Collinear Motion of two balls

Classical Mechanics Level pending

A ball A A moving with constant velocity V V strikes a stationary ball B . B. Both balls continue on in a collinear motion.

What can be said about the total kinetic energy of the system comprising of both balls A A and B ? B?

Assume that the balls are of equal masses.

The total kinetic energy increases after the collision None of the above Total kinetic energy is conserved, so it remains the same The total kinetic energy reduces after the collision

Srinivasa Gopal by Srinivasa Gopal , 53, India

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1 solution

Srinivasa Gopal
Aug 9, 2018

Let the Initial velocity of ball A be equal to V Let the Final velocity of Ball A and Ball B after collission be equal to V1 and V2 respectively.

Since momentum is conserved m V = m V1 + m*V2. Therefore V = V1+V2.

So let us compute initial Kinetic Energy as 0.5 m V^2

Final Kinetic Energy = 0.5m*(V1^2 + V2^2)

Since V = V1 + V2, initial kinetic energy can be written as 0,5 m (V1 + 2) ^ 2.

It can be very easily seen that the final Kinetic energy is greater than the initial kinetic energy by m V1 V2 and so the total energy of the system after collission reduces.

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