Physics spring/crate hits another spring problem

[MattNguyen]

Homework Statement

A crate of mass m = 0.29 kg is set against a spring with a spring constant of k1 = 581 N/m which has been compressed by a distance of 0.1 m. Some distance in front of it, along a frictionless surface, is another spring with a spring constant of k2 = 246 N/m.

(a) How far, d2 in meters, will the second spring compress when the crate runs into it?

(b) How fast, v in meters per second, will the crate be moving when it strikes the second spring?

(c) Now assume that the surface is rough (that is, not frictionless). You perform the experiment and observe that the second spring only compresses a distance d2/2. How much energy, in joules, was lost to friction?

Homework Equations

W=change in mech energy=Kf+Uf-Ki-Ui

The Attempt at a Solution

[/B]
I already calculated part a to be 0.1537. I just don't know how/if it relates to part b.

So far I have .5mv^2+.5kx=2.905 for part b. I'm just unsure what x is supposed to be or if I even set it up correctly.

 

[haruspex]

I'm just unsure what x is supposed to be

So am I. It's your equation.
First, I assume you meant x². Secondly, at the point in time indicated for part b, neither spring is under compression.

 

[MattNguyen]

Yeah, that's what I meant. The first spring is stretched, though, so I'm assuming it has potential energy.

 

[haruspex]

Yeah, that's what I meant. The first spring is stretched, though, so I'm assuming it has potential energy.

It does not say it is attached to the first spring, merely pushed against it.