State law of conservation of energy …

Find video lessons, notes, papers, syllabus, solutions to doubts & more Home / Doubts and Solutions/ICSE/Class 10/Physics How to prove law of conservation of energy? Asked by Sushant Kumar9th March 2014, 3:17 PM Answered by Expert Answer: Law of conservation of energy states that the energy can neither be created nor destroyed but can be transformed from one form to another. Let us now prove that the above law holds good in the case of a freely falling body. Let a body of mass 'm' placed at a height 'h' above the ground, start falling down from rest. In this case we have to show that the total energy (potential energy + kinetic energy) of the body A, B and C remains constant i.e, potential energy is completely transformed into kinetic energy. conservation of energy Body of mass m placed at a height h At A, Potential energy = mgh Kinetic energy = 0 [the velocity is zero as the object is initially at rest] Total energy at A = Potential energy + Kinetic energy. Total energy at A = mgh …1 At B, Potential energy = mgh = mg(h - x) [Height from the ground is (h-x)] Potential energy = mgh - mgx Kinetic energy = ½ mv2 The body covers the distance x with a velocity v. Kinetic energy = mgx Total energy at B = Potential energy + Kinetic energy Total energy at B = mgh …2 At C, Potential energy = m x g x 0 Potential energy = 0 Kinetic energy = ½ mv2 The freely falling body has covered the distance h. Here, u=0, a=g and s=h Kinetic energy = ½ mv2 Kinetic energy = mgh Total energy at C = Potential energy + Kienetic energy Total energy at C = mgh …3 It is clear from equations 1, 2 and 3 that the total energy of the body remains constant at every point. Thus, we conclude that law of conservation of energy holds good in the case of a freely falling body.