What is a conservation law? What is the basic approach taken when using a conservation law?

A conservation law is a fundamental principle in science which states that certain measurable properties, or quantities, of an isolated physical system remain constant as the system evolves over time. These properties are said to be "conserved," and the conservation of these quantities is based on the principle of invariance under specific transformations. Conservation laws are used to solve a wide range of problems in physics, chemistry, and engineering.

The basic approach to resolving a problem using a conservation law consists of the following steps: 1. Identify the isolated system: Determine the isolated system/component for which the conservation law will be applied. An isolated system is one which does not experience any significant external inputs/forces. 2. Identify the conserved quantity: Determine which specific property or quantity is thought to be conserved based on the given problem. Commonly conserved quantities include mass, energy, and momentum, although there are other examples within specific branches of science. 3. Set up conservation equations: Write equations that represent the conservation of the identified quantity, both before and after any interactions or transformations within the isolated system. These equations should include terms for the initial and final states of the system. 4. Solve the equations: Use the established conservation equations along with any given or known information about the system to solve for unknown variables or to prove that the conservation law holds true for the specific problem. By following these steps, one can effectively utilize conservation laws to solve various problems in science and engineering.