Find max mass regarding circular motion and tension

[freepancakes]

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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[mukundpa]

The tension T balances the weight mg and provides the required centripetal force mv^2/R both.

 

[rl.bhat]

Find the centripetal force acting on Tarzan and his weight, and equate it to the breaking strength of the vine.

 

[freepancakes]

is the answer 15.625 Kg?

 

[rl.bhat]

is the answer 15.625 Kg?

How did you get that answer. Please show.

 

[reallybanana]

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.