A railroad freight car of mass 3.30 104 kg collides with a stationary caboose car. They couple together, and 16.0% of the initial kinetic energy is transferred to thermal energy, sound vibrations, and so on. Find the mass of the caboose.

Answer 1

Law of momentum applies:
Mf*Vi=(Mf+Mc)Vf and given is mass Mf.

Law of eneryg applies
1/2 Mf(Vi)^2*.84=1/2(Mf+Mc)Vf^2

In equation 1), solve for Vf
Vf=vi(Mf)/(Mf+Mc)
Put that in to the second equation.
1/2 Mf(vi)^2(.84)=1/2 (Mf+Mc)(vi*Mf/(Mf+Mc))^2

.84=Mf/(Mf+mc)

and solve for mc.