State and prove the law of conservation of linear momentum.

Explanation

(i) When an object is thrown upwards its kinetic energy goes on decreasing and consequently its potential energy keeps increasing (neglecting air resistance).
(ii) When it reaches the highest point its energy is completely potential. Similarly, when the object falls back from a height its kinetic energy increases whereas its potential energy decreases.
(iii) When it touches the ground its energy is completely kinetic. At the intermediate points the energy is both kinetic and potential as shown in Figure.
(iv) When the body reaches the ground, the kinetic energy is completely dissipated into some other form of energy like sound, heat, light and deformation of the body etc.

(v) In this example the energy transformation takes place at every point. The sum of kinetic energy and potential energy, i.e., the total mechanical energy always remains constant, implying that the total energy is conserved. This is stated as the law of conservation of energy.
(vi) The law of conservation of energy states that energy can neither be created nor destroyed. It may be transformed from one form to another but the total energy of an isolated system remains constant.
(vii) The figure illustrates that, if an object starts from rest at height h, the total energy is purely potential energy (U = mgh) and teh kinetic energy (KE) is zero at h. When the object falls at some distance y, the potential energy and the kinetic energy remains same as measured at height h. When the object is about to touch the ground, the potential energy is zero and total energy is purely kinetic.