Inelastic Collision
Also known as: perfectly inelastic collision
Grade 9-12
View on concept mapA collision in which the total momentum of the system is conserved but the total kinetic energy is not — some kinetic energy is converted. Most real-world collisions are inelastic — car crashes, sports impacts, and bullet-block problems all lose kinetic energy.
Definition
A collision in which the total momentum of the system is conserved but the total kinetic energy is not — some kinetic energy is converted.
💡 Intuition
Two cars crashing and sticking together: they move as one object and kinetic energy is lost.
🎯 Core Idea
Momentum is always conserved in collisions; kinetic energy is not if objects deform or stick.
Example
Formula
Notation
m_1, m_2 are the masses in kg, v_1, v_2 are the initial velocities in m/s, v_f is the common final velocity in m/s, and \Delta KE is the kinetic energy lost in joules.
🌟 Why It Matters
Most real-world collisions are inelastic — car crashes, sports impacts, and bullet-block problems all lose kinetic energy. Understanding inelastic collisions is critical for vehicle safety design and forensic accident reconstruction.
💭 Hint When Stuck
When solving a perfectly inelastic collision, use conservation of momentum: m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f. Solve for v_f. Then, if asked for energy lost, calculate KE_{\text{before}} - KE_{\text{after}} separately — do not assume kinetic energy is conserved.
Formal View
Related Concepts
🚧 Common Stuck Point
Inelastic doesn't mean momentum is lost — only kinetic energy decreases.
⚠️ Common Mistakes
- Trying to use conservation of kinetic energy — in inelastic collisions, kinetic energy is NOT conserved; only momentum is.
- Forgetting to include both objects' momenta before the collision — if one object is initially at rest, its momentum is zero but it still has mass that affects the final velocity.
- Confusing 'inelastic' with 'perfectly inelastic' — in a perfectly inelastic collision the objects stick together (maximum KE loss), but ordinary inelastic collisions lose some KE without sticking.
Frequently Asked Questions
What is Inelastic Collision in Physics?
A collision in which the total momentum of the system is conserved but the total kinetic energy is not — some kinetic energy is converted.
What is the Inelastic Collision formula?
When do you use Inelastic Collision?
When solving a perfectly inelastic collision, use conservation of momentum: m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f. Solve for v_f. Then, if asked for energy lost, calculate KE_{\text{before}} - KE_{\text{after}} separately — do not assume kinetic energy is conserved.
Prerequisites
Next Steps
How Inelastic Collision Connects to Other Ideas
To understand inelastic collision, you should first be comfortable with conservation of momentum and kinetic energy. Once you have a solid grasp of inelastic collision, you can move on to elastic collision.