# Answer to Question #13430 in Mechanics | Relativity for harisha

Question #13430

A BALL A OF MASS m MOVING WITH A VELOCITY u1 collides HEAD ON WITH ANOTHER BALL B OF SIMILAR MASS MOVING WITH VELOCITY u2 . the COEFFICIENT OF RESTITUTION IS e . THE RATIO OF FINAL & INITIAL VELOCITIES OF THE BALL A IS

Expert's answer

The coefficient of restitution is given by

C = (Vb - Va) / (Ua - Ub)

for

two colliding objects, where

Va is the final velocity of the first object

after impact

Vb is the final velocity of the second object after impact

Ua

is the initial velocity of the first object before impact

Ub is the initial

velocity of the second object before impact

Let the ratio of final and

initial velocities of the ball A is x.

u1f = u1 * x

e = (u2f - u1f) / (u1

- u2) = (u2f - u1 * x) / (u1 - u2)

x = (u2f - e * (u1 - u2)) / u1.

C = (Vb - Va) / (Ua - Ub)

for

two colliding objects, where

Va is the final velocity of the first object

after impact

Vb is the final velocity of the second object after impact

Ua

is the initial velocity of the first object before impact

Ub is the initial

velocity of the second object before impact

Let the ratio of final and

initial velocities of the ball A is x.

u1f = u1 * x

e = (u2f - u1f) / (u1

- u2) = (u2f - u1 * x) / (u1 - u2)

x = (u2f - e * (u1 - u2)) / u1.

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