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Force required to hold a pendulum at an angle

  1. May 2, 2015 #1
    • Member advised about use of the homework template
    What is the minimum horizontal force "F" required to hold a simple pendulum (mass "m") with string of length "l" at an angle of 60 degrees with the vertical. [ given answer = mg/√(3) , veracity uncertain ]


    This at first seemed simple enough, standard mechanics apply, leading to :
    F/mg = tan(θ) where "θ" is the angle of the string from the vertical

    here:
    F/mg = tan(60)
    F = mg√(3)

    My second attempt, using the Law of Conservation of Energy, lead to this :
    Taking "mean" position of pendulum as the Origin and Assuming that bob is brought up -
    Final ( KE + PE ) (of bob) = Initial ( KE + PE ) + Work done on bob
    mgl(1-cos(60)) = 0 + Work done by Tension + Work done by F
    mgl(1-cos(60)) = 0 + 0 + F (l sin(60))
    mgl/2 = Fl √(3)/2
    F = mg/√(3)
    huh.
    Why would they give different solutions?
    I am assuming I did something wrong.
    I apologize if it is hard to understand, I have trouble conveying it without a diagram.
     
  2. jcsd
  3. May 2, 2015 #2

    ehild

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    That is the correct solution. It is not a process, no sense to apply conservation of energy.
     
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