Energy cannot be created or destroyed in any transformation. This powerful accounting principle helps us analyze everything from particle collisions, to the motion of pendulums.

Consider a one dimensional collision between two point masses with different masses \(m_1\) and \(m_2\) and initial velocities \(v_1\) and \(v_2\). We define the ratio \(r\) as the ratio of the difference in initial velocities to the difference in final velocities:

\(r=\frac{|v_{1,i}-v_{2,i}|} {|v_{1,f}-v_{2,f}|}\).

What is \(r\) if the collision is perfectly elastic?

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