Question

What are some examples of coefficients of restitution ?

Answer 1

Hint: To solve this problem learn the definition of coefficient of restitution and look around your surrounding environment, you will find thousands of examples regarding coefficient of restitution. Coefficient of restitution is the ratio of the relative velocity of two bodies in collision.

Complete answer:
We know that the coefficient of restitution is the ratio of relative velocities of the two bodies performing collision. We can also define it as the ratio of the difference of the final velocities of the two bodies to the difference between the initial velocities of the bodies in collision.
\[e = \dfrac{{{v_2} - {v_1}}}{{{u_1} - {u_2}}}\]
where, \[{v_2}\] is the final velocity of the second body, \[{v_1}\] is the final velocity of the first body, \[{u_1}\] is the initial velocity of the first body and \[{u_2}\] is the initial velocity of the second body.
The value of coefficient of restitution always lies between \[0 < e < 1\] for inelastic collision.For elastic collisions the value of coefficient of restitution is \[e = 1\] since it is an ideal collision.

Now, we see in our surrounding so many examples of coefficient of restitution, we can discuss here a few of them:
-When a ball drops from a height and hits the ground it performs inelastic collision and the height reached by the ball is lesser than the initial height due to the coefficient of restitution. In this type of collision one body is always at rest so the coefficient of restitution is the ratio of the final to initial velocity of the ball.
-When a Carrom player hits a puck with the striker the collision between the puck and the striker is inelastic, here also the coefficient of restitution is less than one.
-When two marble balls hit together the collision is inelastic and the coefficient of restitution is also here less than one.
-When a mud ball hits another mud ball gets stuck then the coefficient of restitution is zero since the final velocities of the bodies are the same.

Note: Definition Coefficient of restitution can also be given in terms of kinetic energy of the bodies. Due to collision in the real world the kinetic energy is not conserved due to loss through heat or sound energy or any other form of energy. The coefficient of restitution in terms of kinetic energy can be given as the square root of the final kinetic energy to the initial kinetic energy. \[e = \sqrt {\dfrac{{Final\,K.E}}{{Initial\,K.E}}} \].