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Pendulum with mass attached.

  1. Apr 19, 2013 #1
    1. The problem statement, all variables and given/known data
    A pendulum of mass "m" reaches a height "h" , while the length of the pendulum is R. If the R = 262 cm and h = 136 cm: (a) calculate the max speed in the x-direction.
    (b) calculate the max speed in the y direction.


    2. Relevant equations
    K = 1/2(m)(v)^2.
    U = mgh.
    Vector components.

    3. The attempt at a solution
    Calculating the max speed in the x direction is grand, it obtains a maximum value at the bottom of the arc so using conservation of energy you can calculate it to be v = sqrt(2gh). This is due to the vector components of the pendulum's velocity being v = vcos(θ)x + vsin(θ)y. The x-component obtains a max value when cos(θ) = 1 which occurs at θ = 0 (i.e. the bottom of the arc). Wouldn't the y-component then obtain a max value when θ = pi/2? This angle is never actually reached due to the bob only being raised through a height "h".
    So calculating the max velocity in the y is a little trickier. Could somebody give me some advice on what to do next? I'll attach a picture of the diagram.
     
  2. jcsd
  3. Apr 19, 2013 #2
  4. Apr 19, 2013 #3

    vela

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    You should be able to write down an expression for the potential energy of the mass as a function of ##\theta##. Using it, you can derive an expression for v as a function of ##\theta##.
     
  5. Apr 19, 2013 #4
    I'm not given θ though. Is there enough information given to find it?
     
  6. Apr 19, 2013 #5

    vela

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    ##\theta## is a variable that tells you where the pendulum is. It changes with time. Did you mean ##\theta_0##, the initial value of ##\theta##? You are, in fact, given enough information to find it, but I'm not sure why you'd need it.
     
  7. Apr 19, 2013 #6
    Ok, ok. I see what you're saying now. Misunderstood your first reply. Thanks!
     
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