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## Homework Statement

## Homework Equations

[tex]K_{1}[/tex]+[tex]U_{1}[/tex]+[tex]W_{nc}[/tex]=[tex]K_{2}[/tex]+[tex]U_{2}[/tex]

## The Attempt at a Solution

Using the above equation

1/2m[tex]v^{2}[/tex] + 0 + xmg[tex]\mu[/tex] = 0 + 1/2k[tex]x^{2}[/tex]

On the left side

When it hits the spring there is 0 potential because it has not yet compress the spring and it still remains on a horizontal surface. It has a kinetic energy and kinetic friction work

On the right side

I have 0 kinetic because it just finished compressing the spring and about to decompress so instead I get maximum potential energy.

So solving for K i get

[tex]\frac{mv^{2}+xmg\mu}{x^{2}}[/tex]

But according to the answer it does not depend on the variable X (distance compressed by spring)

So I'm not entirely sure I know where I made my mistake

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