Collisions

What happens during a collision?

A collision is an interaction in which objects exert large forces on each other for a short time. Car crashes, billiard balls, bouncing balls, hockey pucks, and carts bumping on a track are all examples. During a collision, the forces can be complicated and change rapidly. Conservation laws help us understand the overall result without knowing every detail of the force.

The most important rule for many collisions is conservation of momentum. If the system is isolated, meaning external forces are small compared with the collision forces, total momentum before the collision equals total momentum after the collision:

$p_{before} = p_{after}$

This does not mean each object keeps the same momentum. It means the total momentum of all objects combined remains the same.

Action and reaction during collisions

Newton's third law explains why momentum is conserved. When object A pushes on object B, object B pushes back on object A with equal and opposite force. These forces act for the same amount of time, so the impulses are equal and opposite. One object gains momentum while the other loses the same amount.

For example, if two ice skaters push off from each other, they move in opposite directions. Their individual momenta change, but the total momentum remains the same if we ignore outside forces like friction.

Elastic collisions

An elastic collision is one in which kinetic energy is conserved as well as momentum. In an ideal elastic collision, objects bounce without losing kinetic energy to heat, sound, deformation, or internal motion. Collisions between hard steel balls or billiard balls can be approximately elastic, though no everyday collision is perfectly elastic.

In an elastic collision, the objects may exchange velocities or rebound in predictable ways. The key feature is that the total kinetic energy before and after is the same:

$K_{before} = K_{after}$

This condition is in addition to momentum conservation.

Inelastic collisions

An inelastic collision is one in which kinetic energy is not conserved, though momentum still is. Some kinetic energy is transformed into thermal energy, sound, deformation, or other forms. Most real collisions are inelastic to some degree.

A perfectly inelastic collision is a special case where objects stick together after impact. For example, two clay balls colliding and sticking move together afterward. Momentum is conserved, but kinetic energy decreases because some energy goes into changing the shape and internal motion of the clay.

Why cars are designed to crumple

At first, it might seem safer for a car to be very rigid during a crash. In reality, controlled crumpling can protect passengers. A crumple zone increases the time over which the car and passengers slow down. By the impulse idea, a longer stopping time means a smaller average force.

The kinetic energy of the car must go somewhere. Crumpling transforms some of it into deformation of the vehicle structure, thermal energy, and sound. The goal is not to conserve the car's shape; it is to reduce dangerous forces on people.

Center-of-mass motion

Even when objects collide and bounce, stick, or deform, the motion of the system's center of mass follows the total momentum. If no external net force acts, the center of mass continues moving at constant velocity. This gives a deeper way to understand why momentum conservation is so useful.

The big idea

Collisions may look chaotic, but conservation laws reveal order. Momentum is conserved in isolated collisions. Kinetic energy is conserved only in elastic collisions. In inelastic collisions, kinetic energy changes form. These ideas explain sports impacts, vehicle safety, billiards, explosions, recoil, and many laboratory experiments.