Elastic Collisions in Two Dimensions: Successive Oblique Impacts

Elastic Collisions in Two Dimensions: Successive Oblique Impacts

Defining Oblique Collisions

• Elastic collisions involve two dimensions when the direction of velocity changes, referred to as oblique collisions.
• The direction of the post-collision velocity vector depends on the angle of incidence, much like light reflecting off a surface.

Conservation of Momentum

• Conservation of momentum is core to these scenarios, applied separately in the horizontal and vertical direction.
• The line along which the two colliding bodies move after collision is called the Line of Impact.

Coefficient of Restitution

• The coefficient of restitution applies to these collisions, where e = speed of separation / speed of approach.

Conservation of Energy

• The principle of Conservation of Energy implies the combined kinetic energy of the colliding objects remains the same pre and post-collision.

Oblique Bounce

• The physics of oblique bounces assumes a perfectly elastic collision.
• There is no loss of kinetic energy, any energy change is spent on deformation and then fully recovered.

Steps in solving oblique collision problems

• Resolve velocities of both bodies involved in the collision into components perpendicular and parallel to the surface.
• Apply the principle of conservation of momentum along the perpendicular direction to the line of impact.
• Apply the coefficient of restitution in the perpendicular direction (speed of separation = e * speed of approach).
• Combine the resolved velocities post-collision to calculate the final velocity vector.