There are two main types of energy, kinetic energy and potential energy.
Kinetic energy is the energy an object has due to its motion:
Potential energy is the energy an object stores due to its position. Potential energy may be stored due to a gravitational field or in a spring:
Energy is always conserved, so initial energy = final energy. Each energy here is the sum of the kinetic and potential energies. If work is done in the process (due to friction etc), energy is lost, so this must be factored into the equation.
Conservation of energy can be used with conservation of momentum when doing calculations about collisions, and lots of other processes.
It is always observed that energy is conserved, but this is very hard to prove mathematically. There’s a nice proof on YouTube here.
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