Ben Sauerwine
Practice for Qualifying Exams
Problem Source:
CMU Qualification Exam Day 2 (August 2003)
(7)
A particle of mass m is acted upon by a constant gravitational field with acceleration
g.
The particle is also acted upon by a force
F
v
that is directed towards the origin.
The magnitude of this force is
kr
F
=
where r is the distance from the particle to the
origin.
There is a cylinder of radius R into which the particle cannot enter.
The
particle is constrained to slide on the cylinder with no friction.
(a)
Write the kinetic energy K and the potential energy V of the particle in the
cylindrical coordinate system
(
)
z
,
,
φ
ρ
.
Note well that I assume here that k is negative.

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