Potential Energy of a spring problem

[LalaLapras]

Homework Statement

A spring with a spring constant of 2000 N/m is compressed 10.0 cm on a horizontal surface. Then a 1.00 kg object is attached to it and released. At the relaxed-length position of the spring, the mass leaves the spring and the table goes from very smooth to rough, with a coefficient of friction of 0.500. There is a wall 50.0 cm away from the release point. a) Determine whether the mass will make it back to the spring after one bounce off the wall, assuming it rebounds elastically with no speed loss off the wall. b) If it does make it to the spring, how far does it compress it? If it doesn't make it to the spring, where is its final location.

Homework Equations

U=kx^2 (potential energy for the spring, k being the spring constant)
Ff=uFn
KE= 1/2mv^2

The Attempt at a Solution

I first wrote down all the givens:

k=2000 n/m
Δx=-.1 m
m= 1.00 kg

Then, I wanted to find Ff
Ff=uFn
I needed to find Fn, so I knew that Fn=Fg
Fg= ma
Fg=(1.00 kg)(9.80)
Fg=Fn= 9.80 N
so i plugged that back into Ff
Ff=(.500)(9.80)
Ff=4.9 N

Then, I used the equ. Kei+Uei=Kef+Uef
Kei is zero, and I think Uef is zero, too, so Kef=Uei.
so,
1/2mvf^2=1/2kx^2
then, plugging in my values, I was hoping to solve for velocity. I got V=4.47 m/s

...but I don't know what to do after that. Any help would be super appreciated!

 

[JHamm]

You can't use conservation of energy in a problem with friction. Your first step is to find the potential energy of the spring which gives the kinetic energy of the mass just as it reaches the rough part of the table. Now friction will do work on the object, what will that do?