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State and establish principle of conservation of mechanical energy . |
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Answer» Solution :Let this principle will be obtain in one dimension . If a body UNDERGOES distance `Deltax` by conservativeforceF then according to work energy (WE) theorem , `DeltaK = F (x) Deltax ""….(1)` but according to definition of POTENTIAL energy for conservative FORCE , `-DeltaV = F(x)Deltax ""....(2)` From equation (1) and (2) , `DeltaK = - DeltaV ` `:. DeltaK + DeltaV = 0 ` ` :. Delta(K+V) =0` ` :. ` The change of kinetic energy and potential energy is zero . That means sum of kinetic energy for conservative force , ` -DeltaV = F(x) Deltax ""....(2)` From equation (1) and (2) , `DeltaK+DeltaV = 0 ` ` :. Delta(K+V) = 0 ` ` :. ` The chance of kinetic energyand potential energy is zero . That means sum of kinetic energy and potential energy is a constant . ` :. K+V ` = constant Over the whole path , `x_(i) ` to `x_(f)` this means that `K_(i) +V(x_(i))=K_(f) +V(x_(f))` ` :. ` The quantity `K + V(x) ` is called the total mechanical energy of the system . The kinetic energy K and potential energy V(x) is called the total mechanical energy of the system . The kinetic energy Kand potential energy V(x) MAY vary from point to point but the sum remains constant . Mechanical energy is conserved in conservative field . That means as we go above and above form earth.s surface the kinetic energy and potential energy increases . The principle of total mechanical energy is written as under : "The total mechanical energy of a system is conserved if the forces doing work on it are conservative ". "Under INFLUENCE of conservative forces the mechanical energy of a mechanically isolated " system remain constant. |
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