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Pendulum Problem

  1. Apr 3, 2008 #1
    1. The problem statement, all variables and given/known data
    Calculate the maximum speed of 100g pendulum mass when it has a length of 100cm and an amplitude of 50cm.

    2. Relevant equations
    I think that Eg=mgh and Ek=0.5mv^2 are related to this problem.


    3. The attempt at a solution
    I'm not really sure how to start this problem as I don't know how to calculate the height for Eg. However I'm pretty sure that I need to use further on gh=0.5v^2 as mass cancels in this situation. Sorry that I cannot provide a full attempt, but I just don't understand part of the problem.
    I just tried to solve it again and that what I got:
    sqrt(g/L)
    =sqrt(9.8/1)
    =3.13

    v(max)=(.5)(3.13)
    =1.57 m/s
    Anything right?

    Thank you in advance.
     
    Last edited: Apr 3, 2008
  2. jcsd
  3. Apr 4, 2008 #2
    HINT:
    The speed of a simple pendulum is maximum at its center.
    Also ..

    v= -A * omega *cos(omega*t + phase angle ) [S.H.M. EQUATION]

    At center phase angle equals zero.
     
    Last edited: Apr 4, 2008
  4. Apr 4, 2008 #3

    Doc Al

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    Staff: Mentor

    Measure heights from the lowest point. Figure out the initial height of the mass by first figuring out its vertical distance from the support point: Consider the triangle whose hypotenuse is the length of the pendulum and whose base is the amplitude.

    Draw a diagram!
    That's what you need.
     
  5. Apr 4, 2008 #4
    So by I found out the vertical distance from the support point is 86.6cm, however it does not make sense, if the length is 100cm wouldn't the height at rest be the same?
    I can continue from here but I need explanation about the height.
    Thank you again
     
  6. Apr 4, 2008 #5

    Doc Al

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    Staff: Mentor

    Initially the mass is 86.6 cm below the support point. So how high is it above the lowest point? (How high is the support point?)
     
  7. Apr 4, 2008 #6
    I'm really sorry but I'm a bit confused about the wording, if the lowest point is 86.6cm then I just subtract this from 100cm therefore the height of the mass before it is released is 13.6cm? I just can't figure it out. Can you please give me a hint or some further explanation.
    Thank you for you patience.
     
    Last edited: Apr 4, 2008
  8. Apr 4, 2008 #7

    Doc Al

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    Staff: Mentor

    Exactly!

    If you are having a hard time visualizing this, draw a diagram showing the pendulum at its highest and lowest point.

    Note: The highest position of the mass is 86.6cm below the support, which means it is 13.4cm above the reference point.
     
    Last edited: Apr 4, 2008
  9. Apr 4, 2008 #8
    Alright! :D
    So now I need to calculate Eg at h=13.6cm Ek=0 before released.
    But how do I calculate the speed at the bottom?
     
  10. Apr 4, 2008 #9

    Doc Al

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    Staff: Mentor

    Use conservation of energy. You already gave the correct formula.
     
  11. Apr 4, 2008 #10
    Therefore Ek at the bottom will equal the same as Eg before release.
    Ek = 0.5mv^2
    Then I need to find v?
     
    Last edited: Apr 4, 2008
  12. Apr 4, 2008 #11

    Doc Al

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    Exactly.

    Mechanical energy is conserved, so Ek(1) + Eg(1) = Ek(2) + Eg(2). Since we measure Eg from the bottom level, Eg(2) = 0; that gives you:
    Eg(1) = Ek(2)
    mgh = 0.5mv^2
     
  13. Apr 4, 2008 #12
    Thank you very much! :smile:
     
  14. May 23, 2008 #13
    doc could you help me out here
    I am stumped... I just sent you a report on what data I have collected this far
     
  15. May 23, 2008 #14
    nope, got it now. But another note. How do I find the Acc. due to grav.???
     
  16. May 24, 2008 #15

    Doc Al

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    Staff: Mentor

    How does the period of a pendulum depend on its length and the acceleration due to gravity?
     
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