Work done by spring bringin block to rest

[bocobuff]

Homework Statement

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?

Homework Equations

delta K=W_net and W_net=W_spring+W_fric
delta K=K_f-K_i where K_f=0 because v_f=0m/s so delta K=-1/2mv_i²
W_fric=F_fk*deltaX where deltaX=X-X_e=X=0.09m because X_e=0 for spring at equilibrium
F_fk=mu_k*mg
m=2.3kg and g=9.8m/s²

The Attempt at a Solution

I believe I need to find W_spring so:
W_spring=-1/2mv_i² - W_fric
=-1/2mv_i² - mu_k*mgX
But I have no clue how to figure out how fast the block was moving initially, v_i?? I would use v_f²=v_i²+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.

 

[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.

 

[bocobuff]

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

 

[PhanthomJay]

As in W=F*deltaX?
So W_spring=F_spring*X
with F_spring=-kX?

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?

This means the W_spring would be negative but that makes sense right? Because the spring(system) is doing work to the block (the environment)?

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?