← Collision calculations in one and two dimensions

Classify the collision

A ball of putty hits a door and sticks. Two marbles click and roll apart. Two cars bump, dent, and bounce back. Three collisions, three different stories about what happened to the objects.

The course has coined all three names: elastic, inelastic, and perfectly inelastic. This lesson turns the three coins into one sort, decided by two questions asked in order.

Question one: after the impact, do the objects move as one? If yes, the collision is perfectly inelastic. The putty on the door is sorted by this question alone.

Question one sorts the sticking collisionsQuestion 1: do they move as one afterward?Verdictyesperfectly inelasticno (they separate)ask question 2
The first question sorts the sticking collisions out on its own.

If the objects separate, ask question two: is the system's total kinetic energy unchanged? If yes, the collision is elastic. If some kinetic energy became heat, sound, or deformation, the collision is inelastic.

Question two splits the restQuestion 2: is the total kinetic energy unchanged?Verdictyeselasticno (some became heat, sound, or deformation)inelastic
For the collisions that separate, the second question splits elastic from inelastic.

Run the sort on one pair of lab carts. The carts carry magnetic couplers: they collide, clamp, and roll on together. Move as one: perfectly inelastic.

Same carts, couplers removed, springy steel bumpers fitted: they collide and roll apart, and measurements show the total kinetic energy is unchanged. Separate, energy kept: elastic.

Same carts, a soft foam block taped over one bumper: they collide and roll apart, and the foam is warmer afterward. Separate, some energy transformed: inelastic.

One pair of carts, one feature changed at a timesame two cartswhat happensverdictmagnetic couplersclamp, move as oneperfectly inelasticspringy bumpersroll apart, kinetic energy keptelasticfoam block taped onroll apart, foam warmsinelastic
One pair of carts, one feature changed at a time, three verdicts.

One case gets no class at all. The same two carts, tied together with a cord and towed along, move as one. But nothing exerted a large force for a brief time. No collision happened, so there is no collision to classify.

The evidence in a problem names the class. Sticking means perfectly inelastic. A bounce with the kinetic energy kept means elastic. A bounce with sound, heat, or a dent means inelastic.

Run the sort in order. Question one: do the objects move as one afterward? Yes means perfectly inelastic, and the sort ends. Only when the objects separate does question two, about the kinetic energy, split elastic from inelastic.

A wet snowball hits the back of a sled and stays pressed onto it as the sled slides on. Which kind of collision is this?

Question one: do the objects move as one afterward? Yes, the snowball rides with the sled.

Sticking decides the sort by itself.

The collision is perfectly inelastic.

Two carts collide and roll apart. The impact makes a sharp crack, and one bumper is bent. Which kind of collision is this?

Question one: do the objects move as one afterward? No, they separate.

Question two: is the total kinetic energy unchanged? No, the crack and the bent bumper show some kinetic energy was transformed.

The collision is inelastic.

Quick-fire drill

A rolling luggage cart bumps the cart ahead, their hooks latch, and the pair rolls on together. Which kind of collision is this?

Two shopping carts bump and roll apart. The impact makes a loud bang and bends one basket. Which kind of collision is this?

Two pool balls click and roll apart, and measurements show the system's total kinetic energy is unchanged. Which kind of collision is this?

A leaping receiver catches a thrown football and holds it, and player and ball move on together. Which kind of collision is this?

Two steel ball bearings collide and bounce apart, and the total kinetic energy after equals the total before. Which kind of collision is this?

A rubber ball bounces off a wall. The thud and the slight warming of the ball show some kinetic energy was transformed. Which kind of collision is this?

Your turn

In which case is the collision perfectly inelastic?

A tow truck pulls a car on a rigid tow bar, and the two move down the road as one. How should this interaction be classified?

Margit watches a collision and wants to classify it. Which question should she ask first?