Exam #3 - Physics - Syracuse University

Physics 211, Spring 2010 Practice before Exam 31. Two carts of mass m 1 =3 kg and m 2 =5 kg are attached to each other. There is a compressed spring inbetween them. The spring constant is k=3500 N/m. The carts are moving on frictionless track. Initiallythey are moving with velocity of 1.5 m/s to the right. Then the carts are disconnected. They separate as thespring is allowed to decompress. After the separation, velocity of the cart with mass m 2 is 3.0 m/s to theright.1.5 m/sv 1f = ?3.0 m/sm 1 m 2m 1m 2beforeafter1a. Find final velocity (magnitude and direction) of the cart with mass m 1 after the separation.1b. Find compression of the spring (∆x) before the cart separation (you will need to solve 1a first).Phy211 Spring 2010 Syracuse University Practice before Exam 3 Page 1

2. Find center of mass of the uniform plate outlined below in the coordinate system defined in thefigure. Indicate position of the center of mass in the figure.Phy211 Spring 2010 Syracuse University Practice before Exam 3 Page 2

3. Two identical thin rods of length L=1.5 m and mass m=3 kg each create a letter T. Find total momentof inertia of this object for the axis of rotation parallel to one rod and going through the center of theother as shown below. (See page 6 for a table of moments of inertia.)LAxis of rotationLPhy211 Spring 2010 Syracuse University Practice before Exam 3 Page 3

4. A block of mass m 1 =7kg is suspended on a string which is wrapped around a uniform cylinder ofmass m 2 =4kg and radius R=0.7m. The cylinder rotates without friction about the fixed axis goingthrough its center. The system starts from rest. What is speed of the block after it has descended thedistance of h=3.5m? (Assume g=10 m/s 2 )m 2Rm 1Phy211 Spring 2010 Syracuse University Practice before Exam 3 Page 4

5. What is the acceleration of the block in the previous problem?Phy211 Spring 2010 Syracuse University Practice before Exam 3 Page 5

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