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Expression for Kinetic Energy of a Moving Body |
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Answer» Consider a body of mass 'm' which is initially at rest. When a force 'F' is applied on the body, let it start moving with a velocity 'v' and cover a distance 'S'. The force produces acceleration 'a' in the body. The force 'F' does work when it moves the body through a distance 'S' and this work done is stored in the body as its kinetic energy. By definition, W = F × S ...(1) F = ma [Newton's second law of motion] W = mas ...(2 ) Also, v2 - u2 = 2aS [Newton's third law of motion] v2 - 0 = 2aS [Initial velocity u = 0 as the body is initially at rest] v2 = 2aS or a=v2/2s Substituting the value of 'a' in equation (2) we get, w=(mv2/2S) S w=(mv2/2).....(3) But since work done is stored in the body as its kinetic energy equation (3) can be written as Kinetic energy(T) =1/2mv2 T=1/2mv2 From the above equation we can conclude that the kinetic energy of a body is directly proportional to (1) its mass and (2) the square of its velocity. |
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