Question

A railroad freight car of mass 3.24 ✕ 10^4 kg collides with a stationary caboose car. They couple together, and 21.0% of the initial kinetic energy is transferred to thermal energy, sound vibrations, and so on. Find the mass of the caboose.

Answer 1

First apply conservation of momentum -

m1v1 + m2v2 = mfvf

m1 = 32400 kg

v1 = velocity of freight car
m2 = mass of caboose
v2 = 0 (caboose was stationary)
mf = 32400 + m2
v2 = velocity of both cars after collision

So -

32400*v1 + 0 = (32400 + m2)vf

=> 32400*v1 = (32400 + m2)vf---------------------------------------------------------(i)

Again the second condition is 21 % of the initial kinetic energy is transferred to thermal energy etc.

so, percentage of final energy left = 100-21 = 79%

means -

Kf = 0.79Ki
½(32400 + m2)(vf)² = ½(0.79)(32400)(v1)²

=> vf^2 = [25596/(32400 + m2)]*(v1)²

=> vf = sqrt[25596/(32400 + m2)]*(v1)

put this values in (i)

32400*v1 = (32400 + m2)*sqrt[25596/(32400 + m2)]*(v1)

=> 32400 = (32400 + m2)*sqrt[25596/(32400 + m2)]

squaring both side -

1049760000 = (32400 + m2)*25596

=> m2 = 8613 kg.