Momentum & Collisions

What is Momentum & Collisions?

Slide a billiard ball straight at a stationary one of equal mass. The cue ball stops dead and the target ball rolls off with the original speed. That weird, almost magical exchange is conservation of momentum doing exactly what the math says it must. Now imagine the same hit but with a lump of clay instead — the moving ball plows into it, they stick together, and the combined blob continues at half the original speed. Different outcome, same conservation law: total momentum before equals total momentum after, every time, in any isolated collision. The difference between the two cases is what happens to kinetic energy: conserved in the elastic case, partly dumped into heat and deformation in the inelastic one. This lab launches a moving cart at a stationary target, with adjustable masses, an incoming velocity, and a coefficient of restitution slider so you can blend smoothly from perfectly bouncy to perfectly sticky.

Parameters explained

Mass 1(kg)

Mass 1 is the mass of the moving cart before the collision. In AP Physics 1 and HS-PS2 work, this slider lets students separate mass from speed in the momentum equation p = mv. With Velocity 1 fixed, increasing Mass 1 increases the incoming momentum and usually makes cart 1 harder to slow down or reverse. Compare the Equal Mass Elastic preset with Heavy→Light: the same launch speed produces a very different post-collision split because the larger mass carries more momentum into the interaction. Students can use this slider to test that total system momentum, not either cart's individual momentum, is the conserved quantity.

Mass 2(kg)

Mass 2 is the mass of the target cart, which starts at rest in this HTML model. Changing it alters how the incoming momentum from cart 1 is distributed after contact. Equal masses in an elastic collision produce the classic AP Physics 1 result: cart 1 stops and cart 2 leaves with nearly the original speed. A lighter target shoots away faster; a heavier target changes speed less. This supports HS-PS2-2 because students can use measurements and mathematical representations to show that the final velocities change with mass ratio while total momentum before and after remains constant.

Velocity 1(m/s)

Velocity 1 is the initial velocity of the moving cart. It sets both the sign and size of cart 1's starting momentum, p_1 = m_1v_1, while cart 2 begins at rest. Positive and negative values represent opposite directions, so students can connect vector signs to momentum bookkeeping instead of treating speed as just a positive number. With Mass 1 fixed, doubling Velocity 1 doubles incoming momentum but quadruples kinetic energy. That contrast is central to AP Physics 1: momentum conservation constrains every isolated collision, while kinetic energy conservation depends on whether the collision is elastic.

Restitution Coefficient

The Restitution Coefficient controls how bouncy the collision is. A value of 1 represents the elastic limit, where total momentum and total kinetic energy are both conserved. A value of 0 represents the perfectly inelastic limit, where the carts stick together and share one final velocity. Intermediate values keep momentum conserved but reduce the relative separation speed after impact, modeling real materials that deform, heat, or vibrate. Use the Perfectly Inelastic preset and then raise this slider toward 1 to help students see the HS-PS2 and AP distinction: momentum is the system-level invariant, while kinetic energy can leave the macroscopic motion.

Common misconceptions

• MisconceptionIf two objects collide and stick together, momentum is lost because they slow down.

  CorrectMomentum is conserved in every collision, sticky or bouncy, as long as no external forces act. What changes in a sticky collision is kinetic energy — some of it converts to heat and deformation. The combined mass moves more slowly precisely because momentum (m·v) has to add up to the original total: more m means less v.

• MisconceptionMomentum and kinetic energy are basically the same thing — both measure motion.

  CorrectThey're related but distinct. Momentum p = mv is a vector, conserved in every collision. Kinetic energy KE = ½mv² is a scalar, conserved only in elastic ones. Doubling speed doubles momentum but quadruples KE. The two concepts answer different questions: momentum tells you how hard something is to stop; KE tells you how much damage it can do.

• MisconceptionWhen a moving object hits a stationary one, the moving object always loses speed and the stationary one always speeds up by the same amount.

  CorrectOnly true for equal masses in 1D elastic collisions, like the Equal Mass Elastic preset. With unequal masses or inelastic conditions, the velocity changes are not equal and opposite. What is always equal and opposite — for any isolated collision — is the impulse (Δp) on each object. The forces during contact are equal and opposite by Newton's third law, but the resulting velocity changes depend on Mass 1, Mass 2, and the restitution setting.

• MisconceptionCars in a head-on crash come to a sudden stop because the airbag absorbs all the energy.

  CorrectAirbags don't reduce the energy you have to dissipate — they reduce the peak force by extending the time over which it acts. The impulse-momentum theorem F·Δt = Δp says the same momentum change can be delivered with a small force over a long time or a huge force over a short time. Airbags choose the gentle option, which is why they save lives.

• MisconceptionA heavy truck has more momentum than a fast bullet because trucks weigh more.

  CorrectMomentum is mass times velocity, so a slow massive object and a fast light object can have the same momentum if mv lines up. A 0.01 kg bullet at 1,000 m/s carries 10 kg·m/s of momentum, the same as a 10 kg cart at 1 m/s. The bullet wins on KE (½mv² scales with v²), which is why it does more damage despite the lighter mass.

How teachers use this lab

1. HS-PS2-2 momentum audit: have students run the Equal Mass Elastic, Heavy→Light, and Perfectly Inelastic presets, record p_1, p_2, and p_total before and after, and verify that p_total stays constant even when the visible outcomes look very different.
2. HS-PS2-3 design prompt: ask groups to use Mass 1, Mass 2, Velocity 1, and Restitution Coefficient to design a collision that reduces final kinetic energy while preserving total momentum, then justify how the Perfectly Inelastic preset models energy transfer into deformation or heat.
3. AP equal-mass benchmark: start with Equal Mass Elastic, then change only Mass 2. Students predict whether cart 1 stops, rebounds, or keeps moving, using conservation of momentum and kinetic energy instead of intuition.
4. Mass-ratio investigation: start from Heavy→Light, hold Velocity 1 and Restitution Coefficient fixed, and sweep Mass 1 and Mass 2 through several ratios. Students explain why equal impulses create different velocity changes for the two carts.
5. Restitution comparison lab: keep Mass 1, Mass 2, and Velocity 1 fixed while moving Restitution Coefficient from 1 to 0. Students compare KE_before and KE_after and write a claim-evidence-reasoning response about why momentum conservation survives in both elastic and inelastic cases.