1. Elastic Collision:
* Conservation of Momentum: The total momentum of the system before the collision equals the total momentum after the collision.
* Formula: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
* m₁ and m₂ are the masses of the objects
* v₁ and v₂ are their initial velocities
* v₁' and v₂' are their final velocities
* Conservation of Kinetic Energy: The total kinetic energy of the system remains constant.
* Formula: (1/2)m₁v₁² + (1/2)m₂v₂² = (1/2)m₁v₁'² + (1/2)m₂v₂'²
2. Inelastic Collision:
* Conservation of Momentum: This still holds true for inelastic collisions.
* Formula: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
* Loss of Kinetic Energy: Some kinetic energy is lost during an inelastic collision, typically as heat, sound, or deformation.
* Formula: You can calculate the energy loss by finding the difference in kinetic energy before and after the collision.
Important Notes:
* Vector Quantities: Momentum and velocity are vector quantities, meaning they have both magnitude and direction. You need to account for these directions in your calculations.
* Perfectly Inelastic Collision: This is a special type of inelastic collision where the objects stick together after the collision. In this case, their final velocities will be the same (v₁' = v₂').
Example:
Imagine a 1 kg ball (m₁) traveling at 5 m/s (v₁) collides head-on with a stationary 2 kg ball (m₂).
* Elastic Collision: To find the final velocities, you would use the two conservation equations above.
* Inelastic Collision: You would use the conservation of momentum equation, but you wouldn't have the conservation of kinetic energy equation.
Let me know if you want to work through a specific example or have more questions!
