Pendulum Problem

  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. 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. Doc Al

    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. 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. Doc Al

    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. 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. Doc Al

    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. 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. Doc Al

    Staff: Mentor

    Use conservation of energy. You already gave the correct formula.
     
  11. 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. Doc Al

    Staff: Mentor

    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. Thank you very much! :smile:
     
  14. 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. nope, got it now. But another note. How do I find the Acc. due to grav.???
     
  16. Doc Al

    Staff: Mentor

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