Physics · Mechanics

Collisions

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Projectile MotionApply momentum ideas

Key takeaway

Read momentum conservation on the momentum graph: the cart momentum lines jump at contact, but the total-momentum line stays flat.
Elasticity controls the relative speed after contact. Lower elasticity means less separation speed and more kinetic energy lost.

Common misconception

If momentum is conserved, then the collision should keep the same total kinetic energy and produce basically the same rebound every time.

Momentum conservation fixes the system total, not the total kinetic energy. In an inelastic collision, the total momentum can stay the same while the total kinetic energy decreases.

Keep building the momentum story

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Apply momentum ideasMechanics

Projectile Motion

Launch a projectile, watch the trajectory form, and connect the range, height, and component motion to the launch settings.

Review impulseMechanics

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.

System viewMechanics

Conservation of Momentum

Use two carts to see the conservation rule in action: with no outside push, the system's total momentum stays fixed even while each cart's momentum and speed change.

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Reference and support

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Equation snapshotMomentum of one cart · Momentum conservation across contactShow 2 equations

Momentum of one cart
$p = m v$
This gives one cart's momentum from its mass and velocity.
Momentum conservation across contact
$m_{A} u_{A} + m_{B} u_{B} = m_{A} v_{A} + m_{B} v_{B}$
If no external horizontal force acts on the two-cart system, the total momentum before contact must equal the total momentum after contact.

Why it behaves this way

Explanation

In a collision, each cart can change velocity very quickly, so the motion may look as if it changes all at once. But if the two-cart system is isolated, the total momentum cannot jump at contact even when the individual cart velocities do.

Here you change only mass, incoming speed, and elasticity, then watch the same collision on the track and on the linked velocity, momentum, and energy graphs. That makes it easier to separate three ideas: momentum of the whole system, how the motion is split between the carts, and whether kinetic energy is preserved or lost.

Key ideas

01Read momentum conservation on the momentum graph: the cart momentum lines jump at contact, but the total-momentum line stays flat.

02Elasticity controls the relative speed after contact. Lower elasticity means less separation speed and more kinetic energy lost.

03Mass changes how the same momentum transfer appears as a velocity change, so a heavier cart usually changes speed less.

Worked examples

Solve the collision you see

Open examples when you want to see the same idea walked through step by step.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the current setup as evidence. First find the system's total momentum at the instant shown on the stage. Then use the same masses, incoming speeds, and elasticity to predict the velocities just after contact and compare that result with the stage and graphs.

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Example 1 of 2

Frozen valuesFrozen at 0.00

At $t = 0 s$ , what is the total momentum of the two-cart system?

m_{A}

Mass of A

1.2 kg

v_{A}

Velocity of cart A

1.6 m/s

m_{B}

Mass of B

2.2 kg

v_{B}

Velocity of cart B

-0.7 m/s

1. Write the system-momentum relation

Use

p_{tot} = m_{A} v_{A} + m_{B} v_{B}

for the same instant shown on the stage.

2. Insert the live masses and velocities

p_{tot} = (1.2) (1.6) + (2.2) (- 0.7)

3. Evaluate the sum

p_{tot} = 0.38 kg m/s

System total momentum

p_{tot} = 0.38 kg m/s

Before contact, the system total is already fixed by the incoming masses and velocities, so the collision has not created a new total.

Quick test

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Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

The simulation shows two carts moving along one fixed horizontal track toward a single collision point. Each cart has a mass label and a horizontal velocity arrow, and optional overlays can mark the collision zone, center of mass, momentum bars, and the relative speed before and after contact.

Changing mass, incoming speed, or elasticity updates the same stage, readouts, and linked graphs without changing the track scale. When elasticity is zero, the carts leave together; with higher elasticity, they separate more strongly after contact.

Graph summary

The velocity graph shows each cart's velocity changing at contact and includes a steady center-of-mass velocity line. The momentum graph shows the cart momentum lines changing while the total momentum line stays flat.

The energy graph shows whether total kinetic energy is preserved or drops at contact, which is the main visual difference here between elastic and inelastic collisions.

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