Skip to main content
Physics LibreTexts

15.3: Characterizing Collisions

  • Page ID
    24517
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    In a collision, the ratio of the magnitudes of the initial and final relative velocities is called the coefficient of restitution and denoted by the symbol \(e\),

    \[e=\frac{v_{B}}{v_{A}} \nonumber \]

    If the magnitude of the relative velocity does not change during a collision, \(e = 1\), then the change in kinetic energy is zero, (Equation (15.2.21)). Collisions in which there is no change in kinetic energy are called elastic collisions,

    \[\Delta K=0, \quad \text {elastic collision} \nonumber \]

    If the magnitude of the final relative velocity is less than the magnitude of the initial relative velocity, \(e < 1\), then the change in kinetic energy is negative. Collisions in which the kinetic energy decreases are called inelastic collisions,

    \[\Delta K<0, \quad \text {inelastic collision} \nonumber \]

    If the two objects stick together after the collision, then the relative final velocity is zero, \(e = 0\). Such collisions are called totally inelastic. The change in kinetic energy can be found from Equation (15.2.21),

    \[\Delta K=-\frac{1}{2} \mu v_{A}^{2}=-\frac{1}{2} \frac{m_{1} m_{2}}{m_{1}+m_{2}} v_{A}^{2}, \quad \text { totally inelastic collision } \nonumber \]

    If the magnitude of the final relative velocity is greater than the magnitude of the initial relative velocity, \(e > 1\), then the change in kinetic energy is positive. Collisions in which the kinetic energy increases are called superelastic collisions,

    \[\Delta K>0, \quad \text {superelastic collision} \nonumber \]


    This page titled 15.3: Characterizing Collisions is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Peter Dourmashkin (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.