What Shape Does a Rope Between Two Points Take to Minimize Potential Energy?

[pimpalicous]

Homework Statement

My professor told me about this problem and I wanted to do it to practice for the test.

A rope attached to two fixed points A and B will take the shape that minimizes the potential energy. Find the shape of the curve.

Homework Equations

mgy

df/dy-d/dx(df/dy')=0

The Attempt at a Solution

The rope is an extended object and every point is at a different height. I started by considering the potential energy at one such point as dM*g*Y(x) where dM=row dx.

I was going to intergrate with

U=row*g$$\int y(x)*dx$$
then treat y(x) as my functional.

Am I on the right path?

 

[pimpalicous]

never mind, I got it.