Elastic And Inelastic Collisions In One And Two Dimensios

The meeting of two or more bodies in split-second contact is a collision. The meeting could be due to excitation or the natural motion of the bodies. The event in which two bodies exert forces on each other for a relatively short time is a collision. In everyday usage, the term often implies that these forces cause damage to one or more of the colliding objects. If so, the collision is called an impact. An example of a non-impact collision is when two cars bump each other from several feet away at low speeds to pass on a narrow street without damage to either the car or the people involved.

Types of Collisions 

When two bodies collide and bounce off of each other with the same amount of kinetic energy before the collision, the collision is said to be elastic. An inelastic collision between two bodies is one in which the total kinetic energy of all bodies after the collision is significantly less than before.                                                                                                                                                                                                  Elastic collisions can be further divided into either perfectly elastic or inelastic, depending on whether all kinetic energy is conserved. A perfectly elastic collision results when no kinetic energy is lost during impact. Two bodies brought together in the absence of friction would bounce apart with the same kinetic energy that they came together. This is sometimes referred to as a perfectly inelastic collision or perfectly plastic collision. The total kinetic energy before the collision would equal the total kinetic energy after the collision, with a perfectly elastic collision resulting in no net change in kinetic energy and a perfectly inelastic collision resulting in zero net change.              In reality, none of these is genuinely elastic, even if conservation of momentum is satisfied. A ball bouncing off a rubber surface will show less rebound than expected (due to elastic deformation). However, there will still be some loss of potential energy due to deformation (energy needed to damage internal bonds). 

Energy Transfer in Collisions

1. Kinetic energy may be converted to another form (such as potential) during a collision and converted back into kinetic energy, but only if all mass remains constant (neglecting gravity). However, in a collision between two colliding bodies with equal masses but unequal speeds (such as a bullet and a bulletproof vest), the kinetic energy of one body is converted to potential energy. Still, the potential energy of the other body is converted to kinetic energy. This sometimes causes bullets to pass through heavy vests without exploding. 
2. Similarly, in non-contact collisions between bodies with equal masses but unequal speeds (such as ping-pong balls), the energy is transmitted evenly (from kinetic to potential and back again). The speed at which it occurs depends on how close the bodies are when they collide.
3. In the case of an elastic collision, in which no kinetic energy is lost, the bodies do not move relative to one another. For example, two ping-pong balls colliding just after the bounce appears to be a perfectly elastic collision. In this case, “elastic” refers only to each ball’s shape and other properties (such as mass) before colliding; it does not refer to how they move after they collide. Whether or not a collision is elastic often depends on the speed of each body and what happens to them immediately afterwards.

Collisions are also studied in fields outside particle physics (where conservation laws are assumed). David L. Goodstein has described the word “elastic” when applied to collisions as “a misnomer in general usage since in many collisions between objects there is always some loss of energy.”

When Do Elastic and Inelastic Collisions Occur? 

Usually, colliding objects push each other apart due to energy lost in the collision. Thus, it is reasonable to say that most collisions are not elastic, even though the conservation of linear momentum is satisfied.

An elastic collision occurs when two objects collide, and after the collision, they both emerge with their initial kinetic energy. This includes all forms of energy that the two objects can transfer to each other, including kinetic, potential, elastic, and plastic deformation (of a rigid body) and internal changes in the material composition such as chemical reactions or phase transitions (e.g., from liquid water to steam).

Inelastic collisions occur when the total kinetic energy is significantly different from the initial value. Thus, the final kinetic energy is less than the initial kinetic energy. Inelastic collisions are often characterised by an increase in total energy so that the total is more significant than either individual kinetic or potential energies.

For example, an elastic collision between a golf ball and a tennis ball may result in a net loss of energy for each ball due to friction during the impact, causing their initial speeds to be different from their final speeds calculated from the velocity of impact. This means that neither will hit the hole with its initial speed. Thus, one ball will strike further up on the green than it would have if not for its collision with the other ball (total gravity losses due to both objects being slowed down).

Inelastic Collision in Two Dimension

In an inelastic collision in two-dimension, conservation of momentum can be applied separately in both dimensions. Both axes have a one-one equation for momentum conservation. In the same way, there will be a single energy conservation equation.

When an object having mass m₁ collides with another object having mass m₂ that is stationary, they both move in opposite directions. In addition, the linear momentum of these two masses is conserved in their two-dimensional interaction. The components along the x and y axes will now have the following equations:

m₁u₁ = m₁u₂ cos θ₁ + m₂v₂ cos θ₂

0 = m₁u₂ sin θ₁ – m₂v₂ sin θ₂

This collision phenomenon can be seen while playing carrom, billiards, etc.

Conclusion

Collisions are essential in many fields of science. The study of collisions is called colliding-particle physics. In particle physics, a collision event is usually expressed by an equation of motion for both bodies before and after the collision. The energy exchanged in the collision would be expressed as the sum of kinetic and potential energies, with the total energy conserved (no change in total energy). This conservation principle is the law of conservation of linear momentum, or sometimes just conservation of momentum.