Question

Question 27.
A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to kr2 where k is a constant. What is the total energy of the particle?

Answer 1

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Answer 2

Answer:

A particle of mass m is moving in a horizontal circle of radius r under a centripetal force -k/r^2, where k is a constant. What is the total energy?

Let us assume that the force here is conservative as only conservative forces account to the potential energy. The potential energy is given by

U=−∫∞rF.drU=−∫r∞F.dr

The potential energy is

U=−krU=−kr

Centripetal force makes a particle move in circular motion, therefore

mv2r=kr2mv2r=kr2

mv2=krmv2=kr

Since the kinetic energy of the particle is

K=mv22K=mv22

K=k2rK=k2r

And finally by the conservation of energy

E=U+KE=U+K

E=−kr+k2rE=−kr+k2r

Therefore the total energy of the system is given by

E=−k2r