Skip to content
Open Model LabInteractive concept
HomeConcept libraryPhysicsMechanics
PhysicsMechanicsIntro

Concept module

Momentum and Impulse

Push one cart with a timed force pulse and watch momentum, impulse, and force-time area stay tied to the same motion, readouts, and graphs.

Interactive lab

Loading the live simulation bench.

Progress

Not startedMastery: NewLocal-first

Start exploring and Open Model Lab will keep this concept's progress on this browser first. No finished quick test, solved challenge, or completion mark is saved yet.

Let the live model runChange one real controlOpen What to notice

Try this setup

Jump to a named bench state or copy the one you are looking at now. Shared links reopen the same controls, graph, overlays, and compare context.

Saved setups

Premium keeps named exact-state study setups in your account while stable concept links stay public below.

Checking saved setup access.

This concept can keep using stable links while the saved-setups capability resolves for this browser.

Copy current setup

Stable concept and section links stay public below while exact-state setup sharing stays behind premium.

Stable links

Why it behaves this way

Explanation

Momentum tells you how much motion an object is carrying: in one dimension it is , so a heavier cart or a faster cart has more momentum. The sign matters too, because momentum points with the velocity.

Impulse is what a force does over a stretch of time. In this module one bounded force pulse pushes a cart on a fixed track, so you can see the pulse shape, the accumulated impulse, and the momentum graph move together without inventing a separate subsystem for collisions.

Key ideas

01Momentum is mass times velocity, so the same speed change does not mean the same momentum change for every mass.
02Impulse is the signed force-time area. A short large force and a smaller longer force can produce the same total impulse if the areas match.
03For the same cart, impulse changes momentum directly through $J = \Delta p$, which is why the momentum graph and the accumulated-impulse graph should agree.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough
Solve the pulse you are actually watching. Time-based examples follow the current inspected time unless you freeze them, and the pulse example keeps the full force-duration pair tied to the real controls.

Premium unlocks saved study tools, exact-state sharing, and the richer review surfaces that support this guided flow.

View plans
Frozen valuesFrozen at 0.00

At , what is the cart's momentum?

Time

0 s

Mass

1 kg

Velocity

0.5 m/s

1. Identify the relation

Use for the cart at the currently inspected moment.

2. Substitute the live values

.

3. Compute the momentum

That gives .

Current momentum

Before the pulse starts, the cart keeps its initial velocity, so the current momentum still matches the starting value.

Force-pulse checkpoint

Can you choose a new force-duration pair that leaves the final momentum unchanged?

Make a prediction before you reveal the next step.

Try making the pulse shorter while raising the force, or longer while lowering the force. Predict which pairs should keep the same final momentum.

Check your reasoning against the live bench.

Any pair with the same signed area under the force-time graph gives the same momentum change for the same cart.
This is the bounded version of the impulse idea. If stays the same, then stays the same, so the momentum change stays the same even though the pulse shape looks different.

Common misconception

A bigger force always means a bigger momentum change, even if it acts for less time.

Momentum change depends on the total impulse, not force alone. A large force over a very short interval can match the effect of a smaller force acting longer.

Mass changes how much the velocity shifts for a given impulse, but it does not change the fact that the momentum change itself is set by .

Quick test

Compare cases

Question 1 of 4

Use the force pulse, the cart motion, and the graphs together. Each question checks whether you can reason with momentum and impulse, not just recite a definition.

A force for and a force for act on the same cart in the same direction. Which statement is correct?

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

Accessibility

The simulation shows a cart moving on a fixed horizontal track while a single force pulse turns on during a highlighted time window. The cart label shows mass, a horizontal arrow shows velocity, and overlays can emphasize the force direction, the pulse window, and centered bars for initial, current, and final momentum.

Changing mass, initial velocity, force, or pulse duration immediately updates the cart motion, the pulse timing, the readouts, and the linked graphs without changing the underlying scale.

Graph summary

The force graph shows a rectangular pulse that can point positive or negative. The momentum graph is flat before and after the pulse and changes only while the force acts.

The impulse graph and the change-in-momentum graph should overlap because they represent the same signed quantity for the same cart.