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Sorry I've got so many questions lately. Studying for a midterm right now. Anyway, I've been trying to solve problems involving springs, and I'm getting confused about calculating the work done by a spring when its initial state is already in compression.

The question: A 3-kg block rests on top of a 2-kg block supported by but not attached to a spring with k = 40N/m. The upper block is suddenly removed. Determine the maximum velocity and the maximum height of the 2-kg block.

I figured that the maximum velocity would occur before the block flew off the spring, and probably before it returned to its unstretched length.

In equation: T1 + U1->2 = T2

[tex]U1->2 = 1/2k(x1)^2 - 1/2k(x2)^2 [/tex], where x1 and x2 are measured from the unstretched length of the spring.

I calculated x1 = 1.22625 m. So:

[tex]0 + 30.07 J - 1/2k(x2)^2 = 1/2mv^2[/tex]

Taking the derivative and setting it to zero:

-k(x2)=0, which isn't correct. How am I supposed to approach this problem? I think my equation for work done by the spring is incorrect, but I don't know what it is supposed to be.

Thanks in advance!

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# Homework Help: Work Done by a spring

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