What is the angle at which the vine breaks in Tarzan's swinging problem?

AI Thread Summary
Tarzan swings from a 23.0 m vine, descending 3.2 m, with a weight of 688 N. The maximum tension in the vine is calculated to be 879 N, which exceeds the breaking point of 844.2 N, indicating the vine will break. To determine the angle at which the vine breaks, the velocity at different positions can be calculated using energy conservation principles. Understanding the dynamics of the swing and applying the relevant equations will help solve for the angle. The discussion emphasizes the importance of energy conservation in solving the problem.
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Homework Statement


Tarzan, who weighs 688 N, swings from a cliff at the end of a convenient vine that is 23.0 m long . From the top of the cliff to the bottom of the swing, he descends by 3.2 m. A) If the vine doesn't break, what is the maximum of the tension in the vine? B) The vine will break if the force on it exceeds 844.2 N. Does the vine break? If yes, at what angle does it break (if no enter 180. deg)?
(I already figured out part A)

Homework Equations


F=ma=mv^2/r=T-mg
and KEi+PEi=KEf+PEf

The Attempt at a Solution


Okay, so I figured out part A, and got an answer of 879 N, which is correct according to the online homework system. So, for part B, 879 N > 844.2 N, so the vine WILL break. I have no idea how to solve for the angle. Please help!

Also, sorry I spelled problem wrong in the title. Didn't notice it until I already posted it.
 
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Study the example from University Physics, 5th edition, page 102, attached.

You should be able to determine the velocity for any position using energy conservation. With that knowledge and an understanding of the example above you should be able to solve the problem.

Good luck!
 

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