An elastic collision is one where both momentum and kinetic energy are fully conserved. No energy is lost to heat, sound, or permanent deformation. In practice, perfectly elastic collisions only happen at the atomic and subatomic scale, but several everyday situations come close enough to be treated as elastic for practical purposes.
What Makes a Collision Elastic
Two conditions must both be met. First, the total momentum of the system before the collision equals the total momentum after. This is true of all collisions, elastic or not. Second, the total kinetic energy before and after the collision stays the same. That second requirement is the defining feature. It means no kinetic energy gets converted into heat, sound, vibration, or permanent changes in shape.
Physicists quantify this with the coefficient of restitution, a number between 0 and 1 that compares how fast two objects separate after a collision to how fast they approached. A value of 1 means perfectly elastic: the objects bounce apart at the same relative speed they came together. A value of 0 means perfectly inelastic, where the objects stick together and maximum kinetic energy is lost. Anything in between is partially elastic.
Collisions Between Atoms and Subatomic Particles
The clearest examples of truly elastic collisions happen at the smallest scales. Gas molecules bouncing off each other and off container walls are modeled as perfectly elastic. This assumption is one of the foundations of the kinetic theory of gases: the gas particles have perfect elastic collisions with no energy loss or gain. Without this, the basic gas laws that describe pressure and temperature wouldn’t work.
Subatomic particle scattering is another textbook case. In Rutherford scattering experiments, alpha particles fired at thin metal foils bounce off atomic nuclei. The interaction conserves kinetic energy because the electromagnetic repulsion between the positively charged particles acts like a perfect spring, doing no permanent work on either particle. These experiments, carried out by Hans Geiger and Ernest Marsden in Rutherford’s laboratory, were instrumental in discovering that atoms have a dense, positively charged nucleus.
Collisions between neutrons and atomic nuclei inside nuclear reactors also behave elastically. When a fast-moving neutron strikes a light nucleus (like hydrogen in water), kinetic energy transfers from one particle to the other without being absorbed or converted. This is how reactor moderators slow neutrons down to useful speeds.
Billiard Balls and Other Near-Elastic Impacts
At the macroscopic level, no collision is perfectly elastic. Any impact between everyday objects converts some kinetic energy into sound, heat, and microscopic deformation. But some collisions lose so little energy they’re treated as elastic in physics problems and engineering calculations.
Billiard balls are the classic example. They’re made of hard, rigid material and bounce off each other with relatively little energy loss. That said, the energy retention depends heavily on the specific collision. A billiard ball striking a pool table bumper, for instance, retains only about 64% of its original kinetic energy, which is far from perfectly elastic. Ball-to-ball collisions on a clean, level table fare better, but still lose a few percent to sound and slight heating at the contact point.
Steel ball bearings colliding in a physics lab come closer to elastic behavior. Hard, smooth surfaces minimize deformation and energy loss, pushing the coefficient of restitution closer to 1. Newton’s cradle, the desk toy with swinging metal spheres, relies on this near-elastic behavior to transfer energy cleanly from one end to the other. Over time, each swing gets slightly smaller because the collisions aren’t perfectly elastic.
Gravitational Slingshots in Space
One surprising example of elastic collision physics happens in space, without any physical contact at all. When a spacecraft flies past a planet and uses its gravity to speed up or change direction, the interaction behaves like an elastic collision between two objects of vastly different mass.
From the planet’s reference frame, the spacecraft approaches at some speed and leaves at that same speed, just in a different direction. Kinetic energy is conserved in this frame. But from the sun’s reference frame (which is what mission planners care about), the spacecraft can gain a significant boost in speed. That extra kinetic energy comes from the planet’s own orbital motion, though the planet’s speed decreases by an imperceptibly tiny amount because of its enormous mass compared to the craft. The total kinetic energy of the system is conserved, making this a genuine elastic collision governed by gravity rather than physical contact.
Situations That Are Not Elastic
Understanding which collisions are elastic also means recognizing which ones aren’t. In an inelastic collision, kinetic energy is converted into other forms. A car crash is a dramatic example: metal crumples, glass shatters, heat is generated, and a loud sound is produced. All of that energy came from the vehicles’ kinetic energy before impact.
A ball of clay thrown against a wall is perfectly inelastic. It sticks and stops, converting all its kinetic energy into deformation and heat. A bullet embedding itself in a wooden block behaves the same way. Momentum is still conserved in these cases, but kinetic energy is not.
Even a bouncy rubber ball dropped on a hard floor is only partially elastic. It bounces back to a lower height each time, losing energy to internal friction within the rubber and to sound with every impact. The closer the bounce height gets to the original drop height, the more elastic the collision.
How to Identify an Elastic Collision
If you’re working a physics problem or analyzing a real experiment, here are the key indicators that a collision is elastic:
- Objects fully separate after impact. If they stick together, the collision is perfectly inelastic by definition.
- No permanent deformation occurs. Dents, cracks, or shape changes mean kinetic energy was spent reshaping the material.
- The coefficient of restitution equals 1. The relative speed of separation equals the relative speed of approach.
- Total kinetic energy before and after is the same. You can verify this by calculating the kinetic energy of each object using its mass and velocity, then comparing the totals.
In a classroom or lab setting, you can test whether a collision was elastic by measuring the velocities of both objects before and after using motion sensors or video analysis. Calculate the total kinetic energy for each case. If the numbers match within your measurement uncertainty, the collision was elastic. If kinetic energy dropped, it was inelastic, and the percentage lost tells you how far from elastic it was.