Edexcel A Level (IAL) Physics-4.5 Elastic & Inelastic Collisions- Study Notes- New Syllabus
Edexcel A Level (IAL) Physics -4.5 Elastic & Inelastic Collisions- Study Notes- New syllabus
Edexcel A Level (IAL) Physics -4.5 Elastic & Inelastic Collisions- Study Notes -Edexcel A level Physics – per latest Syllabus.
Key Concepts:
- understand how to determine whether a collision is elastic or inelastic
Determining Whether a Collision Is Elastic or Inelastic
Collisions are classified by examining what happens to kinetic energy during the interaction. In all collisions (if external forces are negligible), linear momentum is conserved, but kinetic energy may or may not be conserved.
Key Definitions
Elastic collision:
- Total linear momentum is conserved.
- Total kinetic energy is conserved.
- Objects rebound without permanent deformation or energy loss.
Inelastic collision:
- Total linear momentum is conserved.
- Total kinetic energy is not conserved.
- Some kinetic energy is transformed into other forms (sound, heat, deformation).
Perfectly inelastic collision:
- Objects stick together after collision.
- Maximum loss of kinetic energy.
Using Kinetic Energy to Classify a Collision
Kinetic energy of a body is:
\( E_k = \dfrac{1}{2}mv^2 \)
Procedure:
- Calculate total kinetic energy before the collision.
- Calculate total kinetic energy after the collision.
- Compare the two values.
Decision:
- If total KE before = total KE after → collision is elastic.
- If total KE decreases → collision is inelastic.
Using Momentum and Kinetic Energy Together
Momentum must always be conserved:
\( \sum p_{\text{before}} = \sum p_{\text{after}} \)
But only elastic collisions also satisfy:
\( \sum E_{k,\text{before}} = \sum E_{k,\text{after}} \)
Important: Conservation of momentum alone does not prove a collision is elastic.
Coefficient of Restitution (Optional Diagnostic)
The coefficient of restitution \( e \) compares relative speeds before and after collision:
\( e = \dfrac{\text{relative speed of separation}}{\text{relative speed of approach}} \)
- Elastic collision: \( e = 1 \)
- Inelastic collision: \( 0 < e < 1 \)
- Perfectly inelastic collision: \( e = 0 \)
Practical Indicators
- Objects sticking together → perfectly inelastic.
- Noticeable sound or heating → inelastic.
- Rebound with little deformation → approximately elastic.
Example (Easy)
Two identical balls collide and stick together after impact. Is the collision elastic or inelastic?
▶️ Answer / Explanation
- Objects stick together.
- Kinetic energy is not conserved.
- This is a perfectly inelastic collision.
Example (Medium)
A \( 1.0\ \mathrm{kg} \) ball moving at \( 4.0\ \mathrm{m\,s^{-1}} \) collides with a stationary ball of mass \( 1.0\ \mathrm{kg} \). After collision, both move at \( 2.0\ \mathrm{m\,s^{-1}} \). Determine the type of collision.
▶️ Answer / Explanation
Initial kinetic energy:
\( E_{k,i} = \dfrac{1}{2} \times 1.0 \times 4.0^2 = 8.0\ \mathrm{J} \)
Final kinetic energy:
\( E_{k,f} = 2 \times \dfrac{1}{2} \times 1.0 \times 2.0^2 = 4.0\ \mathrm{J} \)
Conclusion:
- Kinetic energy decreased.
- Collision is inelastic.
Example (Hard)
Two particles collide and rebound. Measurements show total momentum is conserved and total kinetic energy before and after the collision is equal within experimental uncertainty. What type of collision is this?
▶️ Answer / Explanation
- Momentum is conserved.
- Kinetic energy is conserved.
- This satisfies the conditions for an elastic collision.