What is the angle of a suspended rod supported by two springs?

[cegraves]

Homework Statement

A uniform 1.3-kg rod that is 0.71 m long is suspended at rest from the ceiling by two springs, one at each end of the rod. Both springs hang straight down from the ceiling. The springs have identical lengths when they are unstretched. Their spring constants are 57 N/m and 32 N/m. Find the angle that the rod makes with the horizontal.

Homework Equations

F_x=kx

The Attempt at a Solution

I tried to determine the difference in the lengths of the two stretched springs using the spring constants and the mass of the rod.
(1.3kg)(9.8m/s²)=(57N/m)(x), x=0.224m
(1.3kg)(9.8m/s²)=(32N/m)(x), x=0.398m

I used the difference, 0.174m, and the hypotenuse, 0.71m, to make a triangle and solve for the angle using the function sin^-1(0.174/0.71) to find the angle with the horizontal. The solution I got was 14.19^o, which was incorrect.

 

[ehild]

The springs share the weight of the road, so your equations are not true.

ehild

 

[cegraves]

Okay, so I divided the force due to gravity by 2 and worked through the problem and got the answer. I hadn't considered that the springs would share the restoring force. Thanks for the help!