Question

A railroad freight car with mass 30,000 kg collides is moving in the +x direction at 2.00 m/s when it collides with a stationary caboose car. The two cars couple together, and move down the track at Vf. During the collision, 50.0% of the original kinetic energy is lost to thermal energy, sound, vibrations, and so on. Find the mass of the caboose in kg.

Answer 1

Answer: 30,000 kg.

Explanation:

Assuming no external forces can act during the collision, this means that the total momentum must be conserved, as follows:

mrf . vo = (mrf + mc) . vf = 30,000 kg . 2 m/s = 60,000 N.m. (1)

As we have two unknowns and only one equation, we need another one.

We are told that the final kinetic energy of the complete system (railroad freight + caboose) is half of the original, (due only to the railroad freight, as the caboose was originally at rest).

So, we can write the following equation:

½ (mrf + mc) vf2 = 0.5 (½ mrf . vo2) = 30,000 kJ (2)

Dividing both sides in (2) and (1), and solving for vf, we have:

vf = 1 m/s

Replacing in (1) and solving for mc, we finally get the following:

mc = 30,000 kg.

Step-by-step explanation: