Elastic Collision vs. Inelastic Collision: What's the Difference

What Is an Elastic Collision

According to HyperPhysics, a collision is elastic when both the momentum and the kinetic energy of the system are conserved. There’s no kinetic energy loss at all: everything present before the collision shows up again, unchanged, afterward.

A perfectly elastic collision assumes no dissipative forces act during the impact — no internal friction, no permanent deformation of the bodies. It’s an ideal limiting case: in practice, every real macroscopic collision converts at least some kinetic energy into internal energy, meaning heat or deformation of the materials involved.

What Is an Inelastic Collision

Real macroscopic collisions are almost always of this kind, HyperPhysics notes: they don’t conserve kinetic energy. The system’s total energy, including its non-kinetic forms, is always conserved under the general principle of energy conservation, but the kinetic share drops.

The missing part becomes internal energy — heat and deformation of the colliding bodies. A telling case, from the same source, is a much more massive body hitting a small, stationary one: the large body loses only a negligible share of its own kinetic energy, the way a car barely changes speed after hitting an insect. The limiting case is the perfectly inelastic collision: the two bodies stay joined after impact, and the kinetic energy loss is the largest one possible while momentum stays conserved. OpenStax describes it the same way in the chapter on collision types in University Physics: any collision that leaves the bodies joined together carries the maximum kinetic energy loss consistent with that conservation.

What Always Stays Conserved

Momentum, inside an isolated system, is conserved in every type of collision — elastic, inelastic or perfectly inelastic — without exception. Kinetic energy is conserved only in the particular case of an elastic collision; in most real collisions, it isn’t.

The Conservation Formulas

The conservation of momentum is written as the sum of the bodies’ momenta before the collision, equal to the sum of their momenta after it:

m₁v₁ + m₂v₂ = m₁v₁’ + m₂v₂’

Here m₁ and m₂ are the masses of the two bodies. The unprimed letters denote velocities before the collision, the primed ones the velocities afterward. This equation holds for any collision, elastic or inelastic.

An elastic collision adds a second condition: the system’s total kinetic energy before the collision equals the total after it. That second equation doesn’t hold for an inelastic collision, where final kinetic energy is lower than the initial value.

Practical example: OpenStax describes an inelastic collision between a 1,200 kg car traveling at 27.5 m/s and a stationary 3,000 kg truck. After the collision, the truck moves at 11.0 m/s, a figure the source derives from the friction built up over the 10 meters it skids once hit. The system’s kinetic energy before the collision is 4.5×10⁵ J; after it, 1.8×10⁵ J. The difference, 2.7×10⁵ J, turns into heat and deformation during the impact and the skid that follows it.

Newton’s Cradle: Nearly Elastic Collisions

Newton’s cradle, the device with metal balls suspended in a row, familiar from desks everywhere, demonstrates both the conservation of momentum and, to a good approximation, of kinetic energy. The Department of Physics at the University of California, Santa Barbara describes it this way in its collection of lecture demonstrations.

When a number of balls is lifted and released against the others at rest, momentum travels down the row: the same number of balls swings out the far side, at the same speed. The whole thing runs on a series of approximately elastic collisions.

In reality, the cradle gradually loses height with every cycle. The collisions between the balls are never perfectly elastic: part of the kinetic energy turns into heat, on top of friction losses in the supports.

The idea connects to mechanical energy: across nearly elastic collisions, the system’s mechanical energy stays close to constant from one collision to the next, while in an inelastic collision part of it converts into other forms of energy already at the first impact. For how bodies move between one collision and another, Newton’s three laws of motion matter too: it’s the second law, together with the conservation of momentum, that describes the force acting during the brief instant of the collision.