Finding angle of rod hanging by springs

[TmrK]

Homework Statement

A uniform 1.4-kg rod that is 0.60 m long is suspended at rest from the ceiling by two springs, one at each end. Both springs hang straight down from the ceiling. The springs have identical lengths when they are unstretched. Their spring constants are 59 N/m and 39 N/m. Find the angle that the rod makes with the horizontal.

Torque and F_y is 0 since rod is in equilibrium,

Homework Equations

F=kx, where k is the spring constant and x is the distance of the spring itself
[itex]\tau[/itex]=Fl, where l is the lever arm.

The Attempt at a Solution

I tried to plug in the different equations, but I always keep getting blocked by the fact that the torque and F_y is 0.

 

[Sebastian H]

Hi
I'm not certain, but how about taking moments on each end, using that the force acting upwerds on each end will be the product of the Spring Constant and the displacement of each end.
Then subtract the difference in the displacements, and you'll be left with a triangle with 2 known sides.
I can make a calculated example if you want?

 

[technician]

If the rod is uniform and the supports at each end are vertical then the force in each support is the same.
Convert the mass of the rod into its weight in Newtons and you should be able to state the force in each support spring.
Use the spring constant to calculate how much each spring will extend.
The sloping rod connecting the springs is 0.6m long so you should be able to calculate an angle.