Conservation of Energy Equation

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According to equation of conservation of energy , energy can’t be created nor be destroyed but it transforms from one form to another form. 
 
This law of energy conservation is universally true. It holds very well at all scales of measurement. For example, at the atomic domain the spectra of atoms is being defined by this law.
 
In Mechanical system, Total energy     =    Kinetic energy  + Potential energy
 
It is not mandatory that the right hand side consists of only two term but it may involve some
other form of energy i.e.Heat energy dissipated due to friction,




 Suppose a ba certain heightin height falls on the floor. At the highest
 point the all energy of the ball is purely potential energy.As this ball begins to fall down towards the floor then its energy transforms from potential energy to kinetic energy. At the lowest point the total energy of the ball is purely kinetic.  But in between the height and the floor the total energy of the ball is partially potential and partially kinetic energy.                                         

 Exmaple1.  Consider a ball of mass 50 g  falls from height 2 m on the floor. Calculate the velocity
with which it  strikes the floor ?

Solution   As from equation of conservation of energy; Potential energy converts into the kinetic energy at the bottom.  
             
  Potential energy    =   Kinetic energy

   mgh =     ½ mv2

    v     =     (2gh) ½

and this gives us,
                                                                    
v     =      4.4 m/s


 Example 2  A golf ball of mass 25 g  is thrown upwards with a velocity 5 m/s. Calculate the height at
which it comes at rest ?

Solution   energy of the ball at the lowest point is purely kinetic and this energy being completely transferred
into potential at highest point.
 
So,     1/2mv2   =    mgh

                  h     =     v2/2g

                  h     =     2.5 m

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