Successive Elastic Collisions in One Dimension (AS)

Basics of Successive Elastic Collisions

Successive collisions refer to a series of collisions involving more than two objects, where one object collides with another, which in turn collides with another, and so forth.
Elastic collisions are collisions in which both linear momentum and kinetic energy are conserved. The total momentum and total kinetic energy before the first collision equal the total momentum and total kinetic energy after the last collision.

In considering one-dimensional collisions, motion is along a straight line.
For a system of particles undergoing successive elastic collisions, the coefficient of restitution is the same for all collisions.
A key principle in analyzing successive elastic collisions is the conservation of momentum: the total momentum before the first collision equals the total momentum after the last collision.

Calculation often involves splitting the problem into separate collisions, applying the principles of conservation of momentum and kinetic energy separately for each collision.
The relative speed of separation and approach is used in the formula for the coefficient of restitution. Remember that these speeds should be calculated just before and just after each separate collision.
As per the conservation laws, velocity and momentum are calculated before and after every collision. These values are compared to determine if energy was conserved, thus confirming the collisions as elastic in nature.
Free body diagrams and vector calculations are invaluable resources when dealing with collisions, as they help in visualizing the problem and breaking it down into manageable steps.