How Does Friction Affect the Speed of a Block Hitting a Spring?

[bulldog23]

Homework Statement

A moving 1.3 kg block collides with a horizontal spring whose spring constant is 491 N/m.The block compresses the spring a maximum distance of 5.0 cm from its rest postion. The coefficient of kinetic friction between the block and the horizontal surface is 0.49.What is the speed of the block when it hits the spring?

Homework Equations

W_spring=1/2kx^2
KE=1/2mv^2

The Attempt at a Solution

I do not understand how to calculate the blocks velocity. Can someone help me out with this one?

 

[Chi Meson]

There is one more equation, having to do with the work done by friction.

Think energy:

What happens to the KE of the moving block? (Where does it "go"?)

 

[bulldog23]

Does the kinetic energy go against the friction force. So would it be F_fric=U_k*mgd?

 

[Chi Meson]

energy is energy, force is force. Energy doesn't "go against" force.

The work done by friction, is $$F_f d$$

And that is what I think you have written: $$W_f = \mu mgd$$

When the spring is at full compression, how much KE has been "lost"? Some of it has transformed (conserved as mechanical energy) and some has been dissipated (as heat). All energy has to be accounted for.

3 equations, put them together.

 

[bulldog23]

W_f=umgd
KE=1/2mv^2
W_spring=1/2kx^2

How do you relate these three equations to get a speed? That is what I am struggling with.