Question

(3p.) A m-ton railroad freight car collides with a stationary caboose car. They couple together and 50% of the initial kinetic energy is dissipated as heat. Find the mass M of the caboose.

Please Write clearly and do not skip steps.

Answer 1

Since both cars are coupled after collision, So Using Momentum conservation:

Pi = Pf

Suppose mass of Caboose is M, and initial velocity of freight car is U, then

m*U + M*0 = (m + M)*V

V = m*U/(m + M)

Now also given that 50% KE is lost, So

dKE = KEi - KEf

Since dKE = (1/2)*KEi, So

(1/2)*KEi = KEi - KEf

(1/2)*KEi = KEf

(1/2)*[(1/2)*m*U^2 + (1/2)*M*0^2] = (1/2)(m + M)*V^2

Since V = (m*U)/(m + M), So

(1/4)*m*U^2 = (1/2)*(m + M)*[(m*U)/(m + M)]^2

(1/2)*m*U^2 = m^2*U^2/(m + M)

(1/2) = m/(m + M)

1*(m + M) = 2m

m + M = 2m

M = m

So Mass of caboose = Mass of freight car = m