{"id":7394,"date":"2022-08-01T16:29:55","date_gmt":"2022-08-01T16:29:55","guid":{"rendered":"https:\/\/physics.educour.in\/isc-physics\/?p=7394"},"modified":"2022-08-03T03:53:22","modified_gmt":"2022-08-03T03:53:22","slug":"elastic-and-inelastic-collision","status":"publish","type":"post","link":"https:\/\/physics.educour.in\/isc-physics\/elastic-and-inelastic-collision\/","title":{"rendered":"Elastic and Inelastic Collision"},"content":{"rendered":"\t\t
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Collision of Bodies<\/strong><\/span><\/h1>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Contents:<\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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  1. What is collision?<\/a><\/li>
  2. Types of collision<\/a><\/li>
  3. Elastic collision<\/a><\/li>
  4. Inelastic collision<\/a><\/li>
  5. One Dimensional collision or Head on collision<\/a><\/li>
  6. Elastic collision in one Dimension or Head on elastic collision<\/a><\/li>

  7. Inelastic collision in one Dimension or Head on Inelastic collision<\/a><\/p><\/li>

  8. Perfectly Inelastic Collision in One Dimension<\/a><\/p><\/li>

  9. Two Dimensional Collision or Oblique Collision<\/a><\/p><\/li>

  10. Important Theorem on Inelastic Collision<\/a><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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    COLLISION<\/strong><\/span><\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    <\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    When two bodies (or particles), either physically strike against each other or if the path of the motion of one is influenced by the other, Collision is said to occur between the two bodies.<\/em><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    For a collision it is not necessary that the bodies are actually coming in contact. Only condition is that they must apply force on each other such that their motion changes suddenly.<\/p>

    When two bodies collide, they exert interacting forces on each other. These interacting forces are always equal and opposite (Newton\u2019s 3rd<\/sup> Law). So, if we consider the two bodies together as a system, total linear momentum of the system must remain conserved in every type of collision.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    <\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    There are two types collision:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    <\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    Elastic Collision:<\/strong><\/span><\/h3>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    The type of collision in which total Kinetic energy of the system of bodies remain same before and after collision, it is known as elastic collision.<\/p>

    So, in case of elastic collision total momentum and the total kinetic energy of the system (the two bodies together) remain constant.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    • In case of elastic collision all the interacting forces acting between the two bodies are conservative in nature.<\/li>
    • The collisions between the atomic, nuclear and fundamental particles are elastic collisions.<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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      <\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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      Inelastic Collision:<\/strong><\/span><\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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      The type of collision in which total Kinetic energy of the system of bodies doesn\u2019t remain same before and after collision, it is known as inelastic collision.<\/p>

      So, in case of inelastic collision only the total momentum of the system (the two bodies together) remains constant.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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      • Most of the collisions occurring between two bodies around us are examples of inelastic collision.<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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        <\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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        One dimensional collision or Head \u2013 on collision<\/strong><\/span><\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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        When two particles that make collision move such that before and after collision their center of mass move on the same straight line, it is called one \u2013 dimensional collision or head on collision.<\/span><\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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        During collision the two bodies apply force on each other according to Newton’s third law and\u00a0<\/p>

        \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\"\"\u00a0.<\/span><\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 If we consider both the bodies together as a system, the net external force on the system is zero. So, according to principle of conservation of momentum.<\/p>

        \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Pi<\/sub> = Pf<\/sub><\/span><\/strong><\/h3>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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        m1<\/sub>u1<\/sub> + m2<\/sub>u2<\/sub> = m1<\/sub>v1<\/sub> + m2<\/sub>v2<\/sub> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 — (i)<\/span><\/h4>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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        This equation is valid for every type of one-dimensional collision<\/strong>.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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        <\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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        Elastic collision in one Dimension or Head on elastic collision<\/strong><\/span><\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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        In case of elastic collision the total Kinetic energy of the system remains conserved i.e. for elastic collision total Kinetic energy of the system of bodies before collision remains same as its value after collision. So,<\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Ki<\/sub> = Kf<\/sub><\/h4>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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        \u00bd m1<\/sub>u1<\/sub>2<\/sup> + \u00bd m2<\/sub>u2<\/sub>2<\/sup> = \u00bd m1<\/sub>v1<\/sub>2<\/sup> + \u00bd m2<\/sub>v2<\/sub>2<\/sup>\u00a0 ———- (ii)<\/span><\/h4>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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        By \u00a0\u00a0 (i) \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0m1<\/sub> (u1<\/sub> – v1<\/sub>) = m2<\/sub> (v2<\/sub> – u2<\/sub>)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ———- (iii)<\/p>

        Similarly by (ii)\u00a0\u00a0\u00a0\u00a0\u00a0 m1<\/sub>u1<\/sub>2<\/sup> – m1<\/sub>v1<\/sub>2<\/sup> = m2<\/sub>v2<\/sub>2<\/sup> – m2<\/sub>u2<\/sub>2<\/sup><\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 m1<\/sub> (u1<\/sub>2<\/sup> – v1<\/sub>2<\/sup>) = m2<\/sub> (v2<\/sub>2<\/sup> – u2<\/sub>2<\/sup>) \u00a0\u00a0\u00a0\u00a0———- (iv)<\/p>

        By (iv) \/ (iii)\u00a0 \u00a0 \u00a0\u00a0\"\"\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (u1<\/sub> + v1<\/sub>) = (v2<\/sub> + u2<\/sub>)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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        u1<\/sub> – u2<\/sub> = v2<\/sub> – v1<\/sub>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 —-<\/strong>— (v)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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        In case of elastic collision in one dimension the velocity of approach before collision is equal to the velocity of separation of the bodies after collision.<\/span><\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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        by eq. (v).\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 v2<\/sub> = u1<\/sub> – u2<\/sub> + v1<\/sub><\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Putting the value of v2<\/sub> in eq. (i)<\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 m1<\/sub>u1<\/sub> + m2<\/sub>u2<\/sub> = m1<\/sub>v1<\/sub> + m2<\/sub> (u1<\/sub> – u2<\/sub> + v1<\/sub>)<\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 m1<\/sub>u1<\/sub> + m2<\/sub>u2<\/sub> = m1<\/sub>v1<\/sub> + m2<\/sub>u1<\/sub> – m2<\/sub>u2<\/sub> + m2<\/sub>v1<\/sub><\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 m1<\/sub>u1<\/sub> + m2<\/sub>u2<\/sub> = (m1<\/sub>+m2<\/sub>) v1<\/sub> + m2<\/sub> (u1<\/sub>-u2<\/sub>)<\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (m1<\/sub> – m2<\/sub>) u1<\/sub> + 2m2<\/sub>u2<\/sub> = (m1<\/sub> + m2<\/sub>) v1<\/sub><\/p>

        Or\u00a0 \u00a0\"\"<\/p>

        \u00a0<\/p>

        Again by (v), \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 v1<\/sub> = v2<\/sub> – u1<\/sub> + u2\u00ad<\/sub><\/p>

        Putting the value of v1<\/sub> in eq. (i)<\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 m1<\/sub>u1<\/sub> + m2<\/sub>u2<\/sub> = m1<\/sub> (v2<\/sub> – u1<\/sub> + u2<\/sub>) + m2<\/sub>v2<\/sub><\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 m1<\/sub>u1 <\/sub>+ m2<\/sub>u2<\/sub> = m1<\/sub>v2<\/sub> – m1<\/sub>u1<\/sub> + m1<\/sub>v2<\/sub> + m2<\/sub>v2<\/sub><\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 m1<\/sub>u1<\/sub> + m2<\/sub>u2<\/sub> = – m1<\/sub>u1<\/sub> + m1<\/sub>u2<\/sub> + (m1<\/sub> + m2<\/sub>) v2<\/sub><\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 2m1<\/sub>u1<\/sub> + (m2<\/sub> – m1<\/sub>) u2<\/sub> = (m1<\/sub> + m2<\/sub>) v2<\/sub>\u00a0<\/span><\/p>

        \"\"
        <\/sub><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t

        Special Case:<\/strong><\/span><\/h4>

        Case 1.<\/u><\/strong>\u00a0<\/span>\u00a0<\/h4>

        If both the bodies are of same mass<\/p>

        i.e. if \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 m1<\/sub> = m2<\/sub> = m (let)<\/p>

        By eq. (vi)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\"\"\u00a0 \u00a0\u00a0<\/span><\/p>

        Or,\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 v1<\/sub> = u2<\/sub><\/strong><\/p>

        And, by eq. (vii)\u00a0 \u00a0\"\"<\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Or,\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 v2<\/sub> = u1<\/sub><\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t

        The bodies exchange their velocities after collision if the bodies of same mass make elastic collision in one dimension.<\/em><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t

        Case 2.<\/u><\/strong><\/span>\u00a0\u00a0\u00a0<\/h4>

        If the bodies are of same mass and the second body is initially at rest.<\/p>

        i.e. if m1<\/sub> = m2<\/sub> = m (let); u2<\/sub> = 0<\/p>

        by eq. (vi)\u00a0 \u00a0 \u00a0\"\"\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/p>

        Or, \u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0v1<\/sub> = 0<\/strong><\/p>

        by eq. (vii)\u00a0 \u00a0 \u00a0\"\"\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/p>

        Or,\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 v2<\/sub> = u1<\/sub><\/strong>\u00a0<\/sub><\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t

        In this case the first body will come to rest and the second body will move with velocity of first body after collision.<\/em><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

        \n\t\t\t\t
        \n\t\t\t\t\t\t\t
        <\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t

        Inelastic collision in one Dimension or Head on Inelastic collision<\/strong>:<\/span><\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t

        When the kinetic energy of the system doesn’t remains conserved, the collision is called inelastic collision.<\/p>

        In case of inelastic collision there is loss in energy.<\/p>

        The loss in energy is<\/p>

        \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u0394K = Kf<\/sub> – Ki<\/sub><\/span><\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t
        \u0394K = (\u00bd m1<\/sub>v1<\/sub>2<\/sup> + \u00bdm1<\/sub>v2<\/sub>2<\/sup>) – (\u00bdm1<\/sub>v1<\/sub>2<\/sup> + \u00bdm2<\/sub>u2<\/sub>2<\/sup>)\u00a0\u00a0 \u2026\u2026\u2026.(viii)<\/span><\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
        \n\t\t\t\t
        \n\t\t\t\t\t\t\t
        <\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t

        Perfectly Inelastic Collision in One Dimension:<\/strong><\/span><\/h3>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t

        If after collision the two bodies stick to each other and move together after collision, then it is called perfectly inelastic collision.<\/p>

        In this case\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 v1<\/sub> = v2<\/sub> = V (let)<\/p>

        By eq. (i), we get\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 m1<\/sub>u1<\/sub> + m2<\/sub>u2<\/sub> = m1<\/sub>V + m2<\/sub>V<\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 m1<\/sub>u1<\/sub> + m2<\/sub>u2<\/sub> = V (m1<\/sub> + m2<\/sub>)<\/p>

        Or,\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\"\"<\/p>

        \u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

        \n\t\t\t\t
        \n\t\t\t\t\t\t\t
        <\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t

        Two Dimensional Collision or <\/strong>Oblique Collision<\/strong><\/span><\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t

        When the center of mass of the colliding bodies move in different directions in a plane before or after the collision, it is called two dimensional collision or oblique collision.<\/em><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t

        During oblique collision the two bodies apply interacting force on each other such that the direction of these forces is normal to the surfaces in contact. So, direction of the interacting forces \u00a0is different than their original direction of motion. As a result after the collision the two bodies move in different directions [let at angle \u03b81<\/sub><\/span> and \u03b82<\/sub><\/span>] with velocities\u00a0\"\"and\u00a0<\/span>\"\"\u00a0. If we consider the two bodies together as a system, there is no external force so, the total momentum of the system remains conserved.<\/span><\/p>

        \"\"
        <\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t

        along\u00a0 x – axis<\/u><\/strong><\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Pix<\/sub> = Pfx<\/sub><\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 m1<\/sub>u1<\/sub> + 0 = m1<\/sub>v1<\/sub> cos\u03b81<\/sub><\/strong><\/span> + m2<\/sub>v2<\/sub> cos\u03b82<\/sub><\/strong><\/span><\/p>

        Or, \u00a0 m1<\/sub>u1<\/sub> = m1<\/sub>v1<\/sub> cos\u03b81<\/sub><\/strong><\/span> + m2<\/sub>v2<\/sub> cos\u03b82<\/sub><\/strong><\/span> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 — (xi)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\t

        Along y – axis<\/u><\/strong><\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Piy<\/sub> = Pfy<\/sub><\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 = m1<\/sub>v1<\/sub>sin\u03b81<\/sub><\/span> + m2<\/sub>v2<\/sub>sin\u03b82<\/sub><\/span>\u00a0 —— (xii)<\/p>

        In case of elastic collision the total kinetic energy remains conserved<\/p>

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 i.e.\u00a0\u00a0 Ki<\/sub> = Kf<\/sub><\/p>

        \u00a0<\/sub>\"\"<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

        \n\t\t\t\t
        \n\t\t\t\t\t\t\t
        <\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
        \n\t\t\t\t
        \n\t\t\t\t\t\t\t\t\tOblique collision<\/a>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

        Collision of Bodies Contents: What is collision? Types of collision Elastic collision Inelastic collision One Dimensional collision or Head on collision Elastic collision in one Dimension or Head on elastic collision Inelastic collision in one Dimension or Head on Inelastic collision Perfectly Inelastic Collision in One Dimension Two Dimensional Collision or Oblique Collision Important Theorem … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"post_folder":[54],"class_list":["post-7394","post","type-post","status-publish","format-standard","hentry","category-11-lecture-notes"],"_links":{"self":[{"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/posts\/7394","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/comments?post=7394"}],"version-history":[{"count":223,"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/posts\/7394\/revisions"}],"predecessor-version":[{"id":7686,"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/posts\/7394\/revisions\/7686"}],"wp:attachment":[{"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/media?parent=7394"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/categories?post=7394"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/tags?post=7394"},{"taxonomy":"post_folder","embeddable":true,"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/post_folder?post=7394"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}