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Raziel2701
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Homework Statement
A pendulum of length L is initially held horizontal, and is then released. The string runs into a peg a distance d below the pivot. What is the smallest value of d for which the string remains taught at all times?
Homework Equations
The Attempt at a Solution
I did a free body diagram for the mass when it's winding about the peg. I got [tex]T+mg=\frac{mv^2}{L}[/tex]
Then I used conservation of energy:
[tex]\frac{1}{2}mv^2 +mg(L-d)=mgL[/tex]
I solved for v^2 in the force equation and plugged into my conservation of energy equation to get my answer of:
[tex]d=\frac{1}{2}L(\frac{T}{mg} +1)[/tex]
Does that seem ok?