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Homework Help: Pendulum speed given length and angle

  1. May 11, 2012 #1
    1. The problem statement, all variables and given/known data
    A circular pendulum of length 1.2 m goes around at an angle of 25 degrees to the vertical.

    Predict the speed of the mass at the end of the string. Use g = 9.8 m/s2.

    Answer in units of m/s

    2. Relevant equations

    1/2mv^2 = mgh
    h = L - Lcosθ

    3. The attempt at a solution

    I used the above formula doing:
    1/2mv^2 = mgh
    v = √2g(L - Lcosθ)
    Plug n' chug:
    v = √2*9.8*(1.2 - 1.2cosθ)
    v = 1.448 m/s

    I've seen variations of this problem before, but I'm not really sure what I'm doing wrong.
  2. jcsd
  3. May 11, 2012 #2


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    Staff: Mentor

    What's the difference between a "circular pendulum" and a regular "pendulum"? The difference will make all the difference :smile:
  4. May 11, 2012 #3
    How did you apply conservation of energy? :confused: There was an external force that made the pendulum start its circular revolutions from its initial state.

    As I see the problem, the pendulum is revolving about the vertical axis. Drawing a diagram will help :smile:
  5. May 11, 2012 #4
    To be honest I'm not really sure, I don't remember paying attention to pendulums too much. I'm assuming it also rotates/spins as it moves? Not sure what can I tie with that.

    Am I doing this problem the right way? But having that idea, maybe I should add rotational kinetic energy?:

    1/2mv^2 + 1/2IW^2 = mgh

    W = v/r

    Am I going on the right track?

    Initially, another idea I had was to use centripetal force: mv^2/r, and using force diagrams.
  6. May 11, 2012 #5


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    Staff: Mentor

    Your initial idea was a good one. Follow it up!
  7. May 11, 2012 #6
    The pendulum only revolves about the vertical axis.

    Try this out :smile:

    Edit : somehow gneill is way faster!
  8. May 11, 2012 #7
    I see, this was the way I saw it at first but I thought it's more complicated.


    Fx = Tsinθ = mv^2/r
    Fy = Tcosθ = mg

    T = mg/cosθ; plugging that in for Fx..
    mv^2/r = mgtanθ, so..

    v = √rgtanθ, where r = Length ? Not sure if I derived everything correctly.

    Assuming I did everything right, final answer came to be v = 2.3417 m/s.. though I tried that a long time ago but got it wrong.
  9. May 11, 2012 #8
    r is the radius of the horizontal circle where the pendulum is revolving. So, what component of the length will give you that?
  10. May 11, 2012 #9
    Would that be Lsinθ?


    v = √g*Lsinθ*tanθ

    v = 1.52234 m/s
  11. May 11, 2012 #10
  12. May 11, 2012 #11
    Got it right on my last try. Thanks!
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