Conservation Of Momentum⚠ unverified
Physics / Mechanics · Compute the common final velocity of a perfectly inelastic collision
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| mass1 | mass1 | kg | 1.0 | Mass of the first body |
| velocity1 | velocity1 | m/s | 1.0 | Initial velocity of the first body |
| mass2 | mass2 | kg | 1.0 | Mass of the second body |
| velocity2 | velocity2 | m/s | 1.0 | Initial velocity of the second body |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | vf | m/s | Final velocity shared by the combined mass, in metres per second (m/s) |
The science & history
Understanding the Parameters
- $m_1, m_2$ — inertial masses; total mass $m_1+m_2$ carries the combined momentum after sticking.
- $v_1, v_2$ — signed speeds on a line (opposite directions ⇒ opposite signs).
- $v_f$ — single post-collision velocity of the stuck pair. Kinetic energy is not conserved (lost to deformation/heat).
Derivation (Approaching a Proof)
If external impulse is negligible during the collision, total linear momentum is conserved:
$$m_1 v_1 + m_2 v_2 = m_1 v_{1f} + m_2 v_{2f}.$$
For a perfectly inelastic collision the bodies share one velocity $v_f$:
$$m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f \quad\Rightarrow\quad v_f = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2}.$$
Elastic collisions need a second equation (energy or coefficient of restitution) and generally two distinct final speeds — not implemented here.
History
Momentum conservation follows from Newton’s laws (or spatial translation symmetry / Noether). The inelastic common-velocity formula is the standard first collision example in introductory mechanics.
Related Concepts: Momentum, Impulse, Kinetic Energy, Reduced Mass
Notes: Registry calculator conservation-of-momentum (unverified). Heuristic scope: 1-D
perfectly inelastic only. Name suggests general conservation; the equation is the sticky special case.