# Work done by spring bringin block to rest

1. Nov 4, 2008

### bocobuff

1. The problem statement, all variables and given/known data
A moving 2.3kg block collides with a horizontal spring whose spring constant is 258 N/m. The block compresses the spring a maximum distance of 0.09m from its rest position. The coefficient of friction (mu) between the block and the horizontal surface is 0.32. What is the work done by the spring in bringing the block to rest?

2. Relevant equations
delta K=Wnet and Wnet=Wspring+Wfric
delta K=Kf-Ki where Kf=0 because vf=0m/s so delta K=-1/2mvi2
Wfric=Ffk*deltaX where deltaX=X-Xe=X=0.09m because Xe=0 for spring at equilibrium
Ffk=muk*mg
m=2.3kg and g=9.8m/s2

3. The attempt at a solution
I believe I need to find Wspring so:
Wspring=-1/2mvi2 - Wfric
=-1/2mvi2 - muk*mgX
But I have no clue how to figure out how fast the block was moving initially, vi?? I would use vf2=vi2+2aX but I don't know the acceleration, a, of the block either. I think I could get it from one of the Forces but I don't know which? Any help to point me in the right direction would be greatly appreciated.

2. Nov 4, 2008

### PhanthomJay

The work done by a spring can be calculated from a well known equation that I'm guessing you've seen? Some of that other stuff is extraneous to the solution.

3. Nov 4, 2008

### bocobuff

As in W=F*deltaX???
So Wspring=Fspring*X
with Fspring=-kX?
This means the Wspring would be negative but that makes sense right? Because the spring(system) is doing work to the block (the environment)?

4. Nov 5, 2008

### PhanthomJay

you've got to be careful, this is not correct, you can't just say that work is F*X, where F = kX, because F is a variable force, which varies from 0 when the spring is uncompressed, to kX when compressed a length of X. You could say, then, that work is (F_avg)*X, but there is also another equation for the work done by a spring , that relates to its potential energy. Do you know that one?
A spring can do either positive work or negative work. The work is negative if the force exerted by the spring on the block is opposite to its displacement, and the work is positive if the force exerted by the spring on the block is in the same direction as the displacement. What's the case here?