A particle slides at constant speed in a horizontal circular path on the frictionless inner surface of an
inverted right circular cone. How is the particle’s kinetic energy related to its potential energy
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5 Answers
1The slanting surface of the cone provides the normal reaction.
The normal reaction has 2 components.
The vertical component balances the weight of the particle
The horizontal component balances the centripetal force due to the movement of the particle in horizontal path.
Hence .....
Nsin∞= mv2/r
Ncos∞= mg .... where m is the mass of the particle.
tan∞=v2/rg
r=v2/gtan∞
Let us cosider the ht. at which the particle is present is h
h=rtan∞
h=v2/gtan∞ * tan∞
h=v2/g
PE=mgh=mg*v2/g
PE=mv2
KE=1/2*mv2
Therefore ....... PE=2*KE. [Relation]
1Nishant sir ... would u please check if my logic is correct ... ???
62The logic is correct but the underlying assumption is that the PE at the vertex of the cone is zero.