The student is expected to demonstrate and apply the laws of conservation of energy and conservation of momentum in one dimension.
The conservation laws apply to closed systems. The overall energy and momentum of the closed system does not change with the evolution of the system.
The conservation laws imply the symmetry of nature. As one object gains momentum or energy from a collision, the colliding object loses an equal amount of momentum or energy.
Momentum in a closed system is conserved whether the impact is elastic or inelastic.
Because the conservation laws are universal, they always hold true.
Conservation of Energy
Energy can be neither created nor destroyed. It can only transform from one type to another within a closed system. The closed system is a relative concept. It is the isolated object that we investigate. The overall energy and momentum of a closed system does not change with the evolution of the system.
Conservation of Momentum
In the collision example shown in the figure below, the closed system includes two balls with different velocities. The total momentum of this system, p, does not change whether it is an elastic collision or inelastic collision. This is what the Law of Conservation of Momentum tells us.
Diagram of collisions.
In a two body collision, the Law of Conservation of Momentum can be written:
Formula for the conservation of momentum.
Inelastic Collisions: If it is an inelastic collision, part of the kinetic energy is converted to other forms of energy, such as sound energy. Although inelastic collisions may not conserve kinetic energy, they do obey conservation of momentum. Collisions where the objects stick together, as shown in the example, are always inelastic. Collisions involving objects that don’t stick together may be inelastic as well. Partially inelastic collisions are the most common form of collisions in the real world where the collisions do not stick, but some kinetic energy is still converted in several ways:
Thermal Energy: Friction between the objects could cause some of it to be converted to heat (thermal energy).
Reshaped: If the object was permanently changed (broken, bent, snapped, twisted, etc.) from its original shape. This includes if the objects are stuck together after the collision.
Sound or Light Energy: Some energy might have been converted into the energy of a sound or light that was released.
Friction and Heat: Friction and heat are some ways the kinetic energy can be lost through partial inelastic collisions.
Elastic Collisions: In the elastic collision, which is rare, both the momentum and kinetic energy of the system are conserved. In reality, only collisions involving microscopic objects such as atoms and molecules are elastic. However, collisions involving rigid objects like billiard balls and lab carts can often be treated as elastic.
How to Identify the Difference Between Elastic and Inelastic Collisions
1) Start off by calculating, individually, the kinetic energy of each object beforethe collision. Add them together to get the total initial kinetic energy.
2) Then calculate, individually, the kinetic energy of each object after the collision. Add them together to get the total final kinetic energy.
3) If the collision is elastic, the two totals will be the same. If the collision is inelastic, the initial total will be bigger than the final total.
Redistribution of Energy and Momentum
The symmetry of nature is reflected in the conservation laws. As one object gains momentum or energy from a collision, the colliding object looses an equal amount of momentum or energy. This implies that within a certain system, the total energy and momentum are conserved, and the function of collision is to redistribute the energy and momentum.
The conservation laws are universal, and they always hold true. Although in an inelastic collision the kinetic energy could change, the total energy is still conserved. The lost kinetic energy after an inelastic collision may transfer to another type of energy form, such as heat. To sum up, we can say that, momentum of the system is conserved in both elastic and inelastic collisions however; kinetic energy is conserved only in the elastic collisions.