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# s_exams - 1 Sample Exam Questions ME 274 2 Problem No 1...

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1 Sample Exam Questions ME 274

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2 Problem No. 1 Given: A particle P is traveling in the xy-plane on a path given by: x y = 6 ; x and y are given in ft and in such a way that the x-component of the velocity is a constant 20 ft/sec. Find: At position of x = 2 feet: a) determine the Cartesian components of the velocity and acceleration of P. b) make an accurate sketch of the velocity and acceleration vectors found in a) as well as the path unit vectors e t and e n on the figure provided below. c) determine the rate of change of speed and the radius of curvature for the path of P. d) is the speed of P increasing or decreasing? Provide an explanation for your response. x y P
3 Problem No. 2 Given: Blocks A and B are connected by a cable that has a length of L = 10 meters with the cable being pulled over a pulley at C. Block A is constrained to move along a guide in such a way that the its acceleration is a function of the position s A as: a A = 0.3 s A 2 (meters/sec 2 ) with the speed of A being zero when s A = 0. Block B is constrained to move along a surface that is perpendicular to the guide for A. Assume that the cable does not stretch or go slack during the motion of the system. Also assume that the pulley C is small compared to the other dimensions of the problem. Find: When s A = 4 meters, a) find the speed of block A. b) find the speed of block B. B A S A 3 meters C cable S B

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4 Problem No. 3 Given : A particle P travels on a circular path with a constant speed of v = 20 m/sec . A observer at point O watches the motion of P in terms of the radial distance r and rotation angle of θ . At the position shown θ = 36.87° and P is directly above the circle’s center C Find : For the position of P shown: a) draw the path and polar unit vectors for P. b) determine numerical values for ˙ r and ˙ ! . c) determine numerical values for ˙ ˙ r and ˙ ˙ ! . P C O 3 m r θ v
5 Problem No. 4 Given: Bar BC is pinned to ground at pin C and is pinned to bar AB at pin B. Pin A at the left end of bar AB is constrained to move within a circular slot having a radius of 2 meters and center at point O. Pin A is known to be traveling with a constant speed of 12 meters/sec. At the instant shown, bar BC is vertical, AB is horizontal and point A is on the same horizontal line as point O. Find: At the position shown: a) determine the angular velocity of bars AB and BC. b) determine the angular acceleration of bars AB and BC. Express your answers as vectors. 3 m 1 m A B C 2 m v A slot O

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6 Problem No. 5 Given: A disk having a radius of r = 1.5 ft is rolling without slipping on a rough horizontal surface to the right with its center O moving at a CONSTANT speed of v O = 20 ft / sec . A rigid bar AB having a length of 4 ft is attached to point A on the circumference of the disk. The other end of AB is attached a second rigid bar, BD (having a length of 3 ft), at pin B with point D pinned to ground. At the position shown, bar AB has a horizontal orientation, bar BD has a vertical orientation and point A is on the same horizontal line as point O.
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