InterviewSolution
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InterviewSolution
| 1. |
Write down the mathematical derivation of both potential and kinetic energy |
| Answer» Let the work done on the object against gravity = WWork done, W = force ×\xa0displacementWork done, W = mg\xa0×\xa0hWork done, W = mghSince workdone on the object is equal to mgh, an energy equal to mgh units is gained by the object . This is the potential energy (Ep) of the object.\xa0Ep = mghDerivation for the equation of Kinetic Energy:The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, S is\xa0\xa0v2 - u2 = 2aSThis gives \xa0S = (v 2 - u 2)/ 2aWe know F = ma. Thus using above equations, we can write the workdone by the force, F as W = ma ×{ v 2 - u 2/ 2a} or\xa0W = 1 /2 m( v 2 - u 2 )If object is starting from its stationary position, that is, u = 0, thenW = 1/2 m v 2It is clear that the work done is equal to the change in the kinetic energy of an object.If u = 0, the work done will be W = 1/2 m v 2 .Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is Ek = ½ mv2 | |