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Conservation of Momentum Calculator

Use our Conservation of Momentum Calculator to solve collision problems fast. Find final velocity, total momentum, and kinetic energy changes for elastic and inelastic collisions.
Final Velocities
v₁' = -3.4 m/s
v₂' = 3.6 m/s
Total Momentum (P)
4 kg·m/s

✓ Momentum Conserved (ΔP = 0)

Kinetic Energy Change
31 J (Final)

100% KE conserved

Collision Physics Breakdown

  • Total System Momentum: P = 4 kg·m/s (Conserved across collision).
  • Center of Mass Velocity: V_cm = 0.8 m/s.
  • Body 1 (m=2 kg): 5 m/s → -3.4 m/s (Δp = -16.8 kg·m/s).
  • Body 2 (m=3 kg): -2 m/s → 3.6 m/s (Δp = 16.8 kg·m/s).
  • Kinetic Energy: 31 J (Initial) → 31 J (Final). 0% converted to thermal/deformation energy.

elastic collision results in v₁' = -3.4 m/s and v₂' = 3.6 m/s. Total momentum 4 kg·m/s is conserved.

What is momentum?

Momentum tells you how much motion an object has. Use p=mvp = mv to find it from mass and velocity. Momentum also has direction, so signs matter in collisions. This helps you solve momentum equations correctly.

What is a Conservation of Momentum?

Conservation of momentum means total momentum stays constant before and after an interaction. This rule works when outside forces do not change the system. It helps find unknown velocities.

Law of conservation of momentum

The law of conservation of momentum says total momentum remains constant in a closed system. Initial momentum therefore equals final momentum during the event. This rule supports collision calculations.

Elastic and inelastic collisions

Elastic and inelastic collisions both conserve momentum. Elastic collisions also conserve kinetic energy, while inelastic collisions lose some kinetic energy. The collision type changes the final results.

Conservation of Momentum Calculator showing two colliding cars, momentum vectors, and collision physics diagrams.

How can you use our Conservation of Momentum Calculator?

Our Conservation of Momentum Calculator solves collision problems using your values. Enter masses and velocities, choose a collision type, then review final velocity and momentum results for common physics problems.

Step 1

Enter Your Collision Values

Enter the masses and initial velocities of both objects.

Step 2

Choose a Collision Type

Select elastic, inelastic, or completely inelastic collision.

Step 3

View Collision Results

Get the final velocities, total momentum, and kinetic energy change instantly.

The conservation of momentum in different types of impact

Momentum stays conserved in all three collision types when outside forces are negligible. Kinetic energy changes differently in each type, so collision type matters. Choose the correct model first.

Perfectly elastic collisions

A perfectly elastic collision conserves both momentum and kinetic energy. The objects bounce apart after impact, with no kinetic energy changing into other forms. This is an ideal model.

Partly elastic collisions

A partly elastic collision conserves momentum, but some kinetic energy changes into heat, sound, or deformation during the impact. The objects usually separate after collision in most cases.

Perfectly inelastic collisions

A perfectly inelastic collision happens when objects stick together after impact. Momentum stays conserved, but some kinetic energy changes into other forms. The objects share one final velocity.

How to calculate Conservation of Momentum manually

Formula:
m1v1+m2v2=m1′v1′+m2′v2′m_1v_1 + m_2v_2 = m'_1v'_1 + m'_2v'_2

Step by step guide:

  1. Choose a positive direction and give opposite velocities negative signs.
  2. Write each mass and velocity using matching units.
  3. Calculate initial momentum for every object.
  4. Set total initial momentum equal to total final momentum.
  5. Solve for the missing mass or velocity.

Practical Example: A 2 kg object moves at 3 m/s. Its momentum is p=2×3=6p = 2 × 3 = 6 kg·m/s. Check your signs and units, then compare total momentum before and after.

Impulse in Engineering and Sport

Impulse changes momentum when a force acts over time. Engineers study it during crashes, while athletes use it to understand impacts, force, and stopping time. This idea helps explain airbags and safe stopping. Use J=FΔt=Δp to connect force, time, and momentum change.

Momentum in Two Dimensions

In two dimensions, momentum has horizontal and vertical components. Conserve each component separately, then combine them to find final momentum and direction. This method helps solve angled collision problems and moving objects on different paths.

Conservation of Momentum in Collisions and Explosions

Conservation of momentum helps solve collisions and explosions when outside forces are negligible. Add all momentum before the event and set it equal to total momentum after. This works for two or more objects. The same rule explains recoil, rocket motion, and many collision problems.

Conservation of momentum in collisions and explosions showing cars colliding, an explosion, projectile motion, and momentum vectors.

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Frequently Asked Questions

These FAQs explain momentum, conservation, collisions, units, calculator limits, and common checks for student physics problems.