Problem from AP French Special Relativity

[george2]

1.Hi!I need some help with the following problem:
A body of mass m1+dm is connected to a body of mass m2-dm by a spring of constant k and negligible mass.The system is at rest on a frictionless table.A burst of radiation is emitted by the first body and absorbed by the second changing the masses to m1 and m2.If the time of transit of the radiation is negligibly small compared to the period of oscillation show that the maximum extension of the spring is given by:x=cdm$$\sqrt{\frac{m_{1}+m_{2}}{km_{1}m_{2}}}$$



2. E=dm$$c^{2}$$, E=cp for the photon



3. I think that energy and momentum conservation are needed.However i don't know which are the initial and final moments for which i should apply energy and momentum conservation. This is not exactly a homework exercise as i use the book for self study, so any help will really be appreciated...

 

[tiny-tim]

A body of mass m1+dm is connected to a body of mass m2-dm by a spring of constant k and negligible mass.The system is at rest on a frictionless table.A burst of radiation is emitted by the first body and absorbed by the second changing the masses to m1 and m2.If the time of transit of the radiation is negligibly small compared to the period of oscillation show that the maximum extension of the spring is given by:x=cdm$$\sqrt{\frac{m_{1}+m_{2}}{km_{1}m_{2}}}$$
…
I think that energy and momentum conservation are needed. …

Hi george2!

Yes … and at the time of maximum extension, the relative velocity of the two masses will be zero, which gives you the extra equation you need.

 

[george2]

Thanks for your reply!
I already used the fact that the relative velocity of the two masses will be zero at the time of maximum extension although i forgot to write that in my previous post.However i didn't get the right result.I will try it again later and if i don't find where my error is i will scan my attempt of solution...

 

[george2]

I tried again but i didn't find the correct result...The fact that "the time of transit of the radiation is negligibly small compared to the period of oscillation" doesn't mean that the second mass has already absorbed the radiation by the time i apply energy conservation for the final moment?
Probably i write wrongly the conservation equations...could you write them?

 

[tiny-tim]

Probably i write wrongly the conservation equations...could you write them?

I could … but I'm not going to …

you write them!

 

[george2]

I tried once more and finally i solved the problem.Anyway, thanks for the help