Maximum Tension in Vine for Tarzan and Jane Pendulum

[estie]

Homework Statement

Tarzan stands on a branch as a leopard threatens. Fortunately, Jane is on a nearby branch of the same height, holding a 25-m long vine attached directly above the point midway between her and Tarzan. She grasps the vine and steps off with negligible velocity.If Jane and Tarzan are initially 8.0 m apart in the figure and Jane's mass is 60 kg, what is the maximum tension in the vine?
http://session.masteringphysics.com/problemAsset/1034229/5/RW-13-54.jpg

Homework Equations

torque=force_{perpendicular}xradius
net torque= torque_gravity+ torque_tension

The Attempt at a Solution

maximum tension occurs at the bottom of the swing.
i think at that moment, torque is zero.
so with the pivot point at the top of the vine, 0=-4T+2mg
where T=force of tension.
i get 297.8 N.
is this correct?

 

[rl.bhat]

If Jane just hangs on the vine the tension in the nine will be 60*9.8 N. When she swing, the tension must be greater than the above value.
First of all what is the vertical distance Jane's initial position to the point of mid way.
From that you can find Jane's velocity at mid way. That will lead you to find the maximum tension in the vine.

 

[estie]

thank you.
okay then, i get the vertical distance to be 25-$$\sqrt{}609$$.
would i use kinematics to find the velocity midway?
and after i do find velocity, how would that help me find tension?

 

[rl.bhat]

.
okay then, i get the vertical distance to be 25-$$\sqrt{}609$$.
?

This is wrong.
In h is the vertical displacement of Jane, then using geometry you can write
4*4 = (50 - h)*h
Solve for h.
Using mgh = 1/2*m*v^2, find v^2.
Then maximum tension on the vine = mg + M*V^2/R

 

[estie]

how did you get the equation for the vertical distance?
nevertheless, i get 2925 N.
however, the program I'm using tells me it's wrong.

 

[estie]

even when i use geometry i get my original answer for the vert distance.
where did the number 50 come from?

 

[rl.bhat]

If you take a perpendicular bisector of a cord of length L, of a circle of radius R, it passes through center. Then larger section of the diameter is 2R - h and smaller section of the diameter will be h. The relation between them is (2R-h)*h = (L/2)^2. In the above problem 2R = 50 and L/2 = 4.

 

[estie]

thank you.
i get 2925 N.
however, the program I'm using tells me it's wrong.

 

[rl.bhat]

I am getting 603.3N. Is it correct?

 

[estie]

yes it is.
thank you!

 

[rl.bhat]

Have you solved it your self? Did you find where you had done mistakes?