AP Physics 1 · Unit 4 · Topic 4 of 6 · 6 min lesson

Collisions

A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.

Quiz this topic · 5 questions Watch the review video ↗

The big idea

In every collision with no outside force, momentum is conserved. Kinetic energy is conserved only in elastic collisions. When objects stick together, the most kinetic energy is turned into other forms like heat and sound.

1. Three kinds of collisions

Elasticmomentum ✓ · kinetic energy ✓

Inelasticmomentum ✓ · some kinetic energy lost

Perfectly inelastic (stick together)momentum ✓ · most kinetic energy lost

Real collisions between cars, clay, or people are inelastic. Steel balls and gliders with magnets come close to elastic.

Equal masses, head-on, elastic, one at rest: they swap velocities. The moving one stops and the other moves off at the original speed.

2. Sticking together

Momentum before and after is the same. Kinetic energy is not.

Use momentum to find the speed after; then compare kinetic energies.

For stuck-together objects, use the total mass after: m₁v₁ + m₂v₂ = (m₁ + m₂)v.

3. Example, then try it

Example

In the figure below, a 3.0 kg cart at 4.0 m/s hits a 1.0 kg cart at rest, and they stick. Find their speed and the kinetic energy lost.

Momentum: (3.0)(4.0) = (4.0)v → v = 3.0 m/s.

K before = ½(3.0)(4.0)² = 24 J; K after = ½(4.0)(3.0)² = 18 J. 6 J becomes heat, sound, and deformation.

Try it · work it on paper first

A 1.0 kg cart moving right at 6.0 m/s hits a 2.0 kg cart at rest. The 1.0 kg cart bounces back at 2.0 m/s. Find the 2.0 kg cart’s velocity. Was the collision elastic?

Momentum before (right = +): (1.0)(6.0) = 6.0 kg·m/s.

Momentum after: (1.0)(−2.0) + (2.0)v = 6.0 → 2.0v = 8.0 → v = +4.0 m/s.

K before: ½(1.0)(6.0)² = 18 J. K after: ½(1.0)(2.0)² + ½(2.0)(4.0)² = 2 + 16 = 18 J.

Compare: kinetic energy is the same before and after, so the collision was elastic.

Answer: the 2.0 kg cart moves right at 4.0 m/s, and the collision was elastic.

4. Common mistakes

Assuming kinetic energy is conserved.Only in elastic collisions. Unless the problem says elastic (or you check), use momentum only.

“Momentum is lost in a crash.”Kinetic energy can be lost. Momentum isn’t, as long as no outside force acts.

Averaging the speeds.For objects that stick, use total momentum ÷ total mass, not the average of the two speeds.

Check yourself

A truck and a car collide and their bumpers lock together. Ignoring friction during the brief collision, which is conserved?

They stick together, so it’s perfectly inelastic: momentum is conserved, but a lot of kinetic energy turns into heat, sound, and bent metal.

Ready to practice?

5 questions on Collisions, each with a hint and an explanation for every wrong answer.

Quiz this topic All of Unit 4