Two particles of mass m, constrained to move along the circumference of a smooth circular hoop of equal mass m, are initially located at opposite ends of a diameter and given velocities #v_o#. The entire arrangement is located in gravity-free space?

Question

Their velocity just before the collision is?!

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Answer 1 · 2017-12-13T19:05:03

#v_p = sqrt7/3v_0#

Considering

#v_p = # particle velocity just before the impact.
#v_h = # hoop velocity at the impact and just before the impact.

#2mv_0 = 3mv_h#

Conservation of energy just before the impact

#2 xx 1/2 m v_0^2 = 1/2 m v_h^2 + 2 xx 1/2 m v_p^2#

Solving for #v_p# we obtain

#v_p = sqrt7/3v_0#