Physics > Centre of Mass and Conservation of Linear Momentum > 9.0 Newton's law of restitution
Centre of Mass and Conservation of Linear Momentum
1.0 Introduction
2.0 Position of centre of mass of continuous bodies
2.1 Rod
2.2 Semicircular ring
2.3 Semicircular disc
2.4 Solid sphere
2.5 Hemispherical Shell
2.6 Rectangular Plate
2.7 Square Plate
2.8 Circular Plate
2.9 Solid Cone
2.10 Hollow Cone
2.11 Questions
2.12 Centre of mass of a rigid complex bodies
3.0 Centre of mass of the remaining portion
4.0 Laws of conservation of linear momentum
5.0 Variable Mass
6.0 Impulse
7.0 Collision
8.0 Types of collision
9.0 Newton's law of restitution
10.0 Head on elastic and inelastic collision
11.0 Collision in two dimension
12.0 Oblique collision
9.2 For collision in two dimension
2.2 Semicircular ring
2.3 Semicircular disc
2.4 Solid sphere
2.5 Hemispherical Shell
2.6 Rectangular Plate
2.7 Square Plate
2.8 Circular Plate
2.9 Solid Cone
2.10 Hollow Cone
2.11 Questions
2.12 Centre of mass of a rigid complex bodies
Coefficient of restitution $(e)$ is given as, $$e = \frac{{{v_{{2_{CN}}}} - {v_{{1_{CN}}}}}}{{{u_{{1_{CN}}}} - {u_{{2_{CN}}}}}}$$
So for collision in two dimension, component of the velocity along the common normal will be taken. Therefore for the given example, coefficient of restitution is, $$\begin{equation} \begin{aligned} e = \frac{{{v_{{2_{CN}}}} - {v_{{1_{CN}}}}}}{{{u_{{1_{CN}}}} - {u_{{2_{CN}}}}}} = \\ e = \frac{{{v_2}\cos \beta - {v_1}\cos \alpha }}{{{u_1}\cos \theta - {u_2}}} \\\end{aligned} \end{equation} $$
Note: The above derived coefficient of restitution $(e)$ is only for the above example.
For different collision different value of $e$ is obtained.
So, we can write the general equation of coefficient of restitution as, $$e = \frac{{{v_{{2_{CN}}}} - {v_{{1_{CN}}}}}}{{{u_{{1_{CN}}}} - {u_{{2_{CN}}}}}}$$