Conservation of Momentum Calculator

Conservation of momentum states that the total momentum of an isolated system remains constant. Momentum is the product of mass and velocity, written p = mv. Because velocity includes direction, momentum is a vector quantity. In a one-dimensional calculation, a positive sign represents one direction and a negative sign represents the opposite direction. The calculator therefore accepts negative initial velocities for objects moving toward the chosen negative axis. Before a collision, total momentum is m1u1 + m2u2. Afterward, it is m1v1 + m2v2. If no external impulse acts on the pair, those totals are equal. A perfectly inelastic collision occurs when the objects stick together. Both objects then share one final velocity, found by dividing the initial total momentum by the combined mass. Momentum is conserved, but kinetic energy usually is not. Some mechanical energy becomes deformation, heat, vibration, or sound. Vehicle impacts and coupled railway cars are useful approximations, although real systems can have additional motion and external forces. A perfectly elastic collision conserves both momentum and kinetic energy. Solving those two conservation equations gives a separate final velocity for each object. Equal masses exchange velocities in the familiar ideal case. Billiard balls and interactions between small particles are often modeled as elastic when energy losses are small enough to ignore. The calculator uses the standard closed-form equations for a head-on, one-dimensional elastic collision. Use one consistent mass unit and one consistent velocity unit. The labels use kilograms and metres per second, so momentum is reported in kilogram metres per second and kinetic energy in joules. The momentum totals before and after should agree apart from display rounding. For an elastic collision, the two kinetic-energy totals should also agree. For a perfectly inelastic collision, the final kinetic energy should be no greater than the initial value. This model assumes two bodies, straight-line motion, instantaneous contact, and no important external force during impact. It does not model spin, impact angle, friction after impact, deformation details, or a coefficient of restitution between zero and one. Those effects require a more detailed mechanics model. Within its assumptions, the calculator provides a quick way to check homework, compare collision types, and understand how mass and signed velocity control the result.