- #1
ZetaOfThree
Gold Member
- 110
- 23
Homework Statement
A rope of mass ##m## forming a circle is placed over a smooth round cone with half angle ##\theta##. Find the tension in the rope.
Homework Equations
##\sum{F}=0##
The Attempt at a Solution
I know how to solve the problem, but I have another way that I think should work but it doesn't. I don't know why.
The way that this problem is done is to consider the tension on a small element spanning an angle ##\alpha## of the rope as shown in the following image:
My question is why do we have to consider a small element of the rope? Why can't we consider half of the rope (that is, an element of the rope spanning ##\alpha = \pi##)? Therefore, the tension acts on the rope as in the following figure:
This leads to the result $$T={m \over 4}g \cot{\theta}$$ What's going wrong?