WE+WF=ΔK+ΔU
Here,
WE=0
WF=0
Hence, for
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1/2g+1/2kxf=0
In most cases, the conservation of mechanical energy is likely to hold true in this scenario.
The law of conservation of energy states that the total energy in the universe is a constant and will remain so for example ( x=y+z ). conservation of energy has to do with reducing the amount of energy used through reduced activity and/or increased efficiency in the performance of a particular task.
Energy
Conservation of mechanical energy is valid in situations where only conservative forces are acting on the system, such as gravitational or spring forces. Non-conservative forces, like friction or air resistance, can cause mechanical energy to be lost from the system, making conservation of energy invalid. Additionally, the system must be isolated from external influences for conservation of mechanical energy to hold true.
Mechanical energy is always conserved in a closed system. It can exist as potential energy (stored energy) and kinetic energy (energy of motion). This conservation principle is known as the law of conservation of mechanical energy.
This simply means that, as long as no mechanical energy is wasted or converted to other types of energy (and no other type of energy to mechanical energy), the total amount of mechanical energy doesn't change. Mechanical energy refers to the sum of kinetic and potential energy. Since energy losses and energy conversions do occur, this is not really a "law". In other words, the law of conservation of energy has not been known to be violated; conservation of mechanical energy is very easily violated.
Conservation of mechanical energy states that the sum of kinetic and potential energy remains constant in a system with only conservative forces at work. On the other hand, conservation of total energy includes all forms of energy including mechanical, thermal, chemical, etc. and states that the total energy of a system remains constant in the absence of external forces like friction or air resistance.
rubbing of two wood
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Mechanical Energy
The energy loss equation states that the total energy input into a system is equal to the energy output plus any energy lost as heat or other forms. This equation relates to the conservation of energy principle, which states that energy cannot be created or destroyed, only transferred or transformed. By accounting for energy losses, we can ensure that the total energy in a system remains constant, in line with the conservation of energy principle.