The Universe's Accounting System
One of the most profound and unbreakable laws of the universe is the Law of Conservation of Momentum.
It states that in a closed, isolated system (meaning no external forces like friction or air resistance are interfering), the total momentum of all objects involved must remain completely constant, regardless of what they do to each other. They can crash, bounce, stick together, or even explode—the total momentum before the event will perfectly equal the total momentum after the event.
Momentum ($p$) is simply an object's mass multiplied by its velocity ($p = mv$).
Perfectly Inelastic Collisions
This calculator models a specific, common scenario: a perfectly inelastic collision in one dimension.
In this scenario, two objects crash into each other and, instead of bouncing off, they mechanically deform, lock together, and continue moving as a single, combined, heavier mass. Examples include two train cars coupling together, a bullet embedding into a block of wood, or two football players tackling each other.
Because the two objects stick together, they share a single, identical final velocity.
The Formula
Example Calculation
Imagine a heavy freight train car (Mass 1 = $10,000 , \text{kg}$) rolling down the track at $5 , \text{m/s}$. It crashes into and couples with a stationary car (Mass 2 = $15,000 , \text{kg}$, Velocity 2 = $0 , \text{m/s}$). How fast do the two linked cars move together after the crash?
- Total Initial Momentum: $(10000 \cdot 5) + (15000 \cdot 0) = 50,000 + 0 = \mathbf{50,000 , \text{kg}\cdot\text{m/s}}$.
- Combined Mass: $10000 + 15000 = 25,000 , \text{kg}$.
- Final Velocity: $v_f = \frac{50000}{25000} = \mathbf{2.0 , \text{m/s}}$.
To conserve the $50,000 , \text{kg}\cdot\text{m/s}$ of total momentum, the newly combined, much heavier $25,000\text{kg}$ object must roll at exactly $2.0 , \text{m/s}$.