Further Mechanics: 2D Collisions

Principles of 2D Collisions

Momentum is conserved in collisions, which remains true even in a two-dimensional (2D) context.
To deal with a 2D problem, split it into two independent one-dimensional problems along perpendicular axes.

Types of Collisions

2D collisions can be either elastic or inelastic, like their 1D counterparts.
In an elastic collision, both momentum and kinetic energy are conserved.
In an inelastic collision, only momentum is conserved. The kinetic energy is not conserved due to factors such as heat, sound, or deformation.

Collision Calculations

When calculating 2D collisions, handle the x-direction and the y-direction separately.
Make use of the principle of conservation of momentum, where the total momentum before the collision is equal to the total momentum after the collision.
In an elastic collision, use the principle of conservation of kinetic energy along with the conservation of momentum to solve.

Problem Solving Techniques

Always draw a diagram to visualise the collision, indicating the velocities and directions before and after the collision.
Identify and define a coordinate system. This will help break down velocities into components.
Break down the initial and final velocities of the objects into their horizontal and vertical components.
Apply the conservation laws independently for the x and y-directions. Cross-check the calculations for any discrepancies.

Coefficient of Restitution

The coefficient of restitution in a collision is the ratio of speeds after and before an impact, along the line of the impact.
In 2D collision, the coefficient of restitution ‘e’ can be defined using the relative velocity of approach and separation along the line of impact. The formula is given as: e = (Relative Velocity after collision) / (Relative Velocity before collision).
For a perfectly elastic collision, the coefficient of restitution is 1, while for a perfectly inelastic collision it is 0. For most real-life scenarios the coefficient falls between these two values.