Question

Derivation of conservation of mechanical energy

Answer 1

Answer:

the sum total of an object kinetic and potential energy at any given point in time is its total mechanical energy the law of conservation of energy says energy can neither be created nor be destroyed in a chemical reaction

Answer 2

Dear student,

The conservation of mechanical energy theorem can be derived with the help work-energy theorem and negative work done by the conservative forces or potential energy.

By the work energy theorem, we know that;

                 W(all forces) = ΔK.E.

or,          Wc.f. + W.n.c.f. = ΔK.E.

where,   Wc.f. = work done by

                          conservative forces

and,    Wn.c.f. = work done by

                          non conservative forces

Let the work done by the non conservative forces = 0. Then;

           Wc.f. = ΔK.E. ____(1)

Now, we also know that by potential energy formula that:

           - Wc.f. = Δu _____(2)

Putting (2) in (1), we obtain;

           - Δu = ΔK.E.

               0 = ΔK.E. + Δu

               0 = Δ(K.E. + u)

Through the concept of error analysis;

               K.E. + u = constant

So, we obtain;

       K.E.i + Ui = K.E.f + Uf.

where, K.E.i = initial kinetic energy

           K.E.f = final kinetic energy

             Ui = initial potential energy

             Uf = final potential energy

Hence, we have derived the conservation of mechanical energy theorem and is as stated;

           K.E.i + Ui = K.E.f + Uf.