How Does a Hydro-Pneumatic Shock Absorber Respond to Impact in Thermodynamics?

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Homework Statement



A buffer at the end of a rail track consists of a hydro-pneumatic shock absorber. The gas chamber of the absorber has an cylindrical geometry consisting of a length of 800mm and 0.5 m diameter and a pressure of 5 bar. Calculate the final pressure and stroke if a 2 tonne train hits the buffer at 5 m/s

Answers: (408 mm, 8.12 bar)


Homework Equations



PV^gamma=C

The Attempt at a Solution



I've worked the initial volume to be 1.57m^3, but other than that I'm not sure how to go about the question. I'm assuming that the compression is adiabatic? Is this a correct assumption? Also how to I convert the momentum of the train into something I can use to calculate the answers?

Thanks for any help!
 
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Oh snap. Just realized I can turn it into kinetic energy haha, Ill try that