Key Concepts of Inelastic Collisions

Inelastic collisions occur when objects collide and kinetic energy is not conserved, leading to deformation or sticking together. While momentum remains constant, some energy transforms into other forms, making these collisions common in everyday scenarios like car accidents and sports.

1. Definition of inelastic collisions

   • Inelastic collisions are interactions where kinetic energy is not conserved.
   • Momentum is conserved, but the total kinetic energy after the collision is less than before.
   • Objects may stick together or deform during the collision.

2. Conservation of momentum in inelastic collisions

   • The total momentum of a closed system remains constant before and after the collision.
   • Momentum is calculated as the product of mass and velocity (p = mv).
   • The equation for momentum conservation can be expressed as: m1v1 + m2v2 = m1v1' + m2v2', where primes indicate post-collision velocities.

3. Kinetic energy loss in inelastic collisions

   • Some kinetic energy is transformed into other forms of energy (e.g., heat, sound).
   • The kinetic energy before the collision is greater than the kinetic energy after the collision.
   • The loss of kinetic energy can be calculated using the formula: KE_loss = KE_initial - KE_final.

4. Perfectly inelastic collisions

   • A special case where two objects stick together after colliding.
   • Maximum kinetic energy is lost compared to other types of inelastic collisions.
   • The final velocity of the combined mass can be calculated using momentum conservation.

5. Coefficient of restitution

   • A measure of how elastic a collision is, defined as the ratio of relative velocities after and before the collision.
   • Ranges from 0 (perfectly inelastic) to 1 (perfectly elastic).
   • For inelastic collisions, the coefficient is less than 1, indicating some energy loss.

6. Calculating final velocity in inelastic collisions

   • Use the conservation of momentum to find the final velocity after the collision.
   • For two colliding objects, the formula is: v_final = (m1v1 + m2v2) / (m1 + m2) for perfectly inelastic collisions.
   • Ensure to account for direction when calculating velocities.

7. Center of mass in inelastic collisions

   • The center of mass of a system moves with a constant velocity if no external forces act on it.
   • The center of mass can be used to simplify calculations in collisions.
   • The motion of the center of mass before and after the collision remains unchanged.

8. Examples of inelastic collisions in real life

   • Car accidents where vehicles crumple and stick together.
   • Sports collisions, such as football tackles where players collide and fall together.
   • Clay or putty thrown together that sticks upon impact.

9. Difference between elastic and inelastic collisions

   • In elastic collisions, both momentum and kinetic energy are conserved; inelastic collisions conserve only momentum.
   • Elastic collisions typically occur at the atomic or molecular level, while inelastic collisions are more common in macroscopic interactions.
   • The behavior of objects post-collision differs significantly, with elastic collisions allowing for bounces and inelastic collisions resulting in deformation.

10. Impulse and force in inelastic collisions

    • Impulse is the change in momentum resulting from a force applied over time.
    • The impulse experienced during a collision can be calculated as: Impulse = Force × Time.
    • In inelastic collisions, the force can be large and acts over a short duration, leading to significant changes in momentum.