Tarzan swings across a river (centripical force)

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To determine the largest mass Tarzan can have while safely crossing the river, the centripetal force equation (Fc = mv²/r) must be applied, considering the vine's breaking strength of 1.0 x 10^3 N. Tarzan's weight, which is the product of his mass and gravity, also needs to be factored into the calculations. The total tension in the vine combines the centripetal force required for the swing and the gravitational force acting on Tarzan. By balancing these forces, the maximum mass can be calculated without exceeding the vine's breaking strength. Understanding the interplay of these forces is crucial for solving the problem effectively.
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Homework Statement



Tarzan tries to cross a river by swinging from one bank to another on a vine that is 10.0 m long. His speed at the bottom of the swing , just as he clears the surface of the river, is 8.0 m/s. Tarzan does not know that the vine has a breaking strength of 1.0x10^3 N. What is the largest mass that Tarzan can have and still make it safely across the river? HINT: Don't forget about the effect of Tarzan's weight

m = 10 m

v = 8.0 m/s

F = 1.0 x 10^3 N

Homework Equations



Centripical Force:

Fc = (mv^2)/r

The Attempt at a Solution



I plug everything in but.. the hint gets me confused. I don't know how to include Tarzan's weight ( mass x gravity )
 
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So there are three forces: one that is keeping him going in a circle (centripetal force), another that always pulling him down (gravity), one that keeps the vine from traveling down with Tarzan (tension).
 
http://www.davis.k12.ut.us/staff/ryahne/files/CD4CE3A0784E44B7B861B5697821B99A.pdf
look at 38 :3
 
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