(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The ends of a relaxed spring of length L and force constant k are attached to two points on two walls seperated by a distance L. How much work must you do to push the midpoint of the spring up or down a distance of y?

2. Relevant equations

W = -1/2k(b^{2}-a^{2}) (after integration), moving from y=a to y=b

3. The attempt at a solution

I'm completely lost on this. The first thing that I notice is that when you push down on the midpoint of the spring, you form two right triangles. This leads me to believe that y will go from a value of zero to the value of F_{y}, where F is the downward force on the spring. So I made a force diagram and came up with summation of forces.

[tex]\sum[/tex]F_{x}= 0

w_{x}= 0

F_{x}= L/2

F_{x}= 0

[tex]\sum[/tex]F_{y}= 0

w_{y}= -mg

N = mg

F_{y}= -Fcos[tex]\theta[/tex]

w_{y}-N-F_{y}= 0

F_{y}= w_{y}-N = -2mg

I attempted to use the F_{y}value as b in the W = -1/2k(b^{2}-a^{2}) formula but this led me to a wrong answer. I then tried to put F_{x}into the equation, thinking that maybe I needed to get F_{y}from the net forces. This led me nowhere either (I was grasping at straws here).

I am obviously going about this the wrong way. Since it involves the work on a spring, I know that I must use the W = -1/2k(b^{2}-a^{2}) formula. I just have no idea how to get the value of b. What concept(s) am I missing here?

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# Homework Help: How much work to push a spring up/down a distance of y?

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