What is the equilibrium position of a ball attached to two springs?

[tony873004]

A small ball of mass M is attached t two identical springs of constant k, which are attached to the floor and the roof. The springs have unstretched lengh L/2. At what position will the ball remain at rest?

The back of the book gives the answer.
$$\frac{1}{2}L(1+\frac {Mg}{kL})$$

But the text doesn't do a good job explaining how to arrive at that answer. I've stared at it for 20 minutes. Any thoughts?

 

[Doc Al]

When the ball is exactly in the middle (at L/2) what forces do the springs exert on it? And at a point a distance X beneath that middle point? What does X have to be so that the net spring force balances the ball's weight?

 

[dextercioby]

Okay draw the forces...Apply Newton's second law.And then use the fact that the body is equilibrium.

The answer in the book gives the body-ceiling distance...


Daniel.