A particle of mass m is moving in a horizontal circle of radius r, under a centripetal force equal to (−kr2) where k is constant. What is the total energy of the particle?
As centripetal force is mv2r hence mv2r = kr2
∴ K.E. of particle = mv2 = K2r.
The force acting on a particle is conservative in nature hence we can find potential energy of the particle as
F = -dvdt ⇒ dv = -Fdr
⇒ U = ∫∞rFdr ∫∞rKr2 dr
U = -Kr
∴ Total energy of particle = K.E. + P.E. = -Kr + K2r= -K2r.