Find max mass regarding circular motion and tension

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Homework Help Overview

The problem involves Tarzan swinging across a river using a vine, with a focus on determining the maximum mass he can have without breaking the vine. The subject area includes concepts from circular motion and tension in physics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between tension, weight, and centripetal force. There are attempts to equate these forces to the breaking strength of the vine. Some participants question the assumptions made regarding Tarzan's velocity and acceleration.

Discussion Status

There is ongoing exploration of the problem, with some participants providing guidance on calculating centripetal acceleration and ensuring that the force does not exceed the vine's strength. Multiple interpretations of the problem are being discussed, but no consensus has been reached on the final answer.

Contextual Notes

Assumptions about Tarzan's velocity being constant are under discussion, and there is a lack of explicit equations provided in the original post. The breaking strength of the vine is a critical constraint in the problem.

freepancakes
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Homework Statement


This is the question straight from my worksheet...

Tarzan tries to cross a river by swinging a vine that is 10.0 m long. His speed at the bottom of the swing is 8.0 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 X 10^3 N. What is the largest mass Tarzan can have and make it safly across the river?


Homework Equations



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The Attempt at a Solution


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The tension T balances the weight mg and provides the required centripetal force mv^2/R both.
 
Find the centripetal force acting on Tarzan and his weight, and equate it to the breaking strength of the vine.
 
is the answer 15.625 Kg?
 
freepancakes said:
is the answer 15.625 Kg?
How did you get that answer. Please show.
 
First and foremost, you need to solve for centripetal acceleration of Tarzan. Also, we are assuming that Tarzan is traveling at a constant velocity, or else the centripetal acceleration is changing, in which the problem requires a lot more work, so I'll assume that Tarzan is traveling at a constant velocity throughout the swing.

In that case, centripetal acceleration is v^2 / R. v being the velocity, and R being the radius. I won't show you the work, but from there you solve for acceleration.

Now that you have your acceleration, we need to make sure that Tarzan's force on the rope does not exceed the vine's rated strength of 1.0 x 10^3. so ma < 1.0 x 10^3. m being Tarzan's mass and a being the centripetal acceleration of the Vine.

I think that's enough information for you to solve it.
 

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