Two particles with masses 5 m and 5 m are moving toward each other along the x a

Question

Two particles with masses 5m and 5m are moving toward each other along the x axis with the same initial speeds vi. The particle with mass 5m is traveling to the left, and particle 5mis traveling to the right. They undergo a head-on elastic collision and each rebounds along the same line as it approached. Find the final speeds of the particles.

particle 5m vi particle 5m   
. vi

Two particles with masses 5m and 5m are moving toward each other along the x axis with the same initial speeds vi. The particle with mass 5m is traveling to the left, and particle 5mis traveling to the right. They undergo a head-on elastic collision and each rebounds along the same line as it approached. Find the final speeds of the particles.

Explanation / Answer

In head on elastic collision both momentum and kinetic energy are conserved

first apply conservation of momentum

initial total momentum=5m*Vi -5m*Vi (because they are moving in opposite directions)

=0

let their velocity be V1,V2 after collision

5m*V1+5m*V2=0

V1=-V2

this implies that the magnitudes of their velocities are same but their directions are opposite to each other

let the magnitudes of velocities be V

now apply conservation of kinetic energy

initial kinetic energy=5m*Vi^2 /2+5m*Vi^2 /2

=5m*Vi^2

final kinetic energy=5m*V1^2/2 +5m*V2^2 /2

=5m*V^2

5m*Vi^2=5m*V^2

so V=Vi

so final speeds (magnitude of velocity) of particles is Vi ,Vi

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