exam2 - elastic and after the collision the masses move...

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Phys. 3201 Midterm Exam II 07/13/04 Ground rules: 1. You have 1 hour and 45 minutes to complete all four problems (10 am - 11:45 am). 2. You are not allowed to discuss the problems with others. 3. You are not allowed to use the book or lecture notes. 4. You are allowed to use a piece of paper with anything you like written on it. 5. You are allowed to use a calculator. 1. (10 points) A solid uniform cylinder of radius a with a cylindrical hole of radius b whose center is at height c lies on a plane surface (see figure below). (a) Determine the condition on a , b , and c for which the equilibrium is stable. (b) Find the frequency of small oscillations about the stable equilibrium. c a b 2. (10 points) A mass m 1 collides head on with a mass m 2 . Before the collision m 2 is stationary and m 1 moves with velocity v . Find the ratio of the masses, if the collision is
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Unformatted text preview: elastic and after the collision the masses move with equal and opposite velocities. 3. (10 points) A uniform sphere of mass M and radius R and a uniform cylinder of mass M and radius R are released simultaneously from rest at the top of the inclined plane. Which body reaches the bottom rst, if they both roll without slipping? 4. (10 points) A ring of mass M and radius R lies on its side on a frictionless table. It is pivoted to the table at its rim. A bug of mass m walks around the ring with speed v , starting at the pivot. Assuming the ring is initially at rest, what is the rotational velocity of the ring when the bug is (a) halfway around and (b) back at the pivot point?...
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exam2 - elastic and after the collision the masses move...

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