Two-body collisions - general concepts
No external forces. Collision via massless springs or other force type.
1.1 Momentum exchange and impulse
During collision: internal force causes change of momentum
1.2 An off-axis collision in 2D
Elastic collisions in the Lab frame
Conservation of momentum:
Conservation of energy:
[Note that the motion is in a plane, and the 2D representation can be trivially extended into 3D by rotation of the plane].
2.1 Elastic collisions in 1D in the Lab frame
→ Relative speed before collision = Relative speed after
2.2 Special case in 1D where target particle is at rest
Example: Newton’s cradle
So why does the simple solution always prevail?
Relationship between speeds and angles
Note we can also do this via components of momentum :