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Two identical particles of mass $m$ approach each other at equal and opposite speeds, $v$. The collision is completely inelastic and results in a single particle at rest. What is the mass of the new particle? How much energy was lost in the collision? How much kinetic energy was lost in this collision?

Source: Giancoli, Douglas C., Physics: Principles with Applications, 7th Edition, 2014.

Quick Answer: 

$M = \dfrac{2m}{\sqrt{1-\dfrac{v^2}{c^2}}}$
no energy is lost.
$\textrm{KE}_{lost} = 2mc^2 \left ( \dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}} - 1 \right )$

Giancoli 7th Edition, Chapter 26, Problem 43


Chapter 26, Problem 43 is solved.

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