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Dynamics Final Solutions

Dynamics Final Solutions - Name KEY Last First UNIVERSITY...

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Unformatted text preview: Name:_______ KEY ________ Last First UNIVERSITY OF NEVADA, LAS VEGAS DEPARTMENT OF MECHANICAL ENGINEERING MEG 242, Spring 2009, Final Examination Closed Book, three pages of handwritten notes allowed. Enter the answer for each question into the space provided. Enter correct dimensional SI units where applicable. 1. (10 points) The speedometer of a boat traveling on a river shows a speed of 6 knots. The river current is moving at 2 knots in NE direction. The skipper wishes to maintain a heading straight East. Determine the boat’s heading angle H required for easterly travel. θ = 45 ο i j Water Current flows North East East v B oa t Η = Heading Angle v Boat = v Water + v Boat/Water Using given x-y frame we get v Boat *i = v Water + v Boat/Water i: v Boat = 2*cos(45deg) - 6*cos(H) j: 0 = 2*sin(45deg) - 6*sin(H) Thus sin(H) = 1/3*0.707 Æ H = 13.6 degrees Answer: Boat’s Heading angle = 13.6 degrees Version B v Boat *i = v Water + v Boat/Water i: v Boat = 2*cos(45deg) - 8*cos(H) j: 0 = 2*sin(45deg) - 8*sin(H) Thus sin(H) = 1/4*0.707 Æ H = 10.2 degrees 2. (15 points) Point mass m slides without friction on a vertical circular hoop with radius r. The hoop is spinning around the vertical axis at constant angular velocity ω . Determine the angle θ at which the mass will come to rest....
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Dynamics Final Solutions - Name KEY Last First UNIVERSITY...

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