Homework 6 Due February 20 2007
1) Consider a system where a particle of mass
m
is constrained to move along the xaxis
and the potential energy function of the conservative force acting on the particle (which is
the only force in the system) is:


)
(
x
C
x
U
=
Where C is a positive constant. (NB: this is not
the force law of a spring. It is similar to
the force law for the force between two quarks in a meson)
(a)
What are the SI units of
C
?
(b)
What is the force on the particle as a function of position (hint consider +ve and –
ve values of x separately)
(c)
Make a schematic graph of the potential energy as a function of x.
(d)
Let E>0 be the mechanical energy of the system. On the graph in part c, draw a
horizontal line at E and indicate where the turning point(s) are for this mechanical
energy. Give an algebraic expression for the position of the turning point(s) in
terms of E and C. Also indicate on the graph which regions of the xaxis are
excluded to the motion of the particle.
(e)
Describe the motion of the particle.
(f)
Suppose that the particle is released at rest at the point x=+A. Write an equation
for the position as a function of time for the particle as it moves from x=A to x=0.
How long does the particle take to return again to x=+A (the period T)? Sketch a
graph of the position as a function of time for the time period t=0 to t=2T.
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 Spring '08
 HerreraSiklody
 Energy, Force, Mass, Potential Energy, Work

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