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301 (S999) Exam #4

# 301 (S999) Exam #4 - Physics 301(Spring 1999 Fourth Exam...

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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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2. [25 points total] Strawberry: A yo-yo 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 yo-yo and the incline.] A. [3 points] What is the equation of constraint that relates
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301 (S999) Exam #4 - Physics 301(Spring 1999 Fourth Exam...

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