Inelastic Collision

An inelastic collision is a collision in which the system's total momentum is conserved but its total kinetic energy is not, because some kinetic energy converts to other forms like thermal energy or deformation. If the objects stick together and move with one shared velocity, it's perfectly inelastic.

What is Inelastic Collision?

An inelastic collision is any collision where kinetic energy is lost. Momentum is still conserved (as long as the system is closed, with no net external force), but some kinetic energy gets converted into thermal energy, sound, or permanent deformation of the objects. The crumpled bumpers in a car crash are kinetic energy that didn't survive the collision.

Here's the distinction that trips people up. "Inelastic" does NOT automatically mean the objects stick together. Sticking together is the special case called a perfectly inelastic collision, where the objects share one final velocity and the system loses the maximum possible kinetic energy. A regular inelastic collision can have the objects bounce apart, just with less total kinetic energy than they started with. Your one reliable tool in every case is conservation of momentum, m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂', because that holds whether or not energy is conserved.

Why Inelastic Collision matters in AP Physics 1

Inelastic collisions live in Unit 5 of AP Physics 1, threading through Topic 5.2 (representing changes in momentum), Topic 5.3 (open and closed systems), and Topic 5.4 (conservation of linear momentum). The concept is where the exam checks whether you understand the difference between momentum conservation and energy conservation, which are two separate laws with separate conditions. Momentum is conserved in any closed system, period. Kinetic energy is only conserved in elastic collisions. A huge share of collision questions are really asking one thing, which is whether you know which quantity to track. Inelastic collisions are the test case that exposes anyone who thinks "conservation" is one blanket rule.

How Inelastic Collision connects across the course

Conservation of Linear Momentum (Unit 5)

This is the law that actually solves inelastic collision problems. Kinetic energy is off the table, so momentum conservation is the only equation connecting before and after. Every inelastic collision calculation starts with the total momentum of the system staying constant.

Perfectly Inelastic Collision (Unit 5)

The extreme version of inelastic. The objects stick together, share one final velocity, and the system loses the maximum kinetic energy possible while still conserving momentum. The math gets simpler because there's only one unknown final velocity, which is why exam problems love it.

Elastic Collision (Unit 5)

The opposite end of the spectrum. In an elastic collision both momentum AND kinetic energy are conserved, so you get two equations instead of one. Comparing the total kinetic energy before and after a collision is how you classify which type you're looking at.

External Forces and Open vs. Closed Systems (Unit 5)

Momentum conservation only holds when the net external force on the system is zero. Friction with the floor during a long collision, or a wall pushing on one of the objects, makes the system open and breaks the conservation argument. Defining your system carefully is step one of any collision FRQ.

Energy Transformations (Unit 3)

The kinetic energy "lost" in an inelastic collision isn't destroyed. It transforms into thermal energy, sound, and deformation. Connecting collision analysis back to energy accounting is exactly the kind of cross-unit reasoning that strong paragraph-length responses show off.

Is Inelastic Collision on the AP Physics 1 exam?

Collisions show up in both multiple choice and FRQs, usually with two blocks or carts on a horizontal surface. The 2024 Short FRQ had Block A (6 kg) sliding into Block B (2 kg) at rest, the classic setup. Expect to do three things. First, apply momentum conservation to find a final velocity. Second, compare kinetic energy before and after to classify the collision as elastic, inelastic, or perfectly inelastic. Third, justify in words why momentum is conserved (closed system, no net external force) while kinetic energy is not. MCQ stems often hand you numbers and ask which collision type occurred, so practice computing KE_before and KE_after quickly. If KE drops, it's inelastic. If the objects also stick together, it's perfectly inelastic.

Inelastic Collision vs Perfectly Inelastic Collision

Many study resources (and plenty of students) define inelastic as "the objects stick together," but that's only the perfectly inelastic case. Inelastic just means kinetic energy is lost; the objects can still bounce apart. Perfectly inelastic is the subset where they stick, move with one shared final velocity, and lose the maximum possible kinetic energy. On the exam, read carefully whether the problem says the objects stick together before assuming a single final velocity.

Key things to remember about Inelastic Collision

• In an inelastic collision, momentum is conserved but kinetic energy is not.

• The lost kinetic energy converts to thermal energy, sound, or deformation, so total energy is still conserved even though kinetic energy drops.

• Inelastic does not require the objects to stick together; sticking together is the special perfectly inelastic case, which loses the maximum kinetic energy.

• Momentum conservation only applies when the system is closed, meaning the net external force on the system is zero during the collision.

• To classify a collision on the exam, calculate total kinetic energy before and after. Equal means elastic, smaller means inelastic, and one shared final velocity means perfectly inelastic.

• Conservation of momentum (m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂') is your go-to equation for any inelastic collision problem, because the energy equation won't help you.

Frequently asked questions about Inelastic Collision

What is an inelastic collision in AP Physics 1?

It's a collision where the system's momentum is conserved but kinetic energy is not, because some kinetic energy converts to thermal energy, sound, or deformation. It's covered in Unit 5 alongside conservation of linear momentum.

Do objects always stick together in an inelastic collision?

No. Objects only stick together in a perfectly inelastic collision, which is the special case with maximum kinetic energy loss. A regular inelastic collision can have the objects bounce apart, just with less total kinetic energy than before.

Is momentum conserved in an inelastic collision?

Yes, as long as the system is closed (no net external force). That's the whole point. Momentum conservation holds for every type of collision; it's kinetic energy that gets lost in the inelastic case.

How is an inelastic collision different from an elastic collision?

In an elastic collision both momentum and kinetic energy are conserved, so the total kinetic energy after equals the total before. In an inelastic collision only momentum is conserved and kinetic energy decreases. Comparing KE before and after is how you tell them apart on the exam.

How do I find the final velocity after a perfectly inelastic collision?

Set total momentum before equal to total momentum after, with the combined mass moving at one shared velocity. So v' = (m₁v₁ + m₂v₂)/(m₁ + m₂). For example, a 6 kg block hitting a 2 kg block at rest (like the 2024 FRQ setup) gives a combined 8 kg mass after sticking.