Perfectly Inelastic Collision

The shared velocity follows directly from the momentum balance: the sum of each object’s mass multiplied by its initial velocity equals the combined mass multiplied by the final velocity. Thus, the final motion depends on both masses and on the directions and magnitudes of their initial velocities. Opposing velocities can reduce or reverse the resulting motion.

Kinetic energy is not conserved because the impact redirects part of the system’s organized motion into internal forms of energy. Deformation, heating, sound, and related internal changes account for the decrease. Momentum can still remain constant because it describes the system’s total translational motion, whereas kinetic energy tracks motion available as mechanical speed.

The greatest kinetic-energy loss occurs when the post-impact motion is constrained to one common velocity rather than allowing separate speeds afterward. The more the initial velocities differ, the more kinetic energy can be converted during contact, while the momentum condition still fixes the allowable shared motion. This makes sticking collisions a useful limiting model.

Isolation is the key condition for applying momentum conservation without adding an external impulse. During analysis, treat the colliding objects as one system and account for their total momentum before and after contact. If outside effects matter, the simple shared-velocity result no longer follows from momentum conservation alone, so the model must be applied cautiously.

To analyze an event, first record each object’s mass and initial velocity, including direction. Add the initial momenta, combine the masses after contact, and use the momentum balance to determine their common final velocity. A useful final check is to compare total kinetic energy before and after impact and identify the decrease as converted internal energy.

After contact, the missing kinetic energy has not disappeared; it has changed form within the system. Deformation may alter the objects, while heat and sound carry energy away from the original bulk motion. Tracking these channels explains why a perfectly inelastic collision can conserve momentum yet produce a lower post-impact kinetic-energy value.

Vehicle impacts provide a practical setting for estimating the motion of joined masses after impact. In a ballistic pendulum, a projectile and target can be treated through the same momentum-based reasoning, while particle interactions offer a smaller-scale application. Across these cases, the model connects measured masses and velocities with the resulting common motion.

Comparing the system’s kinetic energy before and after contact reveals how much mechanical kinetic energy was converted into internal energy. That comparison provides information beyond the final velocity and helps distinguish momentum conservation from kinetic-energy conservation. This distinction is central when interpreting collision experiments, impact outcomes, and the physical changes produced during contact.