Arailroad 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.

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.

Explanation:

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