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Eugen
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Homework Statement
A ball of mass m is attached to a string of length L and released from rest at point A. Show that the tension in the string when the ball reaches point B is 3mg, independent of the length l. (there is an image in attachment )
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Homework Equations
K = mv2/2
U = mgh
Fcp = mv2/r
The Attempt at a Solution
The mechanical energy at point A must equal the mechanical energy at point B. h is the vertical distance between A and B.
So mv2/2 - mgh = 0 and v2 = 2gh
The net force acting on the ball at point B is the centripetal force, which is mv2/L and is equal with T - mg.
mv2/L = T - mg.
So T = mv2/L + mg.
T = 2mgh/L + mg
θ is the angle between the string and the vertical when the ball is at point A.
If I write h = L - Lcosθ I get to the equation T = mg(2 - 2cosθ + 1), which is 3mg only when θ is 90°. Something must be wrong.
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