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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.

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Why it behaves this way

Explanation

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 $p = mv$.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough
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.

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View plans
Frozen valuesFrozen at 0.00

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?

Make a prediction before you reveal the next step.

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

Check your reasoning against the live bench.

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?

Use the live bench to test the result before moving on.

Accessibility

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.