The conservation of mechanical energy states that the total mechanical energy of a system remains constant, meaning it is neither created nor destroyed, but only transformed between its potential and kinetic forms, provided that the only forces doing work are conservative forces.
Understanding Mechanical Energy
Mechanical energy is the sum of an object's potential energy (energy due to position or configuration) and kinetic energy (energy due to motion).
- Potential Energy (PE): Energy stored in an object due to its position or configuration. Examples include gravitational potential energy (PE = mgh) and elastic potential energy (PE = 1/2 kx^2).
- Kinetic Energy (KE): Energy possessed by an object due to its motion. It is calculated as KE = 1/2 mv^2.
The Principle of Conservation
The principle of conservation of mechanical energy holds true only when conservative forces are acting within the system.
Conservative Forces
Conservative forces are forces for which the work done in moving an object between two points is independent of the path taken. Examples include:
- Gravity: The force of attraction between objects with mass.
- Elastic Force: The force exerted by a spring when stretched or compressed.
- Electrostatic Force: The force between electric charges.
If only conservative forces are acting, the total mechanical energy (E) remains constant:
E = KE + PE = Constant
This means that as an object loses potential energy, it gains an equal amount of kinetic energy, and vice-versa.
Non-Conservative Forces
Non-conservative forces are forces for which the work done depends on the path taken. Examples include:
- Friction: A force that opposes motion between surfaces in contact.
- Air Resistance: A force that opposes the motion of an object through the air.
- Applied forces with external energy input: Forces like a motor driving a car.
When non-conservative forces are present, mechanical energy is not conserved. Some of the mechanical energy is converted into other forms of energy, such as heat (due to friction). The work done by non-conservative forces changes the total mechanical energy of the system.
Examples
- A falling object: As an object falls under the influence of gravity (a conservative force), its potential energy decreases, and its kinetic energy increases, but the total mechanical energy (PE + KE) remains constant (ignoring air resistance).
- A pendulum: As a pendulum swings, it exchanges potential and kinetic energy. At the highest point of its swing, it has maximum potential energy and minimum kinetic energy. At the lowest point, it has minimum potential energy and maximum kinetic energy. If we ignore friction and air resistance, the total mechanical energy remains constant.
- A roller coaster: As a roller coaster car moves along a track, it converts between potential and kinetic energy. At the top of a hill, it has maximum potential energy and minimum kinetic energy. At the bottom of a valley, it has minimum potential energy and maximum kinetic energy. If friction and air resistance are negligible, the total mechanical energy of the roller coaster remains constant.
In summary
The conservation of mechanical energy is a fundamental principle stating that the total mechanical energy (kinetic plus potential) of a system remains constant if only conservative forces are doing work. This means energy can be transformed between potential and kinetic forms, but the total amount stays the same.
