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Rope Sliding off a Peg

  1. Oct 4, 2014 #1
    1. The problem statement, all variables and given/known data
    A limp rope with a mass of 2.4 kg and a length of 1.5 m is hung, initially at rest, on a frictionless peg that has a negligible radius, as shown in the Figure. y1 is equal to 0.48 m. What is the vertical velocity of the rope just as the end slides off the peg?

    2. Relevant equations
    PE = mgh
    KE = 1/2mv^2

    3. The attempt at a solution
    Because the kinematics of this system seemed incredibly complicated, I figured it best to use conservation of energy in the system. Knowing that the center of mass will fall 0.48 meters, I assumed:

    mgΔH = 1/2mv^2
    2.4*9.81*0.48 = 1/2*2.4*v^2
    v = 3.06881084461 m/s

    Unfortunately, this seems to be incorrect.
     
  2. jcsd
  3. Oct 4, 2014 #2

    Simon Bridge

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    Welcome to PF;
    How do you know the answer is incorrect?
    Some of the rope is falling, but some of the rope is lifting. How did you account for the work done lifting part of the rope?

    The behavior is not kinematic - since the acceleration will not be constant.
    You can, however, use Newton's laws or conservation of energy to set up a differential equation.
     
    Last edited: Oct 4, 2014
  4. Oct 5, 2014 #3

    ehild

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    I do not see any figure.

    ehild
     
  5. Oct 5, 2014 #4

    haruspex

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    As I understand the term, kinematics concerns the geometry of motion, such as the movement of linkages. It does not concern itself with forces, energy, etc.
     
  6. Oct 5, 2014 #5

    Simon Bridge

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    Fersure - constant acceleration is a subset of kinematics, which is, strictly, the geometry of motion.

    Kinematics at the secondary education level, is usually given as the geometry of motion where acceleration is a constant.
    That is the level I was answering at - leaving OP to contradict me if I got it wrong. I suspected that OP did not want to use the suvat (or kinematic) equations. Probably should have been more careful.
     
  7. Oct 5, 2014 #6

    ehild

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    from Encyclopedia Britannica.


    ehild
     
  8. Oct 5, 2014 #7
    My apologies. Here's the image.
     

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  9. Oct 5, 2014 #8

    Simon Bridge

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    Cool - that's what I figured: what about the questions in post #2?
     
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