Distinguish elastic from inelastic collisions, explain that momentum is conserved in both while kinetic energy is conserved only in elastic collisions, and analyze recoil and explosion situations (MA STE Introductory Physics, Motion and Forces).

What this topic is asking

Not all collisions are the same, and the Massachusetts Introductory Physics MCAS expects you to tell them apart. You must distinguish elastic from inelastic collisions, explain that momentum is conserved in both while kinetic energy is conserved only in elastic collisions, and analyze recoil and explosion situations where objects push apart. This deepens conservation of momentum and links it to energy, hitting the crosscutting concept of energy and matter alongside systems.

Elastic and inelastic collisions

The dividing line is what happens to the kinetic energy:

• In an elastic collision, no kinetic energy is lost; it is shared between the objects but the total stays the same. Hard objects like billiard balls or steel spheres come close to elastic.
• In an inelastic collision, some kinetic energy is transformed into heat, sound, and the energy of bending or breaking. Most real collisions, especially car crashes, are inelastic.

In every case, as long as no external force acts, momentum is conserved. This is the key separation the MCAS tests: momentum is always conserved, but kinetic energy is only conserved when the collision is elastic.

Why momentum is conserved but kinetic energy may not be

Momentum is conserved because the internal forces in a collision are equal and opposite (Newton's third law), so one object gains exactly the momentum the other loses. That argument says nothing about energy. Kinetic energy can be transformed into other forms during the collision, for example into the energy that crumples metal or warms the surfaces, without breaking any conservation law, because the total energy (including the new forms) is still conserved. So a crash conserves momentum and total energy, but not kinetic energy.

Recoil and explosions

A recoil or explosion is a collision run in reverse: objects that start together (or at rest) push apart. Because the total momentum is conserved and usually starts at zero, the pieces fly off with equal and opposite momenta. A rifle firing a bullet, a skater throwing a ball, and a balloon releasing air all work this way: the small fast object (bullet, ball, air) carries momentum one way, and the large object (rifle, skater, balloon) recoils the other way with equal and opposite momentum.

Because momentum is mass times velocity, the lighter object moves much faster: a light bullet leaves at hundreds of meters per second while the much heavier rifle recoils slowly.

Reference-sheet note

The reference sheet gives momentum ($p = mv$) and kinetic energy ($KE = \tfrac{1}{2}mv^2$), but not the conservation of momentum statement. You recall that momentum is conserved in all collisions and that kinetic energy is conserved only in elastic ones. Being able to compute kinetic energy before and after with $KE = \tfrac{1}{2}mv^2$ lets you show that an inelastic collision loses kinetic energy.

Try this

Q1. State which quantity is conserved in all collisions (no external force), and which is conserved only in elastic collisions. [2]

• Cue. Momentum is conserved in all; kinetic energy only in elastic collisions.

Q2. A balloon releases its air and shoots forward. Explain this using momentum. [2]

• Cue. The air is pushed backward with some momentum, so the balloon gains equal and opposite momentum forward, keeping the total (initially zero) conserved.