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Tension in a massive cable

  1. Oct 22, 2016 #1
    1. The problem statement, all variables and given/known data
    Why is the tension always tangent to the portion of the cable?
    Snap1.jpg
    The correct situation is on points A and B.
    Why can't be like on C and D?

    2. Relevant equations
    Newton's force-mass: ##F=ma##

    3. The attempt at a solution
    If i move the portion of the cable and examine, for equilibrium, portion CD, then what about portion AC, does it pull up now, while in position A the portion of the cable on the left of A, if the tension wouldn't be only along the cable, would have pulled down since it was part of the examined cable.
    So the tension is only along the cable from symmetry only. is it true? i sense it's not the single reasoning.
     
  2. jcsd
  3. Oct 22, 2016 #2

    mfb

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    Staff: Mentor

    Forces in other directions are only possible if your cable is stiff. Which can happen, but that is not the typical rope problem.
     
  4. Oct 22, 2016 #3

    haruspex

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    Consider a very short elemental section of the cable. It is almost straight. The forces on it are a small gravitational force and the two much larger tensions. The tensions won't be quite tangential, but most be close to it. They must be almost equal and opposite, and if not almost tangential they would apply a net torque. In the limit, as the length and mass of the element tend to zero, the tensions are tangential.
     
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