1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    gneill

    User Avatar

    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

    gneill

    User Avatar

    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.

    So:

    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?

    so

    v = √g*Lsinθ*tanθ

    v = 1.52234 m/s
     
  11. May 11, 2012 #10
    Yep!
     
  12. May 11, 2012 #11
    Got it right on my last try. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook