College Physics II – Mechanics, Sound, Oscillations, and Waves
Definition
An elastic collision is a type of collision between two objects where the total kinetic energy of the system is conserved. In an elastic collision, there is no net loss of kinetic energy, and the objects simply exchange momentum without any deformation or change in internal energy.
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In an elastic collision, the total momentum of the system is conserved, meaning the sum of the initial momenta is equal to the sum of the final momenta.
Elastic collisions are characterized by the absence of any energy dissipation, such as heat or deformation, during the collision process.
The kinetic energy of the system is also conserved in an elastic collision, meaning the sum of the initial kinetic energies is equal to the sum of the final kinetic energies.
Elastic collisions are often used to model the behavior of particles in particle accelerators, as well as the interactions of atoms and molecules in gases and solids.
The coefficient of restitution, a value between 0 and 1, is used to quantify the degree of elasticity in a collision. A coefficient of 1 indicates a perfectly elastic collision.
Review Questions
Explain how the principle of conservation of energy applies to an elastic collision.
In an elastic collision, the total kinetic energy of the system is conserved. This means that the sum of the initial kinetic energies of the colliding objects is equal to the sum of the final kinetic energies after the collision. Since there is no loss of energy during the collision, the total energy of the system remains constant, in accordance with the principle of conservation of energy.
Describe the relationship between the coefficient of restitution and the elasticity of a collision.
The coefficient of restitution is a measure of the elasticity of a collision. It ranges from 0 to 1, with 1 representing a perfectly elastic collision where no energy is lost. As the coefficient of restitution approaches 1, the collision becomes more elastic, and the objects exchange momentum without any significant loss of kinetic energy. Conversely, as the coefficient of restitution decreases towards 0, the collision becomes more inelastic, and a greater portion of the kinetic energy is converted into other forms, such as heat or deformation.
Analyze the role of elastic collisions in the context of particle physics and the behavior of atoms and molecules.
Elastic collisions play a crucial role in the study of particle physics and the behavior of atoms and molecules. In particle accelerators, such as the Large Hadron Collider, particles are accelerated to high energies and made to collide with each other. These collisions are often modeled as elastic, as the total kinetic energy and momentum of the system are conserved, allowing researchers to study the fundamental properties and interactions of subatomic particles. Similarly, in the study of gases and solids, the interactions between atoms and molecules are often approximated as elastic collisions, which helps in understanding the transport properties, thermodynamics, and phase transitions of these systems.
An inelastic collision is a type of collision where the total kinetic energy of the system is not conserved. In an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or deformation.
Impulse is the product of the force acting on an object and the time over which the force is applied. It is equal to the change in momentum of the object.
The principle of conservation of linear momentum states that the total linear momentum of a closed system is constant, unless an external force acts on the system.