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

A block of mass m = 4.30 kg slides along a horizontal table with speed v0 = 8.50 m/s. At x = 0 it hits a spring with spring constant k = 68.00 N/m and it also begins to experience a friction force. The coefficient of friction is given by μ = 0.200. How far did the spring compress when the block first momentarily comes to rest?

m=4.30 kg

v_{o}=8.50m/s

k=68.00N/m

μ=.200

x=?

2. Relevant equations

K_{f}-K_{i}=W

K=1/2mv^{2}

F_{s}=-kx

F_{fric}=μN_{f}

W=Fd

3. The attempt at a solution

First I found the work of the whole system (friction and spring forces) by using

K_{f}-K_{i}=W.

For the initial kinetic energy, I used

K=1/2mv^{2}=155J.

For the final kinetic energy, I used 0, because I'm measuring the distance after the mass came to a stop. So, plugging the numbers into the Work equation, I simply get

W=-155J

I'm pretty sure I'm on the right track so far?

Then, using

W=Fd (just multiplying the forcexdistance because both vectors are in the same direction)

I plugged in:

W=(-kx+μN_{f})x

I work it out to a quadratic by plugging the numbers in...

-68x^{2}+8.44366x+155=0

I solve then for x (using the quadratic root finder on my calculator, so I'm not screwing up the quadratic..), but both of the answers it gives me are incorrect..

What am I doing wrong? Help please!!

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# Distance spring decompresses when friction is involved

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