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Concept module

Conservation of Momentum

Watch two carts trade momentum through one bounded internal interaction and see the total stay fixed while the individual momenta, velocities, and center-of-mass motion update together.

The simulation shows two carts on one horizontal track with a fixed time window for an internal interaction. Each cart has a mass label, a velocity arrow, and optional force arrows that appear in equal and opposite directions during the interaction window. Optional overlays can draw an isolated-system boundary around both carts, a center-of-mass marker, and centered momentum bars for cart A, cart B, and the system total. Changing the masses, system velocity, internal force, or interaction duration updates the carts, readouts, and linked graphs without changing the underlying track scale. At t = 0 s, cart A has 0 kg m/s and cart B has 0 kg m/s. The total momentum is 0 kg m/s, and the center of mass continues with no net drift at 0 m/s. Before the interaction starts, both carts move together with the shared system velocity.

Interactive lab

Keep the stage, graph, and immediate control feedback in one working view.

Time

0.00 s / 2.40 sLivePause to inspect a specific moment, then step or scrub through it.
0.00 s2.40 s

Conservation of Momentum

Two carts exchange momentum through one bounded internal interaction. The total stays fixed, the center of mass stays honest, and compare mode never needs a separate collision sandbox.

Liveisolated interaction windowF_A = -2 N, F_B = 2 NLive isolated systemCMTrack position-6-3036x (m)Current setups stay within about +/-2.63 m on the fixed +/-8 m track, so compare mode never rescales the system.A 1.2 kgLiveB 2.4 kgLiveLive momentum barsp_A0 kg m/sp_B0 kg m/sp_tot0 kg m/sInternal forces redistribute momentum between the carts, but the isolated-system total remains unchanged.System statet0 sx_cm0.5 mv_cm0 m/sp_A0 kg m/sp_B0 kg m/sp_tot0 kg m/sF_int0 NBefore the push, both carts share the same system velocity and the same center-of-mass drift.Track the flat total-momentum line and the steady center-of-mass drift together.

Graphs

Switch graph views without breaking the live stage and time link.

Internal forces vs time

Shows the equal and opposite internal force pair during the interaction window and the zero external-force baseline.

time (s): 0 to 2.4force (N): -4 to 4
Force on AForce on BNet external force
Internal forces vs timeShows the equal and opposite internal force pair during the interaction window and the zero external-force baseline.00.61.21.82.4-4-2024time (s)force (N)
Hover or scrub to link the graph back to the stage.time (s) / force (N)

Controls

Adjust the physical parameters and watch the motion respond.

1.2 kg

Change cart A without changing the shared interaction pair.

2.4 kg

Change cart B and compare how the same momentum exchange appears in its velocity.

0 m/s

Give the whole isolated system a leftward or rightward drift before the internal push begins.

2 N

Positive values push A left and B right. Negative values swap those directions.

More tools

Secondary controls, alternate presets, and less-used toggles stay nearby without crowding the main bench.

Hide
0.4 s

Set how long the internal force pair acts during the fixed interaction window.

More presets

Presets

Predict -> manipulate -> observe

Keep the active prompt next to the controls so each change has an immediate visible consequence.

ObservationPrompt 1 of 2
Notice that the force graph shows an equal and opposite pair, not one force winning over the other.

Try this

Watch the force arrows on the stage and the force graph together. One line should always mirror the other.

Equation map

See each variable before you move it.

Select a symbol to highlight the matching control and the graph or overlay it most directly changes.

Mass of A
1.2 kg

Changing A's mass changes how much its velocity responds to the shared momentum exchange.

Graph: Velocities and center-of-mass speedGraph: Object and total momentumOverlay: Momentum bars

Equations in play

Choose an equation to sync the active symbol, control highlight, and related graph mapping.

More tools

Detailed noticing prompts, guided overlays, and challenge tasks stay available without taking over the main bench.

Hide

What to notice

Use the live prompt as a short guide while you change the masses and internal interaction. The best prompt should point at something the stage and the current graph already show honestly.

ObservationPrompt 1 of 2
Graph: Internal forces vs time
Notice that the force graph shows an equal and opposite pair, not one force winning over the other.

Try this

Watch the force arrows on the stage and the force graph together. One line should always mirror the other.

Why it matters

Those equal and opposite internal forces are why the system total momentum does not change.
Control: Internal forceControl: Interaction durationGraph: Internal forces vs timeGraph: Object and total momentumOverlay: Force pairEquationEquation

Guided overlays

Focus one overlay at a time to see what it represents and what to notice in the live motion.

4 visible

Overlay focus

System boundary

Marks the two-cart system that is being treated as isolated.

What to notice

  • The boundary contains both carts at once, so the conservation statement applies to their combined momentum.
  • Changing what happens inside the boundary does not by itself create an external impulse.

Why it matters

Momentum conservation is a system-level statement. The boundary reminds you which objects belong in the total.

Control: System velocityGraph: Object and total momentumGraph: Velocities and center-of-mass speedEquation
At t = 0 s, cart A has 0 kg m/s and cart B has 0 kg m/s. The total momentum is 0 kg m/s, and the center of mass continues with no net drift at 0 m/s. Before the interaction starts, both carts move together with the shared system velocity.
Equation detailsDeeper interpretation, notes, and worked variable context.

Momentum of one object

Each cart's momentum comes from its own mass and velocity.

Mass of A 1.2 kg Mass of B 2.4 kg System velocity 0 m/s

Total momentum

The system total is the vector sum of the object momenta. In this one-dimensional lab the signs carry the direction.

System velocity 0 m/s

Equal-and-opposite redistribution

Internal interactions move momentum from one object to the other by equal and opposite amounts.

Mass of A 1.2 kg Mass of B 2.4 kg Internal force magnitude 2 N Interaction duration 0.4 s

Conservation of momentum

If the net external impulse is zero, the system total momentum stays constant.

System velocity 0 m/s

Progress

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Let the live model runChange one real controlOpen What to notice

Try this setup

Copy the live bench state and reopen this concept with the same controls, graph, overlays, and compare context.

Stable links

Short explanation

What the system is doing

Conservation of momentum is the system version of the impulse story. If no external impulse acts on the system, then the total momentum of all the objects together stays constant even while the objects shove, pull, or collide with one another internally.

This module keeps that idea bounded with two carts on one track and one internal interaction window. You can change the masses, the shared system drift, and the internal force pair, then watch the individual momenta redistribute while the total momentum and center-of-mass motion stay honest.

Key ideas

01Momentum conservation applies to the whole isolated system, not to each object separately.
02Internal forces come in equal and opposite pairs, so they change the objects' momenta in opposite directions without changing the system total.
03Equal momentum changes do not imply equal velocity changes. The lighter cart usually changes speed more because $p = mv$.

Live conservation checks

Solve the exact state on screen.

Solve the redistribution you are actually watching. Time-based checks follow the inspected moment, and the final-split check stays tied to the current masses, shared system speed, and internal interaction pair.
Live valuesLive at t = 0.00 s

At , what is the system's total momentum?

Time

0 s

Momentum of A

0 kg m/s

Momentum of B

0 kg m/s

1. Add the object momenta

Use for the same instant shown on the stage.

2. Substitute the live values

.

3. Compute the total

So .

Current total momentum

The total momentum is essentially zero here, so the center of mass stays at rest even while the carts separate.

System-total checkpoint

Can you make cart A reverse direction while the system total momentum stays positive?

Prediction prompt

Try giving the whole system a rightward drift, then strengthen the internal push until cart A turns around.

Check your reasoning

Yes. A rightward-moving system can keep positive total momentum even if cart A ends up moving left after the internal interaction.
Momentum conservation constrains the sum, not each object's direction. Cart B can keep enough rightward momentum that the total stays positive while cart A reverses.

Common misconception

If two objects push on each other, the larger force winner keeps more of the system momentum.

Inside an isolated system there is no momentum winner. The internal force pair changes the objects' momenta by equal and opposite amounts, so the system total stays fixed.

Mass changes how the shared momentum redistribution shows up as velocity. A heavier object can keep a smaller speed change while still taking part in the same opposite momentum exchange.

Quick test

Reasoning

Question 1 of 4

Use the live force pair, the momentum split, and the center-of-mass motion together. These checks are about reasoning with an isolated system, not just reciting a slogan.

Which statement best describes momentum conservation in this two-cart lab?

Choose one answer to reveal feedback, then test the idea in the live system if a guided example is available.

Accessible description

The simulation shows two carts on one horizontal track with a fixed time window for an internal interaction. Each cart has a mass label, a velocity arrow, and optional force arrows that appear in equal and opposite directions during the interaction window.

Optional overlays can draw an isolated-system boundary around both carts, a center-of-mass marker, and centered momentum bars for cart A, cart B, and the system total. Changing the masses, system velocity, internal force, or interaction duration updates the carts, readouts, and linked graphs without changing the underlying track scale.

Graph summary

The force graph shows equal and opposite internal force lines during the interaction window plus a zero external-force baseline. The momentum graph shows the carts' individual momentum lines changing in opposite directions while the total line stays flat.

The velocity graph shows how the same momentum exchange can create different speed changes for different masses, while the center-of-mass speed stays constant for the whole isolated system.