While working with problems on elastic collisions, I have come across this observation, that the elastic potential energy of a two-body system is the maximum when the relative velocity equals zero. In fact, the same applies when we are talking about a 2-block+spring system. Why is it so?

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Makenna Lin · Accepted Answer

In case you need some mathematical insight,Nothing specific to add but when you calculate the kinetic energy of a system(I will assume it to be a 2 body system but you can generalize) the Kinetic Energy at a given point of the system is given by:      1    2              m              t        o        t        a        l                  V          C      M        2    +      1    2        μ              V              r        e        l            2      where   μ is reduced mass:                     m        1                    m        2                            m        1            +              m        2            As total energy is constant you need to minimize kinetic energy to maximize potential energy, as       V          C      M       is constant, PE is max when       V          r      e      l       is 0.Or if you visualize the motion you may think that initially when the bodies collide, compression will take place -&amp;gt; They will move at equal velocity(max compression) -&amp;gt; the spring will regain its natural length.

Elastic potential energy during elastic collisions. Why is it so?

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