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# dyn5 - 2.032 DYNAMICS Fall 2004 Problem Set No 5 Out...

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2.032 DYNAMICS Fall 2004 Problem Set No. 5 Out : Wednesday, October 13, 2004 Due : Wednesday, October 20, 2004 at the beginning of class Problem 1 Consider the motion of a car, as shown in the ﬁgure below. (Out of the four wheels only two are visible.) The mass of the body of the car is m 3 , and each wheel has radius r and mass m . The coeﬃcient of static friction is μ 0 i.e., the tangential force between the wheel and the ground is never greater than μ 0 times the normal force. The torque transmitted from the body of the car to the rear wheel set is M 0 . (a) Assuming pure rolling, use the work-energy principle to ﬁnd the acceleration of the car. (b) What is the largest M 0 for which the car does not slip? 1

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Problem 2 (adapted from PhD Qualifying Exam 2003) A circular ring of radius a is ﬁxed to a vertical shaft AB at O. The plane of the ring is inclined at 60 to the vertical as shown below so that the included angle COB is 60 , where C is the center of the ring. A particle P of mass
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dyn5 - 2.032 DYNAMICS Fall 2004 Problem Set No 5 Out...

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