Tarzan/vine physics problem on work/energy/power

[brnnpink4]

Homework Statement

Tarzan swings across a valley on a vine. The vine is 6m in length. Tarzan has a mass of 85kg. The angle that the vine makes with the vertical in his initial position is 15 degrees. What is his speed at the bottom of the wing? What is the tension of the vine at this point?

All help is appreciated!:)

Homework Equations

f=ma
p=mvcosx
PE-mgh
KE=.5mv^3
KE+PE+W=KEf+PEf

The Attempt at a Solution

KE=.5(85)v^2

PE=85(9.8)h

 

[jackarms]

Try conserving energy for part one: what energy is gained, and what energy is lost?

For the second part, it's an example of uniform circular motion, and you can make use of this equation:
a = \frac{v^{2}}{r}

 

[brnnpink4]

How would you figure out what energy is gained/lost??

 

[jackarms]

Just think about the situation: he starts from rest, and then starts swinging: that's kinetic energy gained. If energy is gained in the system, then that means that somewhere else energy is lost. That's in the potential energy lost when he loses elevation from where he starts to the bottom of the swing.

 

[brnnpink4]

So would you set kinetic energy and potential energy equal to each other and solve for v?

 

[jackarms]

Essentially, but remember that since the energies are changing, you need to find the changes in each of the energies, i.e. final - initial. Then sum those changes and set the result equal to zero (meaning energy is conserved).

 

[brnnpink4]

Ok I think I got it! Thank You!