Conservation of Mechanical Energy - SS1 Physics Lesson Note

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The conservation of mechanical energy is a fundamental principle in physics that states that the total mechanical energy of a closed system remains constant when only conservative forces, such as gravity or elastic forces, are acting on the system. Mechanical energy is the sum of an object's kinetic energy and potential energy.

The principle of conservation of mechanical energy can be stated as follows: In the absence of non-conservative forces like friction or air resistance, the total mechanical energy of a system remains constant.

Mathematically, the conservation of mechanical energy can be expressed as:

Initial Mechanical Energy (KEi + PEi) = Final Mechanical Energy (KEf + PEf)

where KEi and KEf are the initial and final kinetic energies, and PEi and PEf are the initial and final potential energies of the system, respectively.

The conservation of mechanical energy arises from the work-energy theorem, which states that the work done on a system is equal to the change in its kinetic energy. When only conservative forces are at play, such as gravitational or elastic forces, the work done by these forces can be expressed solely in terms of changes in potential energy. Therefore, as long as no non-conservative forces are present, the total mechanical energy of the system remains constant.

This principle has practical implications in various situations. For example:

A swinging pendulum: As a pendulum swings back and forth, its potential energy is continually being converted into kinetic energy and vice versa, but the total mechanical energy of the pendulum remains constant if no external forces, like friction, are present.
A falling object: When an object falls freely under the influence of gravity, its potential energy decreases as it descends, while its kinetic energy increases. The sum of its potential and kinetic energy remains constant as long as no non-conservative forces, like air resistance, are significant.

However, it's important to note that the conservation of mechanical energy applies only to conservative forces and does not account for energy losses due to non-conservative forces. Friction, air resistance, and other dissipative forces can cause a decrease in mechanical energy by converting it into other forms such as thermal energy. It is a valuable tool for analysing and understanding the behaviour of systems subjected to conservative forces and plays a significant role in various areas of physics and engineering.