Finding Length of a Pendulum from Kinetic Energy

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The discussion revolves around finding the length of a pendulum using its kinetic energy and potential energy. The user initially calculated the height from kinetic energy but struggled to connect it to the pendulum's length. They were guided to use the conservation of energy principle, equating maximum kinetic energy to potential energy at a height related to the angle θ. After recalculating, the user resolved their algebra mistake and found the correct values. The conversation emphasizes the importance of careful calculations in applying physics principles.
Dante Tufano
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Okay, so here's the question:

The figure below shows the kinetic energy K of a simple pendulum versus its angle θ from the vertical. The pendulum bob has mass 0.320 kg. What is the length of the pendulum?

W0353-N.jpg


Equations: KE=(mv^2)/2
U=mgh
x(t)=xmcos(wt+phi)

I solved for the height by setting the max kinetic energy equal to the max potential energy, and got .004783, but I have no idea how to use the position equation to find the max velocity or what to do after that. Could I please get some guidance?
 
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when the pendulum is in it's mean position, you know that the KE is maximum.

So, find the velocity there. Then use the conservation of energy principle assuming that that the pendulum bob rises to a height L(1-cosθ). substituting v in that equation you get

L(1-cosθ) is equal some value. You know θ when KE becomes 0 from the graph.
substitute that.
 
Okay, so I solve for the velocity using the max kinetic energy and have a max velocity of .3062 m/s. I set L(1-cosθ) equal to (KEmax/mg) and solved for L using the θ value .1. However, I got the wrong answer, so can I get any more clues as to what I'm doing wrong?
 
Sorry, I made an algebra mistake! The values came out write after I punched them in again. Thanks a lot!
 
oh, haha
happy to help. :smile:
 
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