The conditions for conservation of kinetic energy mainly involve the situation where the external and internal forces on an object do work. Specifically, the conditions for conservation of kinetic energy can be summarized as follows:
1. For a single object (particle)
The net force is zero: When the net force on a single object is zero, that is, the object is in equilibrium, its kinetic energy remains unchanged. This is because a net force of zero means that the object has no acceleration, so the velocity (including magnitude and direction) does not change, and thus the kinetic energy (proportional to the square of the velocity) also remains unchanged.
The algebraic sum of the elementary work done by each force is zero: Another situation is that although an object may be acted upon by multiple forces, the algebraic sum of the elementary work done by these forces on the object (i.e., work on a small displacement) is zero. This also means that the kinetic energy of the object has not changed.
2. For a particle system (multi-object system)
The sum of the work done by the external and internal forces on each particle in the particle system is zero: When considering a system consisting of multiple objects, if the sum of the work done by the external and internal forces on each object in the system is zero, the total kinetic energy of the system is conserved. The external force here refers to the force applied by the outside of the system to the objects in the system, while the internal force is the force of interaction between the objects in the system.
Notes
* Kinetic energy conservation is a special case of mechanical energy conservation. It only focuses on the change of kinetic energy, but does not involve the change of potential energy. Therefore, when judging whether kinetic energy is conserved, there is no need to consider the change of potential energy.
* The conditions for kinetic energy conservation are more stringent than those for mechanical energy conservation. Mechanical energy conservation only requires that the sum of the work done by the external force on the system and the work done by the non-conservative internal force in the system is zero, or zero respectively, while kinetic energy conservation requires that the sum of the work done by the external force and the internal force on the system must be zero.
* In practical applications, the conditions for kinetic energy conservation may be difficult to fully meet, but it can be judged whether kinetic energy is approximately conserved by approximate processing. For example, in the process of collision, explosion, etc., if the internal force is much greater than the external force, it can be approximately considered that the kinetic energy of the system is conserved.
In summary, the conditions for kinetic energy conservation mainly involve the situation where the external force and internal force of the object do work. When determining whether kinetic energy is conserved, analysis and calculation are required based on the specific circumstances.