Physics 301
(Spring 1999)
Fourth Exam (April 16, 1999)
Name
1.
[25 points total]
Vanilla:
A bead of mass 3m is free to slide
horizontally without friction on a wire, as shown.
Attached to
the bead is a pendulum of length b and mass m.
The bob of the
pendulum is released such that all motion is in the plane of the
page.
A. [10 points]
Find the Lagrangian for the system.
Show your
work.
B. [15 points]
Use Lagrange’s method to find the equations of motion.
Show your work.
(Hint:
You should have one equation for x
1
and one equation for
θ
.
The equations will be coupled.)
X
1
θ
b
m
3m
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[25 points total]
Strawberry:
A yoyo of mass m, outer radius R, inner radius b, moment of
inertia I =
1
/
2
mR
2
, and color blue is free to unwind itself along a frictionless plane that is
inclined an angle
β
with respect to the horizontal. [Note:
The incline is frictionless, so there
will be plenty of slipping between the yoyo and the incline.]
A. [3 points]
What is
the equation of
constraint that relates
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 Fall '97
 GregoryFrancis
 Work

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