Title: 碰撞 (Collide (Skillet album))
Section: 非弹性碰撞

在“非弹性碰撞”中一部分动能转化为内能(U)。当物体在碰撞时发生变形或发热时，碰撞称为“非弹性的”。 两个守恒定律依旧生效:碰撞前:                              E                      k            i            n                          =                                                            m                                  1                                            ⋅                              v                                  1                                                  2                                                      2                                {\displaystyle E_{kin}={\frac {m_{1}\cdot v_{1}^{2}}{2}}}                      p        =                  m                      1                          ⋅                  v                      1                                {\displaystyle p=m_{1}\cdot v_{1}}  碰撞后:                              E                      k            i            n                          =                                                            m                                  1                                            ⋅                              v                                  1                                                  ′                                      2                                                              +                              m                                  2                                            ⋅                              v                                  2                                                  ′                                      2                                                                        2                          +        U              {\displaystyle E_{kin}={\frac {m_{1}\cdot v_{1}'^{2}+m_{2}\cdot v_{2}'^{2}}{2}}+U}                                p          ′                =                  m                      1                          ⋅                  v                      1                    ′                +                  m                      2                          ⋅                  v                      2                    ′                      {\displaystyle p'=m_{1}\cdot v_{1}'+m_{2}\cdot v_{2}'}  在完全非弹性碰撞中，尽可能多的动能部分转化为内能。因此两个物质在碰撞后“粘”在一起并按照相同的速度（见下                              v                      2                    ′                      {\displaystyle v_{2}'}  ）继续飞行。例如两个橡皮泥球在碰撞后互相粘在一起并按同一速度继续移动。碰撞后:                              E                      k            i            n                          =                                            (                              m                                  1                                            +                              m                                  2                                            )              ⋅                              v                                  2                                                  ′                                      2                                                                        2                          +        U              {\displaystyle E_{kin}={\frac {(m_{1}+m_{2})\cdot v_{2}'^{2}}{2}}+U}                                p          ′                =        (                  m                      1                          +                  m                      2                          )        ⋅                  v                      2                    ′                      {\displaystyle p'=(m_{1}+m_{2})\cdot v_{2}'}  依据动量守恒定律可微分:                              m                      1                          ⋅                  v                      1                          =        (                  m                      1                          +                  m                      2                          )        ⋅                  v                      2                    ′                −                  m                      2                          ⋅                  v                      2                                {\displaystyle m_{1}\cdot v_{1}=(m_{1}+m_{2})\cdot v_{2}'-m_{2}\cdot v_{2}}                                v                      2                    ′                =                                                            m                                  1                                            ⋅                              v                                  1                                            +                              m                                  2                                            ⋅                              v                                  2                                                                                    m                                  1                                            +                              m                                  2                                                                          {\displaystyle v_{2}'={\frac {m_{1}\cdot v_{1}+m_{2}\cdot v_{2}}{m_{1}+m_{2}}}}  依据能量守恒定律可计算内能                     U              {\displaystyle U}  :                                                                                                                                    m                                              1                                                              2                                                  ⋅                                  v                                      1                                                        2                                                                                              =                                                                            (                                              m                                                  1                                                                    +                                              m                                                  2                                                                    )                      ⋅                                              v                                                  2                                                                          ′                                                      2                                                                                                                2                                                  +                U                                                                                                                                m                                              1                                                              2                                                  ⋅                                  v                                      1                                                        2                                                                                              =                                                                                                    m                                                  1                                                                    +                                              m                                                  2                                                                                      2                                                  ⋅                                                                            m                                              1                                                                    2                                                                                    (                                              m                                                  1                                                                    +                                              m                                                  2                                                                                            )                                                  2                                                                                                                    ⋅                                  v                                      1                                                        2                                                  +                U                                                          {\displaystyle {\begin{aligned}{\frac {m_{1}}{2}}\cdot v_{1}^{2}&={\frac {(m_{1}+m_{2})\cdot v_{2}'^{2}}{2}}+U\\{\frac {m_{1}}{2}}\cdot v_{1}^{2}&={\frac {m_{1}+m_{2}}{2}}\cdot {\frac {m_{1}^{2}}{(m_{1}+m_{2})^{2}}}\cdot v_{1}^{2}+U\\\end{aligned}}}                      U        =                              1            2                          ⋅                                                            m                                  1                                            ⋅                              m                                  2                                                                                    m                                  1                                            +                              m                                  2                                                                    ⋅                  v                      1                                2                                {\displaystyle U={\frac {1}{2}}\cdot {\frac {m_{1}\cdot m_{2}}{m_{1}+m_{2}}}\cdot v_{1}^{2}}