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17 April, 20:48

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.

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  1. 17 April, 22:26
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    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.
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