How is mechanical energy defined in a system?

Mechanical energy in a system is defined as the sum of potential energy and kinetic energy. Potential energy is associated with the position of an object, while kinetic energy is associated with its motion. This combined form of energy allows us to analyze various physical situations involving motion and force.

For example, when an object is raised to a height, it gains potential energy, which can be converted into kinetic energy when the object falls. Similarly, a moving object possesses kinetic energy due to its speed and mass. The interplay between these two types of energy can be observed in systems like pendulums, roller coasters, and falling objects, where energy transitions from potential to kinetic and vice versa, while the total mechanical energy remains constant in the absence of external forces.

This understanding of mechanical energy is essential in mechanics, enabling the prediction and analysis of motion and the effects of forces acting on objects. The idea that mechanical energy encompasses both forms highlights the importance of both position and motion in understanding energy within a system.