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Derive an expression of kinetic energy of a body of mass ‘m’ and moving with velocity ‘v’, using dimensional analysis. |
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Answer» Suppose a stationery object of mass m MOVES because of an applied force.Let u be its initial velocity (here u = 0).Let the applied force be F. This generates an acceleration a in the object, and, after time t, the velocity of the becomes equal to v. The displacement during this time is s.The work done on the object, W=F×sAccording to Newton's second law of motion,F=ma ------------ (1)SIMILARLY, using Newton's second EQUATION of motion However, as initial velocity is zero,u=0s=ut + 1/2 at2s=0 + 1/2 at2s= 1/2 AT2 ------------(2):. W=ma × 1/2 at2 -----------using equations (1) and(2)W=1/2 m(at)2 -------------(3)Using Newton's first equation of motion.............v= u + at:.v= 0 + at:.v= at:.v2 = (at)2 ----------(4):.W=1/2 mv2 -----------using equations (3) and (4)The kinetic energy gained by an object is the amount of work done on the object.:.K.E. = W:.K.E. = 1/2 mv2Hope it helps you |
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