# Max tension of a chain

1. Sep 28, 2009

### djtsmith007

A chain is attached to the top of a vertical pole of height H located at x=0. The other end of the chain is attached to another pole of height H at x=a. Find the maximum tension T of the chain as a function of the length of the chain L. Assume that the weight density of the chain is \$ (lambda)

Last edited: Sep 28, 2009
2. Sep 29, 2009

### tanujkush

Well, how I would go about it is this:

Take a infinitesimally small portion of the chain say at some x, of length dx and do a free body diagram of this. You should end up with a differential equation which you can then
1. integrate to find out the tension at each point in the chain and thus find the max.
OR
2. Find dT/dx from the equation you found and set it to zero, you'll get some value for the angle. That is your position of max tension.

I havent solved this yet, but intuition tells me the max tension should be somewhere near the point of application.