Tarzan swings across a river (centripical force)

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SUMMARY

The problem involves calculating the maximum mass Tarzan can have while swinging across a river on a 10.0 m vine at a speed of 8.0 m/s, given the vine's breaking strength of 1.0 x 10^3 N. The centripetal force equation, Fc = (mv^2)/r, is essential for this calculation. Additionally, Tarzan's weight (mass x gravity) must be factored into the total forces acting on him during the swing. The solution requires balancing the centripetal force with the gravitational force and the tension in the vine.

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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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