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Homework Help: Conservation of Energy,pendulum question

  1. Jun 25, 2010 #1
    1. The problem statement, all variables and given/known data

    A pendulum consists of a mass on a 50 cm long string. It is being held stationary at a 30┬░angle with the vertical. After release, how fast will it be going at the bottom? (Hint: Use trigonometry to find how high the ball is initally)


    2. Relevant equations

    Ek = 1/2mv^2 for sure to find the velocity
    Eg = mgh


    3. The attempt at a solution
    I'm basically brain-dead on this question, I don't know where to start.
     
  2. jcsd
  3. Jun 25, 2010 #2
    Draw a diagram first, that always helps.

    Hint: Trigonometry, you're going to have to consider cos of the angle in this situation. It's like a force, you need to consider the vertical component of the string. In forces that would be the vertical force, but here it's the length.
     
    Last edited: Jun 25, 2010
  4. Jun 25, 2010 #3
    Yes, draw a diagram with both the initial position and the final postion(bottom-most).
    Then find the height difference between the two positions. It will be a function of the angle.
    And then apply energy conservation.
     
  5. Jun 25, 2010 #4
    So basically I've had a go on the question with the help of the previous posts:
    [PLAIN]http://img532.imageshack.us/img532/6052/physicsi.png [Broken]

    So to find the left side of the triangle (lets say n):

    50 x cos30 = n
    n = 43.3

    The string is 50cm
    50 - 43.3 = 6.70 cm
    x = 6.70cm
    =0.0670m

    Since Ep @ top = Ek @ bottom
    m x 9.80 x 0.0670 = 1/2mv^2, m's cancel out I think?

    0.6566 = 1/2v^2
    sqrt 1.3132 = sqrt v^2
    1.15 m/s = v

    I'm not sure about the significant digits, but this is how I tried to solve the question, can anyone confirm the answer?
     
    Last edited by a moderator: May 4, 2017
  6. Jun 25, 2010 #5
    Assuming your arithmetic is all correct that looks to be correct, and yes for this relationship your mass is negligible.

    Joe
     
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