301 (S99) Final Exam

# 301 (S99) Final Exam - Physics 301(Spring 1999 Final...

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Physics 301 (Spring 1999) Final Exam (May 5, 1999) Name 1. [30 points total] A simple pendulum of length b and mass m is suspended from a point on the circumference of a thin massless disc of radius a that rotates with a constant angular velocity ϖ about its central axis as shown. A. [15 points] Find the Lagrangian for the pendulum. Show your work. B. [15 points] Use Lagrange’s method to find the equation of motion. Show your work. (Hint: You should have one equation for θ .) b ϖ t a θ

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2. [30 points total] A dinner bell is constructed in the shape of an equilateral triangle of side b out of a heavy gauge wire of linear mass density λ . The bell pivots about one of the corners. A. [10 points] Show that the center of mass of the bell is located a distance below the pivot. [Hint: No integration required!] B. [10 points] Show that the moment of inertia for the bell about the pivot point is where M is the total mass of the bell. C. [10 points] Find the frequency of small oscillations of the bell about its pivot point. Show your work.
3. [30 points total] A red ball of mass 3m and speed u 1 = 50 m/s collides with a stationary green ball of mass 2m. The red ball is observed to scatter by 37 o in the LAB frame. The experiment is repeated many, many times and it is found that 37

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301 (S99) Final Exam - Physics 301(Spring 1999 Final...

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