Explosion in AP Physics C: Mechanics

In AP Physics C: Mechanics, an explosion is a model for an interaction in which forces internal to a system push the objects of that system apart. Because the forces are internal, the system's total momentum is conserved, even though kinetic energy increases (Topic 4.1).

What is the explosion?

An explosion is what you get when a system flies apart because of forces inside it. A compressed spring releasing two carts, a firecracker bursting into fragments, an astronaut throwing a wrench in space. In every case, the forces doing the pushing are internal to the system, so there's no net external force and the total momentum of the system doesn't change. If the system starts at rest, the total momentum after the explosion is still zero, which means the fragment momenta have to cancel out vector by vector.

Here's the part that trips people up. Momentum is conserved, but kinetic energy is not. Kinetic energy increases, because some stored energy (elastic potential energy in a spring, chemical energy in gunpowder) gets converted into motion. A useful way to think of it is that an explosion is a perfectly inelastic collision run in reverse. In a perfectly inelastic collision, objects stick together and kinetic energy disappears. In an explosion, objects fly apart and kinetic energy appears. Momentum conservation holds in both.

Why the explosion matters in AP® Physics C: Mechanics

Explosions live in Topic 4.1 (Linear Momentum) and anchor the biggest idea in Unit 4, which is that conservation of momentum applies whenever the net external force on a system is zero. Explosion problems are the cleanest test of whether you can define a system, identify forces as internal versus external, and apply momentum conservation as a vector equation. They also force you to keep momentum and energy bookkeeping separate, since p⃗ is conserved while KE jumps up. That distinction is exactly what the exam probes when it asks which quantities are conserved in a given interaction.

How the explosion connects across the course

Collision (Unit 4)

Collisions and explosions are the same physics pointed in opposite directions. Both conserve momentum because the forces are internal, but a perfectly inelastic collision destroys kinetic energy while an explosion creates it from stored energy. If you can solve one, you can solve the other by flipping before and after.

Object model and system selection (Unit 4)

Whether something counts as an explosion depends on where you draw the system boundary. The spring force between two carts is internal if both carts are in your system, and momentum is conserved. Pick just one cart and that same force becomes external, and that cart's momentum changes. Choosing the system is step one of every momentum problem.

Energy storage and conversion (Unit 3)

The kinetic energy in an explosion has to come from somewhere, usually elastic potential energy in a spring or chemical energy. A classic problem hands you the stored energy (say, 40 J in a compressed spring) and asks for the fragment speeds, which makes you run momentum conservation and energy conversion at the same time.

Center of mass motion (Unit 4)

Internal forces can't move a system's center of mass. If two objects on a frictionless surface start at rest and a spring blows them apart, the center of mass velocity stays exactly zero the whole time. A projectile that explodes mid-flight has fragments whose center of mass still follows the original parabola.

Is the explosion on the AP® Physics C: Mechanics exam?

Explosion problems show up most often as multiple-choice questions where a system at rest breaks into two or three fragments and you solve for the unknown fragment's velocity. With three fragments in two dimensions, you set the total momentum to zero and solve component by component. For example, a 4.0 kg object at rest explodes into three pieces, two 1.0 kg fragments move at 2.0î m/s and 2.0ĵ m/s, and you find the third fragment's velocity vector by requiring the momenta to sum to zero. Other stems give you stored spring energy (like 40 J between two carts) and ask for individual speeds or the center of mass velocity, which tests whether you remember the center of mass doesn't move if the system started at rest. On FRQs, explosion setups reward justifying why momentum is conserved (no net external force, internal forces only) and stating explicitly that kinetic energy is not conserved because stored energy converts to KE.

The explosion vs collision

Both are interactions governed by internal forces, so momentum is conserved in both. The difference is the direction of energy flow. In a collision, objects come together and kinetic energy either stays the same (elastic) or decreases (inelastic). In an explosion, objects move apart and kinetic energy increases because stored potential or chemical energy converts to motion. Think of an explosion as a perfectly inelastic collision played backward.

Key things to remember about the explosion

• An explosion is an interaction where forces internal to a system push its objects apart, so the system's total momentum is conserved.

• Kinetic energy is NOT conserved in an explosion; it increases because stored energy (spring, chemical) converts into motion.

• If a system starts at rest, the total momentum after the explosion is zero, so fragment momenta must cancel as vectors, component by component.

• Internal forces cannot change the motion of the center of mass, so the center of mass of an exploding system keeps moving exactly as it did before.

• An explosion is effectively a perfectly inelastic collision in reverse, which is why the same momentum equations solve both.

• Whether a force is internal or external depends entirely on how you define the system, so define your system before writing any equations.

Frequently asked questions about the explosion

What is an explosion in AP Physics C: Mechanics?

It's a model for an interaction where forces internal to a system push the objects of that system apart, like a compressed spring releasing two carts. Since the forces are internal, the system's total momentum is conserved (Topic 4.1, Linear Momentum).

Is momentum conserved in an explosion?

Yes, always, as long as your system includes all the interacting objects. The pushing forces are internal, so there's no net external force and total momentum before equals total momentum after. If the object started at rest, the fragment momenta must sum to zero.

Is kinetic energy conserved in an explosion?

No. Kinetic energy increases because stored energy, like elastic potential energy in a spring or chemical energy in gunpowder, converts into motion. This is the opposite of an inelastic collision, where kinetic energy decreases.

How is an explosion different from a collision?

Both conserve momentum, but in a collision objects come together and kinetic energy stays the same or drops, while in an explosion objects fly apart and kinetic energy goes up. An explosion is basically a perfectly inelastic collision run in reverse.

How do you solve a three-fragment explosion problem?

Set the total momentum after the explosion equal to the momentum before (often zero), then solve the x and y components separately. For example, if a 5.0 kg object at rest breaks into fragments moving east and north, the third fragment's momentum must point southwest to cancel the other two.