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Momentum & Collision Simulator

Set the masses and velocities of two objects, choose a collision type, and watch the result play out. The simulator shows momentum conservation, energy analysis, and step-by-step solutions for elastic, inelastic, and partially inelastic collisions. All calculations run in your browser.

Object 1
Object 2
v₁ (final)
-3.2 m/s
v₂ (final)
2.8 m/s
KE Lost
0 J (0%)
Impulse
14.4 N\u00B7s
BeforeAfterConserved
Momentum2 kg·m/s2 kg·m/sYes
Kinetic Energy22 J22 JYes
Step-by-Step

Reference Guide

Conservation of Momentum

Momentum is the product of mass and velocity. In any closed system, the total momentum before a collision equals the total momentum after, regardless of collision type.

Momentum
p=mvp = mv
Conservation law
m1v1+m2v2=m1v1+m2v2m_1 v_1 + m_2 v_2 = m_1 v_1' + m_2 v_2'

This principle holds for all collision types. It follows directly from Newton's third law: the forces the two objects exert on each other are equal and opposite, so the total impulse is zero.

Elastic Collisions

In an elastic collision, both momentum and kinetic energy are conserved. These two constraints together determine the final velocities uniquely.

Final velocity of object 1
v1=(m1m2)v1+2m2v2m1+m2v_1' = \frac{(m_1 - m_2)v_1 + 2m_2 v_2}{m_1 + m_2}
Final velocity of object 2
v2=(m2m1)v2+2m1v1m1+m2v_2' = \frac{(m_2 - m_1)v_2 + 2m_1 v_1}{m_1 + m_2}

For equal masses, the objects swap velocities. This is why a billiard ball stops dead when it hits another ball of the same mass head-on.

Inelastic Collisions

In an inelastic collision, momentum is conserved but kinetic energy is not. Some kinetic energy is converted into heat, sound, or deformation.

Perfectly inelastic (objects stick together)
v=m1v1+m2v2m1+m2v' = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2}

A perfectly inelastic collision loses the maximum possible kinetic energy while still conserving momentum. The objects move together as a single unit after the collision.

Coefficient of Restitution

The coefficient of restitution measures how "bouncy" a collision is. It is defined as the ratio of relative speeds after and before the collision.

Definition
e=v1v2v1v2e = -\frac{v_1' - v_2'}{v_1 - v_2}

When e=1e = 1 the collision is perfectly elastic. When e=0e = 0 the collision is perfectly inelastic. Values between 0 and 1 describe partially inelastic collisions. Combined with momentum conservation, ee fully determines the final velocities.