When two objects collide, the event is governed by fundamental principles that dictate how motion and energy are exchanged. Physics relies on conservation principles, which state that certain properties of an isolated system remain constant throughout an interaction. This often leads to a perplexing question when dealing with collisions where objects deform or stick together. How can an event lose significant energy yet still obey one of the foundational laws of physics?
The Fundamental Principle of Momentum Conservation
Momentum is a measure of an object’s mass in motion, calculated as the product of its mass and its velocity. Because velocity is a vector quantity, momentum also possesses both magnitude and direction, meaning the direction of travel is just as important as the speed. This concept forms the basis of the Law of Conservation of Momentum, which is one of the reliable laws in the study of mechanics.
This law states that the total momentum of a system remains constant over time. This constancy holds true only if the system is isolated, meaning it is not subject to any net external forces acting upon it. A “system” in physics is a defined collection of objects, and for the conservation law to apply, nothing outside that boundary should be influencing the total motion.
For example, if two ice skaters push off each other on a frictionless surface, the system includes both skaters. The forces they exert on each other are internal, and while their individual momenta change, the total momentum of the two-skater system remains exactly the same. This principle is derived directly from Newton’s second and third laws of motion, establishing it as a universal rule for any isolated collection of masses.
What Defines an Inelastic Collision
An inelastic collision is defined by the fact that kinetic energy is not conserved during the interaction. Kinetic energy, the energy of motion, is lost from the system when the objects meet and interact. This loss distinguishes it sharply from an ideal elastic collision, such as two hard spheres bouncing perfectly, where both momentum and kinetic energy are conserved.
In a real-world inelastic event, the “lost” kinetic energy does not simply vanish but is instead transformed into other forms of energy. A significant portion is often converted into internal energy, manifesting as heat within the colliding materials. Sound energy is also produced as the objects strike one another, carrying away a small amount of the initial kinetic energy.
Furthermore, the energy is used to permanently deform the shapes of the colliding objects, absorbing energy in the process of bending or crumpling materials. In the most extreme case, known as a perfectly inelastic collision, the objects stick together after impact and move as a single combined mass. Partially inelastic collisions involve some deformation and energy loss, but the objects still separate after the event.
Why Momentum Remains Conserved
The key to understanding momentum conservation in an inelastic collision lies in correctly identifying the forces at play. Momentum is conserved because the total net external force acting on the system remains zero. The conservation law depends on this external force condition, not on the state of the system’s internal energy.
During the short duration of the impact, the forces exerted between the colliding objects are considered internal to the system. According to Newton’s Third Law of Motion, these internal forces are equal in magnitude and opposite in direction, meaning they cancel each other out when calculating the net force on the entire system. Therefore, even though the objects are interacting and experiencing changes in their individual velocities, the total momentum vector of the defined system remains constant. Momentum calculation, which involves mass and velocity, is unaffected by the transformation of kinetic energy into heat or sound.
Momentum is a vector quantity, calculated by mass and velocity, while kinetic energy is a scalar quantity, dependent on mass and the square of velocity. The initial total momentum before the impact must equal the final total momentum after the impact, regardless of how the energy was transformed internally.
Real-World Examples of Inelastic Collisions
Inelastic collisions are common occurrences, providing clear demonstrations of the conservation principle. A car crash where the vehicles crumple and interlock represents a perfectly inelastic collision. Although significant kinetic energy is absorbed by the deformation and sound, the total momentum of the two-car system immediately before impact is equal to the momentum of the combined wreckage moving afterward.
Another example involves a bullet embedding itself in a stationary block of wood. The momentum of the fast-moving bullet is transferred to the combined, slower-moving system of the bullet and the block. The conservation of momentum equation (m1v1 + m2v2 = (m1+m2)vf) allows engineers to determine the final speed of the combined mass based on the initial conditions.
Similarly, two football players tackling and moving together as a single unit illustrates a partially inelastic event. Even though the players generate heat and sound upon impact, the total momentum of the two-player system is conserved, dictating the subsequent direction and speed of the combined mass.