Imagine two lumps of clay. You throw one at the other, and they smack together, stick, and move off as one blob. That's the classic inelastic collision. Something is clearly lost — the sound of the impact, a little heat from the deformation, and the fact that the clay is now squished. That "something lost" is kinetic energy. But here's the key: the total momentum of the two lumps before the crash is exactly the same as the momentum of the single combined lump after the crash. Momentum is always conserved in any collision if no external force acts. Energy, however, can change form.
Note
In an inelastic collision, momentum is conserved but kinetic energy is not conserved. Some kinetic energy transforms into other forms — heat, sound, or permanent deformation.
The most extreme version is a perfectly inelastic collision, where the objects stick together after impact. That's the clay example. But not all inelastic collisions are that dramatic. A car crash is inelastic — the cars crumple, metal bends, heat radiates — but they usually don't fuse into one piece. The defining feature is simply that kinetic energy is not the same before and after.
The Precise Statement
For any two objects colliding inelastically (with no external forces):
Momentum conservation:
m1u1+m2u2=m1v1+m2v2
Kinetic energy is NOT conserved:
21m1u12+21m2u22>21m1v12+21m2v22
The "lost" kinetic energy appears as heat, sound, or deformation energy. You cannot write an equation that sets the initial KE equal to the final KE — that would be an elastic collision.
For a perfectly inelastic collision (objects stick together, final velocity v is common):
m1u1+m2u2=(m1+m2)v
Why Does This Happen?
When two objects collide, forces between them do work. In an elastic collision, that work is stored and released like a spring — no permanent change. In an inelastic collision, the material deforms permanently. The work done to squash the clay or crumple the metal is not recovered as motion; it dissipates as heat. That's why the final kinetic energy is less.
A Common Exam Trap
Students often try to "conserve energy" in an inelastic collision by writing:
In any collision, whether elastic or inelastic, the total linear momentum of the colliding bodies is always conserved, provided no external force acts on the system; in an inelastic collision, however, kinetic energy is NOT conserved. …
Momentum is always conserved in a collision (elastic or inelastic); in an inelastic collision kinetic energy is not conserved, some of it converts into other forms of energy.
For an isolated system of colliding bodies, no external force acts during the (very short) time of collision, so by Newton's third law the mutual impulsive forces between the bodies are equal and opposite. This makes the total linear momentum of the system before collision exactly equal to the total linear momentum after collision — this holds for EVERY type of collision, elastic or inelastic.
Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.
CBSE 2026Set ANNUAL1 markMCQ
Q.Match the column - select the correct definition (from Column B) for the term 'Inelastic collision' (Column A):
(a) change in linear momentum
(b) motion opposing force
(c) loss of energy
(d) rate of change of momentum
(e) ability of doing work
(f) rate of doing work
›Reveal solutionSolution
An inelastic collision conserves momentum but not kinetic energy — some kinetic energy is lost.
In any collision, total linear momentum of the colliding system is always conserved (as long as no external force acts). However, kinetic energy is conserved only in a perfectly elastic collision. In an inelastic collision, some of the initial kinetic energy is converted into other forms — heat, sound, and permanent deformation of the colliding bodies — s …
Q.Which of the following is conserved in an inelastic collision?
(a) Kinetic Energy
(b) Momentum
(c) Both
(d) None of these
›Reveal solutionSolution
Momentum is conserved in every collision (elastic or inelastic); kinetic energy is conserved only in elastic collisions.
By the law of conservation of momentum, for an isolated system the total linear momentum before and after collision is always equal, regardless of the nature of the collision, because no external force acts during the (very short) collision time. In an inelastic collision, however, part of the kinetic energy is converted into heat, sou …
Q.What remains conserved in an inelastic collision?
›Reveal solutionSolution
Momentum is always conserved in a collision (elastic or inelastic); in an inelastic collision kinetic energy is not conserved, some of it converts into other forms of energy.
For an isolated system of colliding bodies, no external force acts during the (very short) time of collision, so by Newton's third law the mutual impulsive forces between the bodies are equal and opposite. This makes the total linear momentum of the system before collision exactly equal to the total linear momentum after collision — this holds for EVERY type of collision, elastic or inelastic.