Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

Physics for IIT JAM, UGC - NET, CSIR NET

Created by: Akhilesh Thakur

Physics : Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

The document Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev is a part of the Physics Course Physics for IIT JAM, UGC - NET, CSIR NET.
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Two-body collisions - general concepts

Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

No external forces. Collision via massless springs or other force type.

Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

 

1.1 Momentum exchange and impulse

During collision: internal force causes change of momentum Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

  •  Momentum conserved.

1.2 An off-axis collision in 2D

Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

 

Elastic collisions in the Lab frame

Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

Conservation of momentum: Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

Conservation of energy:Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

[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

Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

→ Relative speed before collision = Relative speed after

 

2.2 Special case in 1D where target particle is at rest

Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

Special cases:

Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

Example: Newton’s cradle

Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

  • If the balls are touching, the most general case is:
    Momentum after collision :Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev
    Energy after collision :Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev2 equations, 3 unknowns
  • The obvious solution: Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev
  • But other solution(s) possible:

Momentum : Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

Energy :Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

So why does the simple solution always prevail?


Relationship between speeds and angles

Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

 Note we can also do this via components of momentum :

Two Body Collisions in Lab Frame - Collisions, Classical Mechanics, CSIR-NET Physical Sciences Physics Notes | EduRev

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