What if balls did not bounce?

Bouncy balls bump and spring apart. Boing!

But some things do not bounce. A ball of clay just goes splat. What if every ball was like that?

Drop a rubber ball and it bounces. Drop a lump of clay and it lands with a splat and stays put. When moving things bump into each other, some spring apart and some squash and stick together.

What would happen in a collision if nothing could bounce? Where would the movement go? In this lab, two pucks slide on a smooth track, standing in for two balls. You can turn their bounciness from "bouncy" all the way down to "no bounce" and watch what happens when they meet.

OpenStax classifies collisions by kinetic energy: in an elastic collision the system's kinetic energy is the same before and after; in an inelastic one it decreases; and when the objects stick together, forming a single object, the loss is the largest possible and the collision is called perfectly inelastic. Momentum is conserved in all three.

The collisions model describes bounciness with the coefficient of restitution e, the ratio of separation speed to approach speed. This lab sets up a head-on hit between equal 1 kg pucks, one moving at 2 m/s, and lowers e from 1 to 0.

First the pucks are bouncy. The orange puck slides into the blue one.

Bump! The orange puck stops. The blue puck zooms away just as fast.

In the model, an orange puck slides at 2 meters per second into a blue puck of the same mass that is standing still. With bounciness set to "bouncy", the orange puck stops dead and the blue puck moves off at 2 meters per second, exactly the speed the orange one had.

None of the movement energy is lost: the energy readout says 0% turned into heat and sound. All the motion has simply passed from one puck to the other, like a hand-over in a relay race.

With m₁ = m₂ = 1 kg, v₁ = 2 m/s, v₂ = 0 and e = 1, the model gives v₁′ = 0 and v₂′ = 2 m/s: equal masses exchange velocities. Momentum is 2 kg·m/s before and after, kinetic energy 2 J before and after, so 0% is lost.

OpenStax College Physics notes that truly elastic collisions happen only with subatomic particles; everyday collisions are very nearly, but not quite, elastic, because some kinetic energy always becomes heat and sound. Its examples of nearly elastic collisions are steel blocks on ice and air-track carts with spring bumpers; the model's pucks also slide on a smooth air track.

Now the pucks cannot bounce. The orange puck slides into the blue one.

Splat! They stick together. They slide on together, slowly, at half the speed.

Now set bounciness to "no bounce". The orange puck hits the blue one and the two stay together, sliding on at 1 meter per second: half the speed. The total amount of motion, called momentum, is still exactly the same as before the crash.

But the energy readout shows that half the movement energy, 50%, has gone. It turned into heat and sound as the pucks squashed together. Try a middle setting, "squashy": they do separate, slowly, and about 38% of the energy is lost.

At e = 0 the model gives v₁′ = v₂′ = 1 m/s. Momentum is still 2 kg·m/s, but kinetic energy falls from 2 J to 1 J: 50% dissipated. For a target at rest, the lost fraction is m₂/(m₁ + m₂), so it depends on the masses: a 3 kg target gives 75% (both move at 0.5 m/s), a 3 kg striker only 25% (1.5 m/s).

At e = 0.5 the pucks separate at half their approach speed, 0.5 and 1.5 m/s, losing 37.5%. Kinetic energy is conserved only at e = 1.

When the pucks bump, they push on each other. That push keeps the motion going.

But squashing makes heat and sound. That uses up some of the movement energy.

When two things collide, each pushes on the other just as hard and for just as long. Those pushes hand motion from one to the other, so the total momentum stays the same in every crash, bouncy or not.

Energy is different. A bouncy ball squashes and then springs back, returning its energy as movement. Something that cannot bounce squashes and stays squashed, and that energy becomes heat and sound instead. Our model is simple: smooth pucks that don't spin, with a single bounciness number for each crash.

Newton's third law gives equal and opposite impulses, so Σmv is unchanged in any collision of an isolated pair. Restitution closes the equations: (v₂′ − v₁′) = −e(v₂ − v₁). At e = 0 the relative velocity after impact is zero, so the pair moves together at (m₁v₁ + m₂v₂)/(m₁ + m₂).

The model's limits, from its documentation: frictionless pucks with no spin, an instantaneous impact with a constant e, and no walls. Real restitution changes with impact speed, and real collisions involve friction between the surfaces, which this model leaves out.

When a goalie catches a puck, the puck stops in the glove and they move together.

That is a crash with no bounce! The puck's movement turns into heat and sound.

OpenStax describes an ice hockey goalie catching a puck. The puck stops in the goalie's glove and the two move together, very slowly. Almost all of the puck's movement energy turns into heat and sound: a perfect no-bounce collision.

OpenStax also works through a crash at a stoplight: a car hits a truck that is standing still, the car stops and the truck slides ahead. The total momentum stays the same, but more than half of the movement energy goes, OpenStax suggests, into denting the vehicles and some heat and sound. In most car crashes, OpenStax notes, the vehicles do not stick together, so less energy is removed than in a sticky crash.

In OpenStax's worked example of a goalie catching a puck, the puck-goalie system conserves momentum, but nearly all of the initial kinetic energy is lost, mostly converted to thermal energy and sound, in a perfectly inelastic collision. OpenStax adds that in most automobile accidents the objects do not stick together and less kinetic energy is removed.

OpenStax University Physics analyses a 1200 kg car that hits a motionless 3000 kg truck at a stoplight and stops, while the truck slides ahead at 11.0 m/s. Momentum conservation recovers the car's speed, 27.5 m/s, while kinetic energy falls from 4.5 × 10⁵ J to 1.8 × 10⁵ J, converted, presumably, into the deformation of the car and truck and some heat and sound: an inelastic collision, though not a perfectly inelastic one.