Lecture

Elastic Collisions: Derivation

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Description

This lecture covers the derivation of elastic collisions, focusing on different types of collisions, calculations in the center-of-mass reference frame, and specific cases like frontal collisions and variable mass systems. The instructor explains the conservation of momentum and kinetic energy, providing detailed calculations for velocities before and after the collision.

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Related concepts (32)

Head-on collision

A head-on collision is a traffic collision where the front ends of two vehicles such as cars, trains, ships or planes hit each other when travelling in opposite directions, as opposed to a side collision or rear-end collision. With railways, a head-on collision occurs most often on a single line railway. This usually means that at least one of the trains has passed a signal at danger, or that a signalman has made a major error. Head-on collisions may also occur at junctions, for similar reasons.

Collision

In physics, a collision is any event in which two or more bodies exert forces on each other in a relatively short time. Although the most common use of the word collision refers to incidents in which two or more objects collide with great force, the scientific use of the term implies nothing about the magnitude of the force. In physics, collisions can be classified by the change in the total kinetic energy of the system before and after the collision: If most or all of the total kinetic energy is lost (dissipated as heat, sound, etc.

Center-of-momentum frame

In physics, the center-of-momentum frame (COM frame), also known as zero-momentum frame, is the inertial frame in which the total momentum of the system vanishes. It is unique up to velocity, but not origin. The center of momentum of a system is not a location, but a collection of relative momenta/velocities: a reference frame. Thus "center of momentum" is a short for "center-of-momentum ". A special case of the center-of-momentum frame is the center-of-mass frame: an inertial frame in which the center of mass (which is a single point) remains at the origin.

Inelastic collision

An inelastic collision, in contrast to an elastic collision, is a collision in which kinetic energy is not conserved due to the action of internal friction. In collisions of macroscopic bodies, some kinetic energy is turned into vibrational energy of the atoms, causing a heating effect, and the bodies are deformed. The molecules of a gas or liquid rarely experience perfectly elastic collisions because kinetic energy is exchanged between the molecules' translational motion and their internal degrees of freedom with each collision.

Conservation of mass

In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass cannot change, so the quantity can neither be added nor be removed. Therefore, the quantity of mass is conserved over time. The law implies that mass can neither be created nor destroyed, although it may be rearranged in space, or the entities associated with it may be changed in form.

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