# What happened to the work done by friction here?

Problem/Solution

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Question

What happened to the work done by friction BEFORE it touched the spring? Why was that neglected? Also they say there is no physical meaning behind the negative root, so what is the "unphysical" meaning behind the negative root? How are we supposed to know that the speed is constant before and just as it makes contact with the spring?

@atomSmasher

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I am referring to the green region. Shouldn't it be

$E_i = \frac{1}{2}mv_A ^2 - f_k(x_b + x_{green distance})$

$E_f = \frac{1}{2}kx_B ^2$

I realize we would have two unknowns then.

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