Inelastic Collision Formula and Step-by-Step Problem Solutions
Inelastic collisions are a fundamental part of the study of mechanics in physics. In such collisions, when two or more objects collide, the total momentum of the system is always conserved. However, a portion of the kinetic energy is not conserved due to transformations into other forms of energy like heat, sound, or deformation. The loss of kinetic energy makes inelastic collisions distinctly different from elastic collisions, where both momentum and kinetic energy remain constant.
Definition and Core Concept
An inelastic collision refers to an event where colliding objects do not retain all their initial kinetic energy after impact. While the total momentum before and after the collision remains the same, some energy is transferred to internal movements, sound, or causes the objects to change shape. In perfectly inelastic collisions, the objects stick together and move as one body after the collision.
Real-world Examples
- Car crash
- Seatbelt action
- Airliner and bird collision
- Ballistic pendulum
Types and Dimensions of Inelastic Collisions
In physics, inelastic collisions can be categorized based on how the colliding objects interact after the impact. Most commonly studied are perfectly inelastic collisions, where objects stick together. Collisions are also analyzed by dimension—one-dimensional (straight-line) or two-dimensional (planar) collisions.
- One-dimensional inelastic collisions
- Two-dimensional inelastic collisions
Key Formulas in Inelastic Collision
| Collision Type | Momentum Conservation | Kinetic Energy Conservation | Key Formula |
|---|---|---|---|
| Inelastic Collision | Yes | No | m1u1 + m2u2 = (m1 + m2)v Final velocity v = (m1u1 + m2u2)/(m1 + m2) |
Step-by-Step Approach: Solving Inelastic Collision Problems
- Identify the system and all participating masses and velocities before collision.
- Write the momentum conservation equation: total momentum before collision = total momentum after collision.
- If objects stick together, set their final velocity as the same. Use the formula:
v = (m1u1 + m2u2)/(m1 + m2) - Solve for the unknown variable (often the final velocity).
- Calculate initial and final kinetic energy to find energy lost (if required).
Application Example
A truck of mass 2000 kg moving at 10 m/s collides with another stationary truck of mass 3000 kg. After collision, the trucks stick and move together. What is their final velocity?
- Initial momentum: (2000 × 10) + (3000 × 0) = 20000 kg·m/s
- Total mass after collision: 2000 + 3000 = 5000 kg
- Final velocity, v = 20000 / 5000 = 4 m/s
Comparing Elastic and Inelastic Collisions
| Feature | Elastic | Inelastic |
|---|---|---|
| Momentum | Conserved | Conserved |
| Kinetic Energy | Conserved | Not Conserved |
| Objects after Collision | Separate | May stick together |
| Example | Billiard Balls | Car Crash |
Relevant Vedantu Resources
- Elastic and Inelastic Collisions
- Collisions in One and Two Dimensions
- Conservation of Linear Momentum
- Kinetic Energy
Practice and Next Steps
- Try solving problems involving both one-dimensional and two-dimensional inelastic collisions.
- Review worked examples of real-world scenarios, such as ballistic pendulum, car collisions, and objects sticking together.
- Focus on writing conservation equations clearly and checking which quantities are conserved in every problem.
For a more comprehensive understanding and deeper practice on inelastic collisions and related concepts, explore the linked resources. Build a solid foundation in these topics to excel in physics and its applications.
FAQs on Inelastic Collision: Definition, Formula, and Exam Examples
1. What is an inelastic collision?
An inelastic collision is a type of collision in which the total kinetic energy of the system is not conserved, but momentum is conserved. During such collisions, some mechanical energy is transformed into other forms such as heat, sound, or deformation energy. In perfectly inelastic collisions, the colliding objects stick together after impact.
2. Is momentum conserved in inelastic collisions?
Yes, momentum is conserved in all inelastic collisions.
• The total linear momentum before the collision equals the total linear momentum after the collision, provided no external force acts on the system.
• Kinetic energy, however, is not conserved; some is lost to other forms.
3. What is lost in an inelastic collision?
In an inelastic collision, some of the system's initial kinetic energy is lost. This energy is transformed into other forms such as:
• Heat
• Sound
• Deformation or internal energy (in the colliding bodies)
4. What is the formula for perfectly inelastic collision?
The formula for the final velocity (v) after a perfectly inelastic collision—when objects stick together—is:
v = (m₁u₁ + m₂u₂) / (m₁ + m₂)
where m₁ and m₂ are the masses, and u₁ and u₂ are their initial velocities, respectively.
5. How is an inelastic collision different from an elastic collision?
The key difference is conservation of kinetic energy:
• Elastic collision: Both momentum and kinetic energy are conserved.
• Inelastic collision: Momentum is conserved, but kinetic energy is not; some energy is lost as heat, sound, or deformation.
• In perfectly inelastic collisions, objects stick together after the collision.
6. Can objects stick together in an inelastic collision?
Yes, in a perfectly inelastic collision, objects stick together after colliding. In general inelastic collisions, objects may not stick together, but in the special case known as a 'completely inelastic' or 'perfectly inelastic collision', they move as a single combined mass after impact.
7. How do you calculate the loss of kinetic energy in an inelastic collision?
The loss in kinetic energy can be calculated using:
• Initial kinetic energy = ½ m₁u₁2 + ½ m₂u₂2
• Final kinetic energy = ½ (m₁ + m₂)v2 (for perfectly inelastic cases where v is the common velocity after collision)
• Energy lost = Initial kinetic energy – Final kinetic energy
8. What is a real-life example of a perfectly inelastic collision?
A classic example is a car crash where two vehicles stick together after colliding. Other examples include:
• Clay balls that stick together after impact
• A bullet embedding into a block
• Dropping a lump of putty onto another so they move together
9. What are the main types of collisions in physics?
The three main types are:
• Elastic Collision: Momentum and kinetic energy are conserved.
• Inelastic Collision: Momentum is conserved, but some kinetic energy is lost.
• Perfectly Inelastic Collision: Maximum kinetic energy is lost; objects stick together after impact.
10. How do you identify if a collision is elastic or inelastic from a problem statement?
To distinguish types of collisions, check for these clues:
• Elastic collision: Both momentum and kinetic energy are conserved after collision.
• Inelastic collision: Objects may stick together, or kinetic energy is not the same before and after collision.
• If the question says objects stick or asks for energy lost, it is generally a (perfectly) inelastic collision.
11. Why is kinetic energy not conserved in inelastic collisions?
Kinetic energy is not conserved in inelastic collisions because some of it is transformed into other energy forms. These include heat, sound, and deformation of the bodies during impact. This transformation causes a reduction in the system's total kinetic energy.
12. What is momentum conservation in the context of inelastic collisions?
Momentum conservation means the total momentum before and after the collision remains equal, provided there is no external force. In formulas:
• m₁u₁ + m₂u₂ = (m₁ + m₂)v (for perfectly inelastic collision)
This law is always valid for isolated systems, no matter the type of collision.
