How Do You Calculate the Potential Energy in a Stretched Two-Spring System?

[jcfor3ver]

Homework Statement

The ends of two identical springs are connected. Their un-stretched lengths Lo are negligibly small and
each has spring constant k. After being connected, both springs are stretched an amount L and their free
ends are anchored at y = 0 and x = ±L as shown . The point where the springs are connected to each
other is now pulled to the position (x,y). Assume that (x,y) lies in the first quadrant


A. What is the potential energy of the two-spring
system after the point of connection has been
moved to position (x,y). Keep in mind that the unstretched length of each spring Lo is much less
than L and can be ignored (i.e., Lo << L).
Express the potential U in terms of k, x, y, and L

Homework Equations

Us=1/2k(deltax)^2

The Attempt at a Solution

So this is what I did. L_o is negligible as stated in the problem. So +or- L is my original length(Xi).
In order for the junction pt 1 of the spring to go from (+or-L,0) to somewhere in the first quadrant of (x,y), a force has to be applied that moves the spring from (+-L,0) to (positive x, positive y).

So, taking both x and y into account for this equation I got:
Us=1/2k((Xf-(+or-L))+(Yf-Yi))^2-------------and Yi=0 so we can disregard that from the equation. Does this seem correct? I feel a bit lost on this problem.

 

[Redbelly98]

The Attempt at a Solution

So this is what I did. L_o is negligible as stated in the problem. So +or- L is my original length(Xi).
In order for the junction pt 1 of the spring to go from (+or-L,0) to somewhere in the first quadrant of (x,y), a force has to be applied that moves the spring from (+-L,0) to (positive x, positive y).

So, taking both x and y into account for this equation I got:
Us=1/2k((Xf-(+or-L))+(Yf-Yi))^2-------------and Yi=0 so we can disregard that from the equation. Does this seem correct? I feel a bit lost on this problem.

You're sort of on the right track. Are you trying to figure out the length of each spring?

The Distance Formula from geometry is

D² = (x₁ - x₂)² + (y₁ - y₂)²​

(It looks like you were not remembering it correctly.)