What are the conditions of the law of conservation of momentum, the law of conservation of kinetic energy and the law of conservation of mechanical energy, What's the difference?

What are the conditions of the law of conservation of momentum, the law of conservation of kinetic energy and the law of conservation of mechanical energy, What's the difference?

When a system is free from external forces or the sum of external forces is zero, the total momentum of the system remains unchanged, which is called the law of conservation of momentum. The law of conservation of kinetic energy: the velocity remains unchanged. 1. The difference and connection between kinetic energy and momentum? (1) connection: both kinetic energy and momentum are physical quantities describing the motion state of an object, which are determined by the mass and instantaneous velocity of the object

Please use Newton's law and kinematics related knowledge to obtain the law of conservation of mechanical energy through theoretical derivation

Take a free falling body as an example: suppose that an object with mass m falls freely from the place with height h, the acceleration is g, the time taken is t, and the speed at the moment of landing is v. then according to the motion related knowledge: H = g * T ^ 2 / 2. Multiply both sides by mg at the same time to get: MGH = mg ^ 2 * T ^ 2 / 2. And GT = v. substitute the above formula to get: MGH = MV ^ 2 / 2. This is the law of conservation of mechanical energy in a free falling body

How to deduce the law of conservation of mechanical energy

A functional thought
If the mechanical energy of the system is conserved, then E1 + E2 = e ^ 1 + e ^ 2, e ^ 1-e1 = e2-e ^ 2, that is, the decrease of one party's mechanical energy in the system is equal to the increase of the other party's mechanical energy