Momentum Problem: Final Momenta, Kinetic Energies Compared

[Maiia]

Homework Statement

Two carts are put back-to back on a track. Cart A has a spring-loaded piston; cart B, which has twice the inertial mass of cart A, is entirely passive. When the piston is released, it pushes against cart B, and the carts move apart. How do the magnitudes of the final momenta p and the kinetic energies K compare?

Please tell me if my approach is correct, because I'm not very clear on momentum:
Well if the piston is pushing against Cart B, then its momentum would be bigger than Cart A because it has both a greater velocity and a greater mass and momentum= velocity * mass. The kinetic energies- wouldn't the KE of cart A be bigger because it has more PE?

 

[tiny-tim]

Please tell me if my approach is correct, because I'm not very clear on momentum:

Hi Maiia!

If there are no external forces, then momentum is always conserved.

 

[Maiia]

that means that momentum inital = momentum final and since momentum inital is zero than momentum final is zero which means that final momentum for both is zero?
hmm but if i use KE= 1/2mv^2 then the KE of cart B would be bigger...?

 

[tiny-tim]

that means that momentum inital = momentum final and since momentum inital is zero than momentum final is zero which means that final momentum for both is zero?

Yes … the total momentum is zero, so one velocity will be twice the other (which one? )

hmm but if i use KE= 1/2mv^2 then the KE of cart B would be bigger...?

Hint: KE = momentum times what?