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Pendulum bobs

  1. Dec 2, 2012 #1
    1. The problem statement, all variables and given/known data

    Conservation of energy: looking for equations to solve the following

    2. Relevant equations

    A pendulum with length l = 0.50 m and with a negligible mass. The string is attached to a fixed point A and the pendulum swings in a vertical plane.

    The pendulum has a speed v = 2.15 m s–1 at the lowest point of its swing.

    I need to work out the pendulums speed at intervals so 10,20,30,40 degrees


    3. The attempt at a solution
    I have already calculated the time period of the swing to T = 2 pi sqrt l/g, which means T= 1.59s, also the height of the swing from lowest point to end is 0.49m

    Any help would be great, thanks
     
  2. jcsd
  3. Dec 2, 2012 #2

    Doc Al

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    Why not use conservation of energy.
     
  4. Dec 2, 2012 #3
    How would i use it to get the speeds at intervals though?
     
  5. Dec 2, 2012 #4

    Doc Al

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    Figure out the height of the pendulum at each of those points.
     
  6. Dec 2, 2012 #5
    I've already worked out the swing heights at any given interval, its the speed in m/s i need.
    Thanks
     
  7. Dec 2, 2012 #6

    Doc Al

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    How would you express conservation of mechanical energy for the pendulum?
     
  8. Dec 2, 2012 #7
  9. Dec 2, 2012 #8
    v=SQRT(2*KE/m).
     
  10. Dec 2, 2012 #9

    Doc Al

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    OK, that how to get velocity from KE.

    What's an expression for the total energy of the pendulum?
     
  11. Dec 2, 2012 #10
    E = mgL[1 - cos(θ0)] ?
     
  12. Dec 2, 2012 #11

    Doc Al

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    That will give you the gravitational PE, measured from the lowest point.

    What's the total energy?
     
  13. Dec 2, 2012 #12
    Sorry i dont know
     
  14. Dec 2, 2012 #13

    Doc Al

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    Look up total mechanical energy (and conservation of energy) in your textbook.
     
  15. Dec 2, 2012 #14
    Tme = pe + ke
     
  16. Dec 2, 2012 #15

    Doc Al

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    Good!

    That's conserved as the pendulum moves.
     
  17. Dec 2, 2012 #16
    Ok so now what - total mech en = pot en + kin en
    What step do i take next?
     
  18. Dec 2, 2012 #17

    Doc Al

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    Energy is conserved. It remains constant:

    E1 = E2

    PE1 + KE1 = PE2 + KE2

    Let position 1 be the lowest point; position 2 being any other position you need to solve for.
     
  19. Dec 3, 2012 #18
    How do i get the speed from that equation though?
     
  20. Dec 3, 2012 #19

    Doc Al

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    Once you have the KE at each point, then you can get the speed using KE = 1/2mv^2. (See the equation you showed in post #8.)
     
  21. Dec 3, 2012 #20
    But i still have no figure for Mass so i cannot calc - KE = 1/2mv^2
     
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