The Foundation of Momentum Conservation: Isolated Systems
Momentum is a fundamental property of moving objects, defined mathematically as an object’s mass multiplied by its velocity. Since velocity is a vector quantity, momentum possesses both magnitude and direction. The principle of conservation states that a property remains constant over time, and the conservation of momentum asserts that the total momentum of a collection of objects never changes, provided the system is isolated.
Momentum conservation is strictly guaranteed only when the net external force acting on the system is zero. An external force is any force originating from outside the defined system, such as friction or air resistance. In the absence of these outside influences, the system’s total momentum cannot be altered.
This conservation is a direct consequence of Newton’s laws of motion. If the net external force is zero, the total change in momentum must also be zero. Therefore, the total momentum before and after any interaction, such as a collision, must be equal. While the momentum of an individual object within the system can change dramatically, the total momentum of the entire system remains constant.
Internal Forces and Newton’s Third Law
The constancy of total momentum is maintained even during the collision event through the action of internal forces between the colliding objects. When two objects interact, the forces they exert on each other are governed by Newton’s Third Law of Motion. This law states that the force exerted by the first object on the second is equal in magnitude and opposite in direction to the force the second object exerts on the first.
These forces are considered internal to the system. Because the forces are equal and opposite, they exert equal and opposite impulses on the objects. Since an impulse is the change in momentum an object experiences, these impulses cancel out, ensuring the net change in the system’s total momentum is zero.
For example, if object A loses momentum, object B must simultaneously gain an equal amount of momentum in the same direction. While the momentum of each object changes during the brief contact, the total momentum of the combined system remains unchanged. This principle ensures momentum is conserved in any collision, regardless of its type, provided the system is isolated.
The Role of Kinetic Energy in Elastic Collisions
The specific term “elastic collision” refers to the behavior of kinetic energy, not momentum conservation. An elastic collision is defined as one where the total kinetic energy of the system is also conserved. Kinetic energy, the energy of motion, remains the same before and after the collision, meaning no energy is converted into other forms.
In a perfectly elastic collision, the objects rebound without permanent deformation, and no energy is lost to heat, sound, or internal vibrations. This is an idealized physical scenario, though collisions between atoms can approximate this behavior. Most macroscopic collisions, such as billiard balls striking each other, involve a minor loss of kinetic energy.
In contrast, an inelastic collision is one where kinetic energy is not conserved, as some is lost to heat, sound, or deformation. Even in an inelastic collision, the total momentum of the isolated system is still conserved. The designation “elastic” specifies the type of collision where both momentum and kinetic energy are conserved quantities.