The conservation of mechanical energy is a fundamental principle in physics that states that the total mechanical energy in a closed system remains constant, regardless of any internal energy transformations. This principle is based on the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed from one form to another.

To understand the conservation of mechanical energy, let's consider a simple system consisting of a block of mass m sliding along a frictionless surface on a horizontal plane. In this system, the mechanical energy is the sum of the kinetic energy (KE) and potential energy (PE), given by the equations:

KE = (1/2)mv^2

PE = mgh

where v is the velocity of the block, g is the acceleration due to gravity, and h is the height of the block above a reference point.

According to the conservation of mechanical energy, if no external forces act on the block, the total mechanical energy of the system remains constant throughout its motion.