Conservation of energy

Why energy is perhaps the most Ubiquitous Quantity in physics - Copilot 

Elastic collisions

Energy skate park        

What is a conservative force 

Potential energy for conservative force   ( Uf -Ui ) = - W conservative force          

Conservation of the mechanical energy       Emech = Ki +Ui = Kf +Uf     or      (Kf-Ki ) + (Uf-Ui) = 0

Gravitational potential energy         GPE = m*g*h

Work of a non-conservative force          

Non conservation of the  mechanical energy         Kf +Uf  =Ki +Ui + Wnon conservative          

Isolated systems and conservation of the  total energy

**Potential energy as mutual energy       W1,2  +    W2,1    =  -   {Change of the mutual potential energy}

 Forms of energy: 

• 1. Gravitational potential energy

  2. Electromagnetic energy

     • • Electrostatic, Chemical

       • Magnetic

       • Light

  3. Nuclear energy

     • • Fission - heavy nuclei

       • Fusion - light nuclei

  4. Macroscopic kinetic energy

     • • Fluid/gas in motion (wind)

       • Solid in motion(asteroid)

  5. Microscopic kinetic energy

     • • Thermal kinetic energy and temperature

       • Thermal potential energy and heat capacity

  6. Matter antimatter energy

  7. Who knows what

     • • Energy of empty space

       • Vacuum energy

       • Dark energy

• Total potential energy as mutual property(coordinate free scalar considerations) in position space    Individual potential energy exist only for non interacting particles immersed in global  force field     Immunity to translation, rotations and boost but NOT time translations    Link between potential energy and force

• Total kinetic energy as a individual  property in velocity space    Immunity to spacial translations and rotations but NOT time translations    Link between kinetic energy and force

• Work as transferred energy either Kinetic to potential or Potential to kinetic

• YES the total energy is immune to TIME translation    In every time interval total kinetic energy gained/lost is equal to the total potential energy lost/gained