Problem involving hookes law and friction

[guitarist2400]

This is a question my professor asked in class and I did not understand his explanation at all, I found your forums hoping someone would break it all down for me

[PLAIN]http://i28.lulzimg.com/0cb917f809.jpg

 

[Villyer]

I'm assuming you already know the answer, and you just need the methods explained more?This problems seems to be an energy problem.

The equations regarding energy are
E_s = kx²/2
E_k = mv²/2
E_g = mgh
Also, the concept that E = fd is helpful.To find velocity at the top, the only energy transfer occurring is from spring energy to kinetic energy.
If you set the equations for those two equal you can solve for v.

Velocity at the bottom is almost the same process.
The transfer of energy is from the velocity at the top and from gravity to velocity at the bottom (you can also set spring energy and gravity energy equal to the kinetic energy at the bottom).
Setting E_ki (or E_s) + E_g = E_kf will allow you to solve for v_f.

Distance the object travels with friction can be used with kinematic equations, if you solve for acceleration.
I find its easier to use energy, since you already will have solved for energy at the bottom (E_kf).
Since the friction will dissipate all of that kinetic energy before the object stops, you can use the E = fd with E being E_kf and F being uF_n.