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4:Linear Momentum - Coggle Diagram

- - - - \[e=1\]
    - - \[0\leq e\leq 1\]
    - - \[e=0\]
- - - - Properties
        
        Total energy is conserved
        
        Total kinetic energy is not conserved
        
        \[u_1=u_2\]
        
        Total linear momentum is conserved
    - - Properties
        
        Total kinetic energy is conserved
        
        \[u_1+v_1=u_2+v_2\]
        
        \[\frac12 m_1u_1^2+\frac12 m_2u_2^2=\frac12 m_1v_1^2+\frac12 m_2v_2^2\]
        
        Total linear momentum is conserved
        
        Total energy is conserved
      - Cases
        
        \[\textrm{When }u_2=0;m_1\ll m_2\]
        
        \[v_1\approx -u_1\]
        
        \[v_2\approx 0\]
        
        \[\textrm{When }u_2=0;m_1\gg m_2\]
        
        \[v_1\approx u_1\]
        
        \[v_2\approx 2u_1\]
        
        \[\textrm{When }m_1=m_2\]
        
        \[v_2=u_1\]
        
        \[v_1=u_2\]
        
        \[\textrm{When }u_2=0\]
        
        \[v_2=\frac{2m_1}{m_1+m_2}u_1\]
  - - - Total kinetic energy is not conserved
        
        \[v_1=v_2\]
      - Total linear momentum is conserved
      - Total energy is conserved