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Mass in circular motion. Draw Diagram and find/explain variables.

  1. Nov 7, 2011 #1
    1. The problem statement, all variables and given/known data
    A ball of mass m is held by a string of length L and swung in a horizontal circle. The string makes an angle θ with the vertical (as shown).
    a. Draw a diagram clearly labeling all forces on the mass.
    b. Find T, the amount of time that it takes for the ball to complete one circle in terms of m,L, g, and θ.
    c. When θ increases, what happens to T? Justify your answer.

    http://imageshack.us/photo/my-images/97/circularmotion.png/"

    2. Relevant equations
    None Given.


    3. The attempt at a solution
    I had many attempts but none seemed to work out.
     
    Last edited by a moderator: Apr 26, 2017
  2. jcsd
  3. Nov 7, 2011 #2

    PeterO

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    Perhaps you could put any one of those attempts here.
     
    Last edited by a moderator: Apr 26, 2017
  4. Nov 7, 2011 #3
    Last edited by a moderator: Apr 26, 2017
  5. Nov 7, 2011 #4

    PeterO

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    You have drawn 4 forces - but two of them are actually one of the forces resolved to allow later calculation, so should not be there. there are only two forces acting, gravity, down, and Tension at an angle.

    For me to comment on the accuracy of you expression for T, I would need to see the steps you used to derive it.
    Certainly you interpretation that if θ increases, T would decrease is valid for the expression you gave.
     
    Last edited by a moderator: Apr 26, 2017
  6. Nov 7, 2011 #5
    Ok. So
    Fx = Fsinθ = ma_rad
    Fy = Fcosθ - mg = 0 (no vertical acceleration)
    a_rad = (4R∏^2)/T^2
    R = Lsinθ

    F = mg/cosθ Sub into Fx
    (mg/cosθ)*sinθ = ma_rad
    a_rad = gtanθ

    gtanθ = (4R∏^2)/T^2

    T = √((4R∏^2)/gtanθ) = 2∏√(R/(gtanθ)) Sub in Lsinθ for R
    T = 2∏√(Lcosθ/g)
     
  7. Nov 7, 2011 #6

    PeterO

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    That looks good, so you should be correct.

    Certainly I know that the period decreases as the angle increases, so it is good that your formula predicts that.
     
    Last edited: Nov 8, 2011
  8. Nov 8, 2011 #7
    I agree strongly with PeterO.
    There are only 2 forces acting on the object (if friction, air resistance can be ignored!!!)
    1) the tension T in the string
    2) The weight (mg) acting vertically down
    The tension has a vertical component which equals the weight of the object and a horizontal component which equals the centripetal force.
    It is not wise to show these component forces on a diagram..... they confuse the picture and give the appearance that there are too many forces acting.
     
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