Question

derive relation for kinetic and potential energy? ​

Answer 1

Derivation for the equation of Potenstial Energy: Let the work done on the object against gravity = W                  Work done, W = force × displacement                  Work done, W  = mg × h                  Work done, W = mgh Since workdone on the object is equal to mgh, an energy equal  to mgh units is gained by the object . This is the potential energy (Ep) of the object.                               Ep = mgh Derivation for the equation of Kinetic Energy: The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, S is                               v2 - u2= 2aS This gives                                S = v 2 - u 2 2a We know F = ma. Thus using above equations, we can write the workdone by the force, F as                             W = ma × v2 - u 2 2a                                   or                             W = 1 2 m( v 2 - u 2 ) If object is starting from its stationary position, that is, u = 0, then                            W = 1 2 m v 2   It is clear that the work done is equal to the change in the kinetic energy of an object. If u = 0, the work done will be  W = 1 2 m v 2 . Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is Ek=  ½  mv2


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