mud and you can’t pull hard enough to get it out. You do, however, have a long cable that you connect taut between your front bumper and the trunk of a stout tree. You now pull sideways on the cable at its midpoint, exerting a force f. Each half of the cable is displaced through a small angle u from the straight line between the ends of the cable. (a) Deduce an expression for the force acting on the car. (b) Evaluate the cable tension for thecasewhereu57.00°andf 5100N
    2. Relevant equations
    Efx=0
    Efy=O


    3. The attempt at a solution

    Efx
    T1cos@ = t2cos@
    T1=T2
    Efy=0
    F = 2tsin@

    Is this right?
     
  2. jcsd
  3. May 20, 2016 #2

    CWatters

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    Close. That's an equation for F.

    The angle is defined in the problem as "u" rather than "@".
     
  4. May 20, 2016 #3
    But is the method of solution correct besides the u?
     
  5. May 20, 2016 #4

    CWatters

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    Your answer is correct if you rearrange it to give an equation for T.

    I don't understand your method.
     
  6. May 20, 2016 #5

    CWatters

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    I would solve it by drawing a fbd for the point on the rope where f Is applied.
     
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