exam01_soln - ME 274 Summer 2011 SOLUTION Examination No. 1...

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Unformatted text preview: ME 274 Summer 2011 SOLUTION Examination No. 1 PROBLEM NO. 1 Given : A taut, inextensible cord attached to particle P is being pulled over a fixed post O. End A of the cord is moving to the left with a constant speed of v A . At the instant shown, the section of cord between O and P is swinging CCW at a rate constant rate of . Find : For this problem, a) Determine the velocity and acceleration of particle P in terms of an appropriate set of polar unit vectors. Clearly indicate your choice of unit vectors in the figure below. b) Determine the rate of change of speed of P. c) Determine the radius of curvature of the path of P. Use R = 2 ft , = 3 rad / sec and v A = 8 ft / sec . Velocity v P = R e R + R e = v A e R + R e = 8 e R + 2 ( ) 3 ( ) e = 8 e R + 6 e ( ) ft / sec Acceleration a P = R R 2 ( ) e R + R + 2 R ( ) e = 2 ( ) 3 ( ) 2 e R + + 2 8 ( ) 3 ( ) ( ) e = 18 e R 48 e ( ) ft / sec 2 Rate of change of speed v P = a P i v P v P = 18 e R 48 e ( ) i 8 e R + 6 e 8 2 + 6 2 = 18 ( ) 0.8 ( ) + 48 ( ) 0.6 ( ) = 14.4 ft / sec 2 Radius of curvature a P 2 = v P 2 + v P 2 2 = v P 2 a P 2 v P 2 = 10 2 18 2 + 48 2 ( ) 14.4 2 = 2.033 ft v A O R P A e R e ME 274 Summer 2011 SOLUTION Examination No. 1 PROBLEM NO. 2 Given : The mechanism shown below is made up of links OA, AD and BC. Links OA and BC are pinned to ground at points O and C, respectively. Pin D of link AD is able to slide within a slot that is cut in link BC, as shown. Pins O and C are on the same horizontal line. At the instant shown, link BC is vertical and rotating CCW at a...
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exam01_soln - ME 274 Summer 2011 SOLUTION Examination No. 1...

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