# Chain on a cone

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1. Oct 10, 2015

### tobix10

1. The problem statement, all variables and given/known data
A loop of flexible chain, of total weight W, rests on a smooth, frictionless right circular cone of base radius r and height h. The chain rests in a horizontal circle on the cone, whose axis is vertical. Find the tension in the chain.

2. Relevant equations
Virtual work, but I've done it with newton's $F = ma$.

3. The attempt at a solution
I considered a part of a chain that spread on an arch of angle $\Delta \theta$ (angle is very small) The forces $T$ on each end of arch exert horizontal force $2T \sin(\frac{\Delta \theta}{2})$ which has to be equalized by horizontal component $N_{x}$ of normal force.
Equations are:
$N_{x} = T \Delta \theta$
$N_{y} = W \frac{\Delta \theta}{2 \pi}$
$\frac{N_{x}}{N_{y}} = \frac{h}{r}$
Solution is:
$T = \frac{W}{2 \pi} \cdot \frac{h}{r}$

Is this answer correct? Any tips how to handle this problem using principle of virtual work?

2. Oct 12, 2015

### andrewkirk

Hello tobix and welcome to physicsforums.