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Equalibrium problem ( i think)

  1. Oct 17, 2011 #1
    1. The problem statement, all variables and given/known data
    Q) To pull a car from a ditch, the driver ties one end of a rope to the car and the other end to a tree 12.5 m away and then pulls sideways at the midpoint of the rope with a 475 N force. How much force is exerted on the car when the driver has pulled the rope 75.0 cm to one side ?
    The book's answer 1990N.

    2. Relevant equations



    3. The attempt at a solution

    My solution assuming this is a torque issue.
    Assuming> the ends are 12.5 meters apart.one end tied to the car, the other tied to the tree.
    > driver is pulls the rope 75 cm from the middle 6.25meters.


    So the radius = 12.5metres/2 = 6.25meters
    Find Ɵ
    0.12 = sin Ɵ.
    Ɵ = 6.89
    The torque is rFsinƟ = 6.25m ( 475N) sin6.89 = 356Nm.


    My solution assuming this is an equilibrium issue:

    Assuming> the ropes ends are 12.5 meters apart.
    > The ropes directions are one end is to the east and the other is to the west
    > assuming the driver is pulling the car 75 cm west of north.
    So the radius = 12.5metres/2 = 6.25meters
    Find
    .75metes / 6.25 meters = 0.12 = cos Ɵ.
    Ɵ = 83.1
    westward - The driver force on the car will be 475Ncos83.1= 57N
    Northward - The driver force on the car will be 475Nsin83.1= 471N

    thanks for your time!
     
    Last edited: Oct 17, 2011
  2. jcsd
  3. Oct 17, 2011 #2
    Why are you using the term 'torque'? And do you assume the vehicle has moved a little when the puller has moved the center of the rope 75cm? Or has the rope stretched?
     
  4. Oct 17, 2011 #3

    I like Serena

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    Homework Helper

    Welcome to PF, charlene w! :smile:

    I'm afraid torque is not applicable in this problem.

    I recommend you draw a picture of the rope.
    Draw vectors on it representing the 3 forces on the rope.
    In particular the car and the tree have a reactive force on the rope.

    For equilibrium the forces must cancel each other.
    From that you can calculate the force on the car.
     
  5. Oct 17, 2011 #4
    Thanks for the replies! I will give your suggestion some thought.
     
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