The theory of colliding bodies
The principle used to solve these collision problems was first enunciated by Huygens and involves the existence of something called the Coefficient of Restitution .
Consider the problem of two balls of masses and sliding on a line (rolling involves a more complicated theory) with velocities and .
If they collide, then linear momentum is conserved.
i.e. the velocities and after collision satisfy
For balls moving in two or three dimensions, similar methods apply, except in those cases when a collision occurs between balls it is only the component of the relative velocity along the line of centres that is affected. The component perpendicular to the line of centres remains unchanged. Similar considerations apply if the collision is with a "wall" or a "corner".
Consider the problem of two balls of masses and sliding on a line (rolling involves a more complicated theory) with velocities and .
If they collide, then linear momentum is conserved.
i.e. the velocities and after collision satisfy
In addition the relative velocities before and after collision satisfy
The fact that is independent of the size of the relative velocties and only depends on the material of the balls is the underlying assumption of this model. It is at least a reasonable first approximation of what happens in practice.
For balls moving in two or three dimensions, similar methods apply, except in those cases when a collision occurs between balls it is only the component of the relative velocity along the line of centres that is affected. The component perpendicular to the line of centres remains unchanged. Similar considerations apply if the collision is with a "wall" or a "corner".