Elastic and inelastic collisions important points to understand about these topics

Here are the important points to understand about elastic and inelastic collisions:

• Elastic Collisions:

  • Momentum is conserved: The total momentum of the system before the collision is equal to the total momentum after the collision. $$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$$ where $m$ is mass, $u$ is initial velocity, and $v$ is final velocity.
  • Kinetic energy is conserved: The total kinetic energy of the system before the collision is equal to the total kinetic energy after the collision. $$\frac{1}{2} m_1 u_1^2 + \frac{1}{2} m_2 u_2^2 = \frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2$$
  • Objects bounce off each other without any loss of internal energy (e.g., heat, sound, deformation).
  • Often idealized; perfect elastic collisions are rare in macroscopic systems but common at the atomic/subatomic level.

• Inelastic Collisions:

  • Momentum is conserved: Just like elastic collisions, the total momentum of the system before the collision is equal to the total momentum after the collision. $$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$$
  • Kinetic energy is NOT conserved: Some of the initial kinetic energy is converted into other forms of energy, such as heat, sound, or deformation of the objects. $$\frac{1}{2} m_1 u_1^2 + \frac{1}{2} m_2 u_2^2 \neq \frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2$$
  • Perfectly Inelastic Collisions: A special case where the colliding objects stick together and move as a single unit after the collision. In this case, they share a common final velocity ($v_1 = v_2 = v_{final}$). $$m_1 u_1 + m_2 u_2 = (m_1 + m_2) v_{final}$$
  • Most real-world collisions (e.g., car crashes, a ball of clay hitting a wall) are inelastic.