Swinging physics teacher problem

[leaf345]

Hey all, I was doing a physics question in preparation for an exam, but I can't seem to figure it out!

The question:

"Your favourite physics teacher who is late for class attempts to swing from the roof of a 24 metre high building to the bottom of an idential building using a 24 metre rope as shown. She starts for rest with the rope horizontal, but the rope will break if the tension force in it is twice the weight of the teacher. How high is the swinging physicist above level when the rope breaks?"

http://img65.imageshack.us/img65/4771/physics27gc.jpg

What I tried was:
Treat is as a centripetal force problem. Find the speed when T=2mg and W=mg. Once I find the speed, I can use conservation of energy to figure out what the height is. The problem is I don't know how to find speed! Any hints on how to figure out the Fnet when T=2mg and W=mg? Or am I doing this all wrong?

Also, just to make sure, in the equation F=[m(v^2)]/r, F stands for Fnet, correct?
If that's the case, then in the case of a rock attached to a string and being swung in a circle vertically:
http://img217.imageshack.us/img217/5808/centripital8en.jpg
Then the net acceleration and force is not directed towards the centre anymore, correct?

 

[Hootenanny]

Your well on your way, but don't forget to resolve the weight. So you have;

$$F_{net} = T - mg\cos\theta$$

Where $\theta$ is the angle the rope makes with the vertical. So as an overall equation you have;

$$T - mg\cos\theta = \frac{mv^2}{r}$$

Now, you can determine the velocity of the teacher at any point using conservation of energy.

 

[arunbg]

Obviously your favourite physics teacher isn't quite strong at physics.
Tarzan would have done better.

 

[mld]

hi.. i am working on the same problem.. however i can't figure it out, even with the help already given... any chance someone can post the complete solution?
thanks for the help!

 

[Hootenanny]

hi.. i am working on the same problem.. however i can't figure it out, even with the help already given... any chance someone can post the complete solution?
thanks for the help!

The forum rules prohibit the posting of complete solutions, however, we can help you through the problem if you show some effort. What have you attempted thus far? What are your thoughts/ideas?

 

[mld]

Ok, well working with what you gave us, I have gotten the equation down to:
T-mgcostheta=(mv^2)/r
2mg-mgcostheta=(mv^2)/r
2g-gcostheta=v^2/r
2(9.8)-9.8costheta=v^2/24

I'm not sure where to go from here. I know that the rope will break when the left side of the equation is equal to the right side, correct? I feel as if I'm a little out of my element here and any help would be great.

 

[Hootenanny]

Ok, well working with what you gave us, I have gotten the equation down to:
T-mgcostheta=(mv^2)/r
2mg-mgcostheta=(mv^2)/r
2g-gcostheta=v^2/r
2(9.8)-9.8costheta=v^2/24

I'm not sure where to go from here. I know that the rope will break when the left side of the equation is equal to the right side, correct? I feel as if I'm a little out of my element here and any help would be great.

Your on the right lines. See the hint in one of my earlier posts,

Now, you can determine the velocity of the teacher at any point using conservation of energy.