Inelastic Collision
An inelastic collision is one in which the total kinetic energy of the system is not conserved, though the total momentum remains conserved. The lost kinetic energy is converted into other forms such as heat, sound, or deformation energy. When two objects collide and stick together, it is termed a perfectly inelastic collision, representing the maximum possible loss of kinetic energy.
Key Formula
vf = (m1×v1i + m2×v2i) / (m1 + m2)
LaTeX: v_f = \frac{m_1 v_{1i} + m_2 v_{2i}}{m_1 + m_2}
| Symbol | Meaning | Unit |
|---|---|---|
| vf | Common final velocity (perfectly inelastic) | m/s |
| m₁, m₂ | Masses of the two objects | Kilogram (kg) |
| v₁ᵢ | Initial velocity of object 1 | m/s |
| v₂ᵢ | Initial velocity of object 2 | m/s |
Worked Example
Problem
A 1,000 kg car moving at 20 m/s east rear-ends a stationary 1,500 kg truck. They lock bumpers and move together. Find the final velocity and the kinetic energy lost.
Solution
Step 1: Apply conservation of momentum. vf = (m₁v₁ᵢ + m₂v₂ᵢ) / (m₁ + m₂) vf = (1000×20 + 1500×0) / (1000 + 1500) vf = 20,000 / 2,500 = 8 m/s (east) Step 2: Calculate initial KE. KEᵢ = ½ × 1000 × 20² = 200,000 J Step 3: Calculate final KE. KEf = ½ × 2500 × 8² = 80,000 J Step 4: KE lost = 200,000 - 80,000 = 120,000 J
Answer
Final velocity = 8 m/s east; Kinetic energy lost = 120,000 J (120 kJ)
Energy Loss in Inelastic Collisions
| Collision Type | KE Conserved? | Coefficient of Restitution (e) | Example |
|---|---|---|---|
| Elastic | Yes (100%) | 1.0 | Steel ball bearings |
| Nearly elastic | Mostly | 0.9–0.99 | Rubber superball |
| Partially inelastic | Partially | 0.5–0.9 | Tennis ball on court |
| Mostly inelastic | Little | 0.1–0.5 | Clay on surface |
| Perfectly inelastic | No (maximum loss) | 0 | Car crash, coupling trains |
Interactive Tools
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Related Terms
Elastic Collision
An elastic collision is one in which both the total kinetic energy and the total momentum of the system are conserved before and after the collision. No energy is lost to deformation, heat, or sound, making it an idealized model most closely approximated by atomic and subatomic particle interactions. Billiard ball collisions and gas molecule interactions are common approximations of elastic collisions.
Conservation of Momentum
The law of conservation of momentum states that the total momentum of a closed, isolated system remains constant if no external net force acts on it. This means the sum of momenta of all objects before an interaction equals the sum after the interaction. It is one of the most fundamental conservation laws in physics and applies equally to collisions, explosions, and all mechanical interactions.
Momentum
Momentum is the product of an object's mass and its velocity, representing the quantity of motion possessed by the object. It is a vector quantity, meaning it has both magnitude and direction aligned with the velocity. Momentum is fundamental to Newton's second and third laws and is the conserved quantity in isolated systems during collisions and interactions.
The prefix "in-" is Latin for "not". "Inelastic" therefore means "not elastic" — not returning to its original form. The term entered mechanics as a counterpart to elastic collision in 18th-century physics.