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MIT16_07F09_hw10

MIT16_07F09_hw10 - NAME Massachusetts Institute of...

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NAME : . . . . . . . . . . . . . . . . . . . . . Massachusetts Institute of Technology 16.07 Dynamics Problem Set 10 Out date: Nov. 7, 2007 Due date: Nov. 14, 2007 Time Spent [minutes] Problem 1 Problem 2 Problem 3 Problem 4 Study Time Turn in each problem on separate sheets so that grading can be done in parallel
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Problem 1 (10 points) Question 1 A cart of mass M 1 rolls on bearings on a frictionless plane. It carries a large disk of radius R 0 mounted by an axle to the cart at its center of mass. The disk is uniform and of mass M 2 . It is free to rotate without friction about its axle. A rope is wrapped around the disk as sketched. Everything is at rest. At t = 0 a constant tension T is applied to the rope. a) What is the linear acceleration of the cart, a ? b) What is the angular acceleration of the disk α ? c) The rope with constant tension T pulls the cart for a distance of X F meters. How much work is done by the external force T ? d) Assuming a conservative system (no friction etc.) what is the kinetic energy when the cart is located at X F ? e) Does this all make sense? (Note: the radius of gyration of a uniform circular disk is R 0 / 2)
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Problem 2 (10 Points) A uniform bar of length L and mass m is lying
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