Exam 1 September 11, 2013

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1 Exam 1 Instructions: You have 60 minutes to complete this exam. This is a closed-book, closed-notes exam. You are allowed to use an approved calculator during the exam. Usage of mobile phones and other electronic communication devices is NOT permitted during the exam. Problem 1 (15 pts) 2 (25 pts) 3 (20 pts) Total Score Exam 1 Page 1 of 9

2 Problem 1 (15 points): Given: The rod OA is rotating in the horizontal plane such that θ = t 3 radians. At the same time, the collar B is sliding outward along OA so that r = (100t 2 ) mm. In both cases, t is in seconds. Find: When t= 1 s, (a) Magnitude of the velocity of collar B (b) Magnitude of the acceleration of collar B Exam 1 Page 2 of 9

3 This page is for extra work related to Problem 1. Exam 1 Page 3 of 9

4 Problem 2 (25 points): Given: The piston rod of the hydraulic cylinder C imparts a constant acceleration to pin A of a A = 0.1 m/s 2 (downward). At the instant when θ = 90 the speed of A is known to be v A = 0.4 m/s (upward). Find: For this instant: (a) The angular velocity of links AB and OB. (b) The angular acceleration of links AB and OB. Exam 1 Page 4 of 9

5 This page is for extra work related to Problem 2. Exam 1 Page 5 of 9

6 Problem 3 (20 points): Part A (6 points): If the velocity of particle A and B are (2î+3ĵ) m/s and (5î+7ĵ) m/s respectively, the relative velocity of A with respect to B is: A particle moving at a constant velocity of 5 m/s along a circular path with a diameter of 10 m, the acceleration of the particle is: Two planes are moving relative to each other. Plane A has a velocity of 10 m/s at 30 to the horizontal, while plane B is observed to have a relative velocity of 20 m/s vertically downward with respect to A. The velocity of plane B is: Exam 1 Page 6 of 9

7 Part B (8 points): ω 2 # O V = 15 #/s A For the picture shown above with no slip between the two rigid bodies: If the velocity of the wheel at the contact point A is zero (no slip condition), then the angular velocity ω of the wheel is: (a) 30 rad/s (b) 0 rad/s (c) 7.5 rad/s (d) 15 rad/s The direction of the angular velocity of the wheel is: (hint: use unit vector notation to define it) Determine the acceleration at point A: If the angular acceleration of the wheel is 4 rad/sec 2, determine the acceleration of point O: Exam 1 Page 7 of 9

8 Part C (6 points): Two blocks shown are interconnected by a cable. Which of the following is correct? (a) v Ax = - v Bx (b) v A = - v B (c) v Ay = - v By (d) All of the above y x Determine the speed of block B when block A is moving down at 6 ft/s while block C is moving down at 18 ft/s. (a) 24 ft/s (b) 3 ft/s (c) 12 ft/s (d) 9 ft/s v A =6 &/s v C =18 &/s Determine the velocity vector of block A when block B is moving downward with a speed of 10 m/s. (a) (8î + 6ĵ) m/s (b) (4î + 3ĵ) m/s (c) ( 8î 6ĵ) m/s (d) (3î + 4ĵ) m/s y x Exam 1 Page 8 of 9

9 Exam 1: Equation Sheet v P = ẋî + ẏĵ = v P ê t = ṙê r + r θê θ a P = ẍî + ÿĵ = v P ê t + v2 P ρ ên = ( r r θ 2 )ê r + (r θ + 2ṙ θ)ê θ v B = v A + ω r B/A a B = a A + α r B/A + ω ( ω r B/A ) Exam 1 Page 9 of 9

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