# Force required to hold a pendulum at an angle

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1. May 2, 2015

### kabirtomer

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. May 2, 2015

### ehild

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