Elastic and inelastic collisions

1. Understanding Collisions

• In all collisions, momentum is conserved in a closed system.
• Kinetic energy $(KE)$ is not always conserved; it may be transformed into other forms (e.g. heat, sound, deformation).
• Two types of collisions:
  1. Elastic Collisions
  2. Inelastic Collisions

2. Differentiating Between Elastic and Inelastic Collisions

Elastic Collisions	Inelastic Collisions
Momentum is conserved.	Momentum is conserved.
Kinetic energy is also conserved.	Kinetic energy is not conserved (some energy is converted into heat, sound, or deformation).
Objects move separately after collision.	Objects may stick together after collision.
Example: Gas molecules colliding.	Example: Car crash, bullet embedding in wood.

• Momentum Conservation Equation (Applies to Both Types): $\sum p_{\text{initial}} = \sum p_{\text{final}}$

$where$ $p=mvp = mv.$

• Kinetic Energy Conservation (Only for Elastic Collisions): $\sum E_{\text{k initial}} = \sum E_{\text{k final}}$

$where$ $E_k = \frac{1}{2} m v^2.$

3. Steps for Solving Collision Problems

Step 1: Calculate total kinetic energy before collision

$E_k = \frac{1}{2} m v^2$

Step 2: Calculate total kinetic energy after collision

Step 3: Compare initial and final kinetic energy

• If $E_{k \text{ initial}} = E_{k \text{ final}} →$ Elastic Collision
• If $E_{k \text{ initial}} > E_{k \text{ final}} →$ Inelastic Collision

6. Key Takeaways

• Momentum is always conserved in a collision.
• Kinetic energy is only conserved in elastic collisions.
• If objects stick together after collision, it is inelastic.