I two object collide, and there is no loss of kinetic energy, the following relationship is true:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]{v'_1}{m'} + {v_1}{m}= {v'_2}{m'} + {v_2}{m} [/tex]

But also by conservation of energy,

[tex]{v'_1^{2}}{m'}/2 + {v_1^{2}}{m}/2= {v'_1^{2}}{m'}/2 + {v_1^{2}}{m}/2 [/tex]

[tex]{v'_1^{2}}{m'} + {v_1^{2}}{m} = {v'_2^{2}}{m'} + {v_2^{2}}{m} [/tex]

That means for any two mass, and velocities that share the relationship

[tex]{v'_1}{m'} + {v_1}{m}= {v'_2}{m'} + {v_2}{m} [/tex]

they also share this relationship

[tex]{v'_1^{2}}{m'} + {v_1^{2}}{m} = {v'_2^{2}}{m'} + {v_2^{2}}{m} [/tex]

which is obviously not true. Why is there a paradox?

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# Homework Help: Momentum and conservation of energy

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