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Conservation of Energy, pendulum problem

  1. Mar 12, 2013 #1
    1. The problem statement, all variables and given/known data

    To form a pendulum, a 0.092 kg ball is attached to one
    end of a rod of length 0.62 m and negligible mass, and the other
    end of the rod is mounted on a pivot. The rod is rotated until it is
    straight up, and then it is released from rest so that it swings down
    around the pivot.When the ball reaches its lowest point, what are
    (a) its speed and (b) the tension in the rod? Next, the rod is rotated
    until it is horizontal, and then it is again released from rest. (c) At
    what angle from the vertical does the tension in the rod equal the
    weight of the ball? (d) If the mass of the ball is increased, does the
    answer to (c) increase, decrease, or remain the same?

    2. Relevant equations

    ƩFy=> t-mgcosθ = ma
    a= (v^2/r) ---> t-mgcosθ = m*(v^2/r)

    Ki+Ui= Kf+Uf

    3. The attempt at a solution

    I have done part A and B already. But im struggling trying to figure out part C.

    I know, that they are asking at what angle, would t=mg(weight of the bob)

    so if we substitute t= mg in t-mgcosθ = ma, we get => mg-mgcosθ=m(v^2/r)

    in this step, the book calculated for velocity and then calculated the height.

    I sincerely dont know how to go about this problem.

    Im having trouble trying to find the height in order to apply it to the equation for conservation of energy.

    In the book solution, they solved it by first using Newtons second law to find V^2f . They didnt show how to solve for height.

    Please, can someone give an insight of possible ways i can approach this problem?

    Thank you in advance.
     
  2. jcsd
  3. Mar 12, 2013 #2

    mfb

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    Staff: Mentor

    The height above the pivot is just r*cosθ (or maybe -r*cosθ depending on your sign definition). As you know the initial height, you can calculate the height difference, which allows to get v as function of θ.
     
  4. Mar 12, 2013 #3
    Im sorry, I dont understand, Im bit more confused than i was before. Would you please elaborate a bit more? how do you the height above is that?
     
  5. Mar 12, 2013 #4

    mfb

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    Staff: Mentor

    Did you draw a sketch? You get the height via simple trigonometry, the expression depends on your definition of the angle θ.
     
  6. Mar 12, 2013 #5
    but isnt height= r(1-cosθ).
    where r=length of the cord?
     
  7. Mar 12, 2013 #6

    haruspex

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    Gold Member
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    It depends where you choose to measure the height from. Simplest is to measure it from the axis of rotation.
     
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