Question

A 28000 kg railroad freight car collides with a stationary caboose car. They couple together, and 20 percent of the initial kinetic energy is dissipated as heat, sound, vibrations, and so on. What is the mass of the caboose?

Answer 1

we have to conserve momentum:
initial p = final p
28000kg * u + 0 = (28000kg + M) * v
so u = (28000 + M)*v / 28000
and u² = (28000 + M)² * v² / 28000²

Initial KE = ½ * 28000kg * u² = 14000kg * u²
Final KE = ½ * (28000kg + M) * v² = 0.8 * Initial KE = 11200kg * u²
Substitute for u² and use k = 28000 for now:
½ * (k + M) * v² = 11200 * (k + M)² * v² / k² → (k + M) * v² CANCELS!
½ = 11200 * (k + M) / k²
k² = 22400 * (k + M) = 22400k + 22400M → replace k
28000² - 22400*28000 = 22400M
M = 7000 kg
hope it helps