- #1
KleZMeR
- 127
- 1
Homework Statement
I am given the weight (force) of the rope as W. It sits on a cone about halfway down, with the cone's top angle ø. Radius at a given placement is r, and h is our height at a given placement.
I need to find the tension, T, in the rope.
Homework Equations
W=mg
Integral (F * dr) = 0
I am taking r to be along the x axis.
L = sqrt(r^2 + h^2)
X = L*cos(ø)
Y = L*sin(ø)
dX = dø*L*-sin(ø)
dY = dø*L*cos(ø)
The Attempt at a Solution
Expressing my equilibrium as:
T*L*dø*cos(ø)-m*g**dø*L*-sin(ø) = 0
I get: T = W*tan(ø)
This seems over simplified? Or am I over-thinking it? It's around a circle radius r and each element of T summed over the circle would be 2*pi*T but the gravitational force is also summed over 2*pi. Perhaps I skipped over the line integral of this? I am very interested in the correct integral setup of this problem because it looks like a future test question, and I also want to know how my 2*pi factor disappears (if it was ever present?) Any help is appreciated.
Last edited: