- #1

tobix10

- 7

- 1

## Homework Statement

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.

## Homework Equations

Virtual work, but I've done it with Newton's ## F = ma ##.

## 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?