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A particle of mass m moves along a circle of radius. R with a normal acceleration varying with time as a_(n) = kt^(2), where k is a constant. Find time dependence of power developed by all the forces acting on the particle and the mean value of this power averaged over the first T seconds after the beginning of the motion. |
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Answer» Solution :Normal acceleration `a_(n) = KT^(2)` `therefore (v^(2))/(R) = kt^(2) or (dv//dt) = sqrt((kR))` We know that in circular motion, work done by normal FORCE is zero. For tangential forces `F_(t) = m(dv//dt) = m sqrt((kR)),` Now Power `P = VEC(F_(t)).vec(v) = F_(t).v cos theta = F_(t).v ""(because theta = 0) = mkRt` Further, `= (int_(0)^(T) P(t) dt)/(int_(0)^(T) dt) = (int_(0)^(T)m k R t dt)/(T) = (m k R[t^(2)//2]_(0)^(T))/(T) = (mkRT)/(2)`. |
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