Momentum, Energy, and Spring problem

[eriadoc]

Homework Statement

A mass of .5kg is resting on a vertical spring with a force constant of 55N/m. A mass of .25kg is dropped from a height of 12 cm onto the larger mass and sticks to it. What is the amplitude of the resulting oscillations?

Homework Equations

p=mv; m_1v_1 + m_2v_2 = (Mtot)V_f; mgh=1/2mv^2 + 1/2kA^2
V^2=V_o^2 + 2ay

The Attempt at a Solution

I really have no idea how to solve this problem. The answer is 5.97cm, but nothing I came up with is even close to that.

I started off by calculating the initial compression of the spring, since there's a weight resting atop it. F=kx; came out to 8.9cm.

Next, I calculated the velocity of the falling mass as it strikes the resting mass, and got 1.5344 m/s.

Next, I used that velocity in my conservation of momentum calculation and found the velocity of the combined mass velocity to be .5115 m/s.

Finally, I did mgh = .5mv^2 = .5kA^2, and A comes out to 0.0845m, or 8.45cm.

I calculated the initial compression, but didn't use it, and I suspect that has something to do with this, but I just can't seem to wrap my head around it. Any assistance is greatly appreciated.

 

[Rick88]

I get x=6.97cm.

But you said it should be 5.97cm, right?

 

[eriadoc]

I get x=6.97cm.

But you said it should be 5.97cm, right?

This was a test question that I missed. The professor released the answer key so we could study for the final (which is this evening), and the answer is 5.97cm. At any rate, 6.97 was not a choice.

 

[Rick88]

Oh yeah, I made a mistake.
I'll look into it.

 

[eriadoc]

Appreciate it. several of my classmates are trying as well, but none of us seem to get it.

 

[grrrace]

find the final velocity of both masses together after the 250 hits the 750 and then use
.5mv^2 = .5kA^2

 

[grrrace]

oops I meant the .25kg hits the .5 kg

 

[eriadoc]

That did the trick, thanks! And now I understand what I was doing wrong. I was conserving energy as if it were an elastic collision, thus setting E_i to mgh and E_f to .5mv^2 + .5kA^2. I appreciate the help!