Elastic vs Inelastic Collision: Key Differences Explained
Elastic collision is a fundamental concept in physics that explains what happens when two objects come into direct contact and exert forces on each other. In these encounters, the forces lead to a brief interaction, changing the motion of both bodies. Collisions are everywhere—from playing billiards to subatomic particle physics—and they are categorized as either elastic or inelastic, depending on the energy transformation involved.
What Is an Elastic Collision?
An elastic collision is a type of collision where the total kinetic energy of the system remains unchanged before and after the event. Both kinetic energy and linear momentum are conserved during such a collision. In real life, perfectly elastic collisions are extremely rare, as most objects lose a small part of kinetic energy to heat, sound, or deformation.
Yet, in idealized physics problems, elastic collisions are useful models for understanding conservation laws. Classic examples include two billiard balls rebounding off one another, or a tennis ball bouncing back after hitting a hard wall.
Elastic Collision: Formulas and Solved Example
To analyze elastic collisions, two fundamental conservation laws are used:
- Conservation of Momentum: Total momentum before collision = Total momentum after collision
- Conservation of Kinetic Energy: Total kinetic energy before collision = Total kinetic energy after collision
m1u1 + m2u2 = m1v1 + m2v2
(1/2)m1u12 + (1/2)m2u22 = (1/2)m1v12 + (1/2)m2v22
Let us understand with an example: Two billiard balls, each of mass 0.20 kg, are involved. The first ball moves at 6 m/s, the second is at rest. After an elastic collision, the first stops and the second moves.
- Initial momentum: 0.20 kg × 6 m/s = 1.2 kg·m/s
- After collision: 0.20 kg × v2 (since first ball stops)
- Setting momenta equal: 1.2 = 0.20 × v2, so v2 = 6 m/s
- Kinetic energy before: 0.5 × 0.20 × 62 = 3.6 J; after: 0.5 × 0.20 × 62 = 3.6 J
- Thus, both momentum and kinetic energy are conserved: this is an elastic collision.
Step-by-Step: How to Solve Elastic Collision Problems
| Step | Action | Purpose |
|---|---|---|
| 1 | Identify and write down values for masses (m1, m2) and velocities before (u1, u2) and after (v1, v2) collision | Clear variable setup |
| 2 | Apply conservation of momentum equation | Create first equation |
| 3 | Apply conservation of kinetic energy equation | Create second equation |
| 4 | Solve simultaneously for the unknown velocities | Find final results |
Key Elastic Collision Formulas
| Quantity | Formula | Description |
|---|---|---|
| Momentum (p) | p = m × v | Product of mass and velocity |
| Total momentum in collision | m1u1 + m2u2 = m1v1 + m2v2 | Sum before equals sum after |
| Kinetic Energy (KE) | KE = (1/2)mv2 | Energy due to motion |
| Conservation of kinetic energy | (1/2)m1u12 + (1/2)m2u22 = (1/2)m1v12 + (1/2)m2v22 | Before = After |
Elastic vs Inelastic Collision: What’s the Difference?
| Feature | Elastic Collision | Inelastic Collision |
|---|---|---|
| Total kinetic energy | Conserved | Not conserved |
| Momentum | Conserved | Conserved |
| Energy transformation | No conversion to other energies | Kinetic energy converted to other forms (heat, sound) |
| Occurrence in real life | Rare | Common |
| Example | Billiard balls, spacecraft flybys | Car crash, dough sticking to wall |
Applications of Elastic Collisions
Understanding elastic collision is important in physics and engineering. One application is in the design of car safety systems. The force experienced by objects in a collision is inversely related to the duration of the collision. Airbags increase the collision duration, reducing the force on passengers, thus minimizing injury.
Elastic collisions are also used to model subatomic particle interactions and in explaining the motion of gas molecules (kinetic energy and gas laws).
Practice More and Next Steps
- For more detailed explanations, visit Elastic Collision (Vedantu).
- Read about elastic and inelastic collisions and their equations in one and two dimensions.
- Revise conservation of momentum and energy concepts to strengthen your understanding.
- Apply your knowledge to practice problems to prepare for exams effectively.
Learning to distinguish between elastic and inelastic collisions is crucial in physics. Elastic collisions are characterized by the conservation of both momentum and kinetic energy, making them a key concept in understanding energy transfer during impacts and interactions in mechanics.
FAQs on Elastic Collision: Meaning, Equations & Solved Questions
1. What is an elastic collision?
An elastic collision is a collision in which both kinetic energy and momentum are conserved. In such collisions:
• The total kinetic energy before and after the impact remains the same.
• The objects bounce off each other without permanent deformation.
• No energy is lost to sound, heat, or other forms; all energy remains as kinetic energy.
• Examples include collisions between billiard balls and gas molecules.
2. What is the difference between elastic and inelastic collision?
The major difference is that elastic collisions conserve both kinetic energy and momentum, whereas inelastic collisions conserve only momentum.
Elastic Collision:
• Kinetic energy is conserved.
• Objects rebound after collision.
Inelastic Collision:
• Kinetic energy is not conserved (some energy transforms into other forms like heat or deformation).
• Objects may stick together (perfectly inelastic) or not fully rebound.
3. What is the formula for elastic collision?
The final velocities (v₁ and v₂) after a one-dimensional elastic collision between two bodies are:
• v₁ = [(m₁ - m₂)u₁ + 2m₂u₂] / (m₁ + m₂)
• v₂ = [(m₂ - m₁)u₂ + 2m₁u₁] / (m₁ + m₂)
Where:
• m₁, m₂ = masses of the two objects
• u₁, u₂ = initial velocities
• v₁, v₂ = final velocities after collision
4. Is momentum conserved in an elastic collision?
Yes, momentum is always conserved in elastic collisions. According to the law of conservation of momentum:
• Total initial momentum (before collision) = Total final momentum (after collision).
• This applies to all collisions, both elastic and inelastic.
5. Is kinetic energy conserved in an elastic collision?
Yes, the defining feature of an elastic collision is the conservation of kinetic energy.
• The total kinetic energy before the collision equals the total kinetic energy after the collision.
• No energy is lost to heat, sound, or deformation.
6. What is a real-life example of elastic collision?
Common real-life examples of nearly elastic collisions include:
• The collision between billiard or snooker balls
• The bouncing of a steel ball on a smooth steel floor
• Gas molecule collisions in kinetic theory (ideal gases)
7. How do you identify if a collision is elastic or inelastic?
To identify the type of collision, compare the total kinetic energy before and after:
• If kinetic energy is conserved, the collision is elastic.
• If some kinetic energy is lost (transformed into heat, sound, etc), it is inelastic.
Stepwise:
1. Calculate total initial kinetic energy.
2. Calculate total final kinetic energy.
3. If both are equal, the collision is elastic.
8. What is the coefficient of restitution for an elastic collision?
The coefficient of restitution (e) measures the degree of elasticity in a collision.
• For a perfectly elastic collision, e = 1.
• It is defined as:
e = (Relative speed after collision) / (Relative speed before collision)
• e = (v₂ - v₁)/(u₁ - u₂) (in one dimension)
9. Can perfectly elastic collisions occur in real life?
Perfectly elastic collisions do not exist in reality but can be closely approximated in certain cases.
• Real objects always lose some energy to sound, heat, or deformation.
• Collisions between gas molecules and billiard balls closely approximate elastic behavior.
10. How is the law of conservation of momentum used in solving elastic collision problems?
To solve elastic collision numericals, the law of conservation of momentum provides one equation:
• m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
1. Write down initial and final momenta for both objects.
2. Apply this law along with kinetic energy conservation to solve for unknowns.
11. What are the steps to solve a numerical on elastic collision?
Follow these steps for any elastic collision problem:
1. List all known values (masses and velocities).
2. Write the momentum conservation equation.
3. Write the kinetic energy conservation equation.
4. Solve the two equations simultaneously to find the final velocities.
12. What happens to the objects after an elastic collision?
After an elastic collision, the objects rebound and move apart without any loss in total kinetic energy.
• Their individual velocities change, but total momentum and kinetic energy remain the same.
• No permanent distortion or sticking together occurs.
