The law of conservation of mechanical energy is a basic law in dynamics.
It describes the law that when there is no external force doing work or only gravity (or elastic force) doing work, the kinetic energy and potential energy (including gravitational potential energy and elastic potential energy) of the object system can be converted into each other, but the total energy of mechanical energy remains unchanged. The following is a detailed explanation of the principle and expression of the law of conservation of mechanical energy:
Principle
Conservation conditions: The establishment of the law of conservation of mechanical energy requires certain conditions to be met, that is, only gravity or elastic force does work inside the system, or the system is not affected by other external forces.
This means that in this process, no mechanical energy is converted into other forms of energy, and no other forms of energy are converted into mechanical energy.
Energy conversion: In a system where only gravity or elastic force does work, the kinetic energy and potential energy of the object will be converted into each other. For example, in free fall, the gravitational potential energy of the object is gradually converted into kinetic energy; in elastic collision, the kinetic energy and elastic potential energy of the object will be converted into each other.
Total energy remains unchanged: Although kinetic energy and potential energy are converted into each other, their sum (i.e. mechanical energy) always remains unchanged.
Expression
The expression of the law of conservation of mechanical energy usually has two forms:
1. Process formula: describes the change of mechanical energy in a certain process.
For example, WG+WFn=ΔEk, where WG represents the work done by gravity, WFn represents the work done by elastic force, and ΔEk represents the change in kinetic energy.
This equation shows that in a process where only gravity and elastic force do work, the sum of the work done by gravity and the work done by elastic force equals the change in kinetic energy.
Another form is E minus=E plus (Ek minus=Ep plus, Ep minus=Ek plus), which means that in a certain process, the decrease in a certain energy is equal to the increase in another energy.
2. State formula: describes the conservation relationship of mechanical energy in different states (or moments, positions). The most commonly used is Ek1+Ep1=Ek2+Ep2, where Ek1 and Ep1 represent the kinetic energy and potential energy of an object in a certain state (or moment, position), respectively, and Ek2 and Ep2 represent the kinetic energy and potential energy of an object in another state (or moment, position), respectively.
This equation shows that in any two states, the sum of the kinetic energy and potential energy of an object is equal, that is, mechanical energy is conserved.
Notes
* When applying the law of conservation of mechanical energy, it is necessary to clarify the scope of the system and determine whether the system meets the conservation conditions.
* When using the state formula, it is necessary to select a unified reference plane to determine the value of potential energy.
* The law of conservation of mechanical energy only applies to inertial reference systems and is only valid in certain special cases (such as ignoring the change in the kinetic energy of the earth in the earth reference system).
In summary, the principle of the law of conservation of mechanical energy is the mutual conversion between kinetic energy and potential energy while the total mechanical energy remains unchanged, and its expression is used to describe the specific manifestation of this conservation relationship in different situations.