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Tractor Stuck in a Ditch

  1. Nov 23, 2008 #1
    One cold winter day, a tractor gets stuck in a ditch. The operator hooks a tow chain to a nearby tree and attempts to move the tractor by jumping up and down on the chain. If the chain is 10 meters long and is stretched level one meter above the ground, and the tree is stationary, how far does the tractor move when the chain is pressed to the ground? Assume the main is in the middle of the chain. If the man has a mass of 100 kg, what is the force on the tractor when the chain just touches the ground?

    I figured that the angle of the bent chain was 78.7 degrees (using tan-1(1/5) and then subtracting that by 90). The weight of the man is 980 N. I'm just not sure how to calculate how far the tractor moves, or the force on the tractor when the chain touches the ground (unless it's just the man's weight, which I doubt). Help please?
     
  2. jcsd
  3. Nov 23, 2008 #2

    PhanthomJay

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    The original chain length is 10m. Assumig it is fairly rigid, when then it moves down a meter at centreline, it's still 10 m long, but the horizontal distance betwen the truck an tree is now less tham 10m. It requires just a little geometry and trig to get the truck movement. The tractor force can be obtaine by applying Newton 1 at the joint where man and chain meet in the new position at the ground.
     
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