Simple Harmonic Motion with Linear Momentum

[lc99]

Homework Statement

Homework Equations

T = 2pi * sqrt(m/k)
mv =m2v2 (LM)[/B]

The Attempt at a Solution

[/B]
So T2 depends on the mass and not velocity. So i can find T2 = 2pi * sqrt([m/2]/k)

For A2 , i know that the amplitude before any collision is 1/2m1v1^2 = 1/2kA1^2
so solving that, i get v1 = A1 sqrt(k/m) .

I know that linear moment is conserved so i can find v2...
m1v1=m2v2 --> mv1 = m/2 * v2 --> v2 = 2v1 = 2A1sqrt(k/m)

With the new velocity, v2, i writing with energy conservation...

1/2mv2^2 = 1/2kA2^2, so i can find A2 in terms of v2... and substituting v2 in terms of A1 from above
solving for A2, i would get A2 = mv2^2 / k = A2^2 --> A2 = sqrt(2A1)


did i do this correctly?

 

[BvU]

I know that linear moment is conserved

That would mean transfer of momentum from the half mass removed to the half mass continuing. I don't read that in the scenario...

 

[lc99]

That would mean transfer of momentum from the half mass removed to the half mass continuing. I don't read that in the scenario...

so linear momentum isn't conserved?

 

[BvU]

Half the block is taken away, momentum included.

 

[lc99]

Half the block is taken away, momentum included.

I'm not sure what should be changed? How would i change my momentum equation?

 

[haruspex]

I'm not sure what should be changed? How would i change my momentum equation?

Consider the two halves of the block before and after separation. Before, each has momentum. If the separation does not involve any forces on them, what happens to each of the two momenta?