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Standard XII

Physics

Average and Instaneous Power

A particle of...

Question

A particle of mass m moves along a circle of radius R with a normal acceleration varying with time as where b is a constant. Find the time dependence of the 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 motion.

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Solution

normal accln: a_n = v²/R = bt²
so v² = bt²R
Kinetic Energy(E) = 1/2 mv² = 1/2*mbt²R
power P =dE/dt = d(1/2*mbt²R) / dt
                            P =mbt²R

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normal accln: an = v2/R = bt2so v2 = bt2RKinetic Energy(E) = 1/2 mv2 = 1/2*mbt2Rpower P =dE/dt = d(1/2*mbt2R) / dt P =mbt2R

normal accln: a_n = v²/R = bt²
so v² = bt²R
Kinetic Energy(E) = 1/2 mv² = 1/2mbt²R
power P =dE/dt = d(1/2mbt²R) / dt
P =mbt²R