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Pendulum Problem with a twist

  1. Sep 28, 2004 #1
    Alright this is the problem, i hope i describe it so you can all understand it

    You start out holding the bob at and angle of 90 degrees (horizontal), with the string tight. Then release the bob, when the angle hits 0 degrees a fixed rod is placed somewhere between the top of the string and the bob. This cuts the lenght of the pendulum so that the pendulum now spins around the fixed rod

    At what spot on the string should the fixed rod be placed that will allow the bob to spin all the way around the fixed rod at least once

    By doing guess and check i concluded that it would be at exactly half way down the string to allow it to spin around the fixed rod

    But i cant figure out how you would figure it out

    i kno you use mg sin theta to find the PE i believe but i cant figure out what to do from there

    If you dont get my description i can prolly make a video to show what i mean
    Last edited: Sep 28, 2004
  2. jcsd
  3. Sep 28, 2004 #2


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    Science Advisor
    Homework Helper

    Try energy conservation!
  4. Sep 28, 2004 #3
    How? When the string reaches the bottom, the potenial energy is at 100%, and then starts to turn into KE in an equal ratio. But i dont see how i can apply it into the problem
  5. Sep 28, 2004 #4
    Alright i got an idea, since the length of the pendulum has been cut in half, (because of the fixed rod) half of the enegery from the original fall is used to get the bob back to horizontal with the x-axis, and the rest of the energy to get it around the bob past the y axis and around to a complete rotation

    If you set the fixed rod up at further down from the midpoint of the string, there is some energy left over

    and if you set the fixed rod about the midpoint of the string, there isnt enough energy to get it to go around it would stop at around a positive angle from the -x axis...

    does this make any sense or sound correct to u guys?
  6. Sep 28, 2004 #5

    Doc Al

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    Staff: Mentor

    This is incorrect.

    As Tide suggested, you will need to use conservation of energy. But be sure that the bob has enough energy at the top of its motion so that the string remains taut. (To find out how much energy is needed to keep the string taut, consider centripetal acceleration.)
  7. Sep 28, 2004 #6
    Alright, so theoretically, if the fixed rod is at halfway between the top of the string and bottom, when the string gets to horizonal with the fixed rod, 50% of the KE is transferred, right? That means theres 50% KE left, but that 50% is not enough to keep the string taut just enough to get it to the very top and then it would fall, correct?
  8. Sep 29, 2004 #7

    Doc Al

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    Staff: Mentor

    When the bob reaches half its original height, it will have half the KE it had at the bottom. And that is not enough to keep the string taut throughout the rest of the motion. When the string goes slack the bob will follow a parabolic path, so it won't even make it to the original height. (It's not being shot straight up: the string changes the bob's trajectory. So it will never make it to the original height if the rod is placed at the halfway point.)
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