Mechanical energy is defined as the total energy of a system, comprising both potential and kinetic energy. In the absence of external forces, the mechanical energy of a closed system remains constant.

Mechanical energy is a fundamental concept in physics, particularly in the analysis of physical systems and their dynamics. It represents the energy associated with an object’s motion (kinetic energy) and its position relative to other objects (potential energy). In essence, mechanical energy is the energy an object possesses due to its motion or its position within a force field.

Kinetic energy is the energy an object has due to its motion. It is determined by the object’s mass and velocity, expressed mathematically as:

where $m$ is the mass and $v$ is the velocity of the object. On the other hand, potential energy is the energy stored in an object due to its position in a force field, such as gravitational or electromagnetic fields, or due to its configuration. The most common types of potential energy include gravitational potential energy (GPE), calculated as:

where $m$ is the mass, $g$ is the acceleration due to gravity, and $h$ is the height above a reference point. Another example is elastic potential energy, which is stored in objects like springs when they are stretched or compressed.

The principle of conservation of mechanical energy states that in an isolated system—one not influenced by external forces—the total mechanical energy remains unchanged. This means energy can transform between potential and kinetic forms, but the overall amount of energy in the system stays constant. For instance, when a pendulum swings, it reaches its maximum potential energy and minimum kinetic energy at the highest point of its swing. Conversely, at the lowest point, the pendulum has maximum kinetic energy and minimum potential energy. Throughout the swing, the total mechanical energy, the sum of potential and kinetic energy, remains constant.

Understanding mechanical energy and its conservation is vital in physics, as it allows us to predict the motion of objects under specific conditions. This concept is foundational to many important principles and equations throughout the field.