# Finding the sag caused by a weight in an equilibrium?

1. Oct 4, 2015

### AObeid

1. The problem statement, all variables and given/known data
Hello there, this is my first thread here !
I've been trying to solve an exercise from my statics course and just couldn't get anywhere.
Basically it's a system of two springs connected by a rope, and each spring is attached to a cylinder (Both Cylinders have same mass).
The question is on question number 2 in the attached file, it requires that we calculate the sag caused by the two cylinders when they weigh 40N each.(Stiffness has been already calculated from question #1)
The attachment also views the lengths given by the problem
Here's a thumbnail of the problem

2. Relevant equations
Well it's equilibrium so no other equations than ΣF=0
Pythagorus in a right triangle
Hook's law T=k∇
Some trigonometry..

3. The attempt at a solution
I managed to solve easily question #1, basically from the length given and the sag caused by the cylinders, I calculated both the unstretched and the final length of one of the springs. Then I calculated the tension in that cylinder in terms of k, did summation of forces on the y axis and managed to find the stiffness.
But the problem is with the second question. Now First I calculated the displacement of the spring in terms of the sag s, the angles in terms of s (some pythagorus done there), then I applied equilibrium. Then I got to an equation involving only the unknown sag s but it was an equation of 4th degree so that sounded absurd..
Am I missing something here? Is there an easy way behind all the messy calculation that should be done here ?

2. Oct 4, 2015

### SteamKing

Staff Emeritus
It's very hard to say. All you have given us to work with is, "I must have done something wrong." You probably did, but we can't say for sure if you don't post your work.

BTW, it's "Pythagoras".

3. Oct 4, 2015

### AObeid

This is what I've done so far.. Question #2 of course.. Sorry not sure why it's rotated though ._.