Exam 2 October 17, 2013

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Cornelius McCoy
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1 Exam 2 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 (20 pts) 2 (20 pts) 3 (20 pts) Total Score Exam 2 Page 1 of 10

2 Problem 1. (20 points): Part A: (5 points) Given: A mechanism is made up of link OA, AB, and DE. Pins D and E on link DE are constrained to move along straight guides. Link OA is pinned to ground at O and pinned to link AB at A. Link AB is also pinned to link DE at point B. Pin D moves to the right with a speed of v D. For the position shown: Find: (a) The location of the instant center for link DE (b) The location of the instant center for link AB (c) The direction of rotation for link AB - clockwise, counterclockwise, or instantaneously at rest. Provide an argument for your answer. Exam 2 Page 2 of 10

3 Part B: (5 points) Given: Particle P, having a weight of W = 5 lb, slides along a rough, curved rod with coefficient of kinetic friction, µ k = 0.4 and R = 3 ft. At the position shown where θ = 53.13, the speed of P is known to be 20 ft/s. Find: (a) The normal force acting on P by the rod (b) The rate of change of speed P, at the instant shown. Exam 2 Page 3 of 10

4 Part C: (10 points) Particle P (of mass m) starts at position 1 with a speed of v 1 and moves to position 2 on a rough guide (coefficient of kinetic friction of µ k ). A spring of stiffness k is attached between P and fixed point A. The spring is unstretched at position 1. A cable is also attached to P with the cable being pulled over a small pulley at B by an constant force F acting at end C of the cable. At position 1, the particle has a speed of v 2. Answer the following questions related to the motion of P. Work done by friction, U (f) 1 2 : (a) U (f) 1 2 > 0 (b) U (f) 1 2 = 0 (c) U (f) 1 2 < 0 (d) more information is needed about the shape of the guide in order to determine the sign of U (f) 1 2. Work done by force F, U (F ) 1 2 : (a) U (F ) 1 2 = F d (b) U (F ) 1 2 = F h (c) U (F ) 1 2 = 2F h (d) U (F ) 1 2 (e) U (F ) 1 2 = F (d + 2h) = F (d h) (f) U (F ) 1 2 = F (d 2h) (g) U (F ) 1 2 = F ( d 2 + h 2 ) (h) more information is needed about the shape of the guide in order to determine U (F ) 1 2. Exam 2 Page 4 of 10

5 Part C (continued): Spring potential energy at position 2, (V 2 ) sp : (a) (V 2 ) sp = 1 2 kd2 (b) (V 2 ) sp = 1 2 kh2 (c) (V 2 ) sp = 1 2k(d 2h)2 (d) (V 2 ) sp = 1 2 k(d2 4h 2 ) (e) (V 2 ) sp = 1 2 k( d 2 + h 2 2h) 2 (f) more information is needed about the shape of the guide in order to determine (V 2 ) sp. Change in gravitational potential, V gr = (V 2 ) gr (V 1 ) gr : (a) V gr > 0 (b) V gr = 0 (c) V gr < 0 (d) more information is needed about the shape of the guide in order to determine the sign of V gr. Speed of P at position 1, v 2, as compared to the speed at position 1, v 1 : (a) v 2 > v 1 (b) v 2 = v 1 (c) v 2 < v 1 (d) more information is needed about the the problem in order to compare v 1 and v 2. Exam 2 Page 5 of 10

6 Problem 2 (20 points): Given: For the vehicle shown below, ω 1 = 0.30 rad/s = constant, θ = 0.5 rad/s = constant, and L = 12 m. Find: When θ = 30, it is desired to use the following equations to determine velocity and acceleration of end P of the boom: v P = v O + ( v P/O ) rel + ω r P/O a P = a O + ( a P/O ) rel + α r P/O + 2 ω ( v P/O ) rel + ω ( ω r P/O ) Provide expressions for the following terms in the above equations: (a) v O = (b) ( v P/O ) rel = (c) ω = (d) r P/O = (e) a O = (f) ( a P/O ) rel = (g) α = Exam 2 Page 6 of 10

7 This page is for extra work related to Problem 2. Exam 2 Page 7 of 10

Problem 3 (20 points): Given: Crates A and B weight 100 lb and 50 lb, respectively. They are initially at rest and then a horizontal force P = 50 lb is applied to Crate A as shown.

8 Problem 3 (20 points): Given: Crates A and B weight 100 lb and 50 lb, respectively. They are initially at rest and then a horizontal force P = 50 lb is applied to Crate A as shown. The coefficient of kinetic friction between the crates and the ground is µ k = Find: For the instant when t = 5 s, (a) the speed of the crates (b) the force exerted by crate A on crate B during the motion Exam 2 Page 8 of 10

9 This page is for extra work related to Problem 3. Exam 2 Page 9 of 10

10 Exam 2: 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 ) v B = v A + ( v B/A ) rel + ω r B/A a B = a A + ( a B/A ) rel + α r B/A + 2 ω ( v B/A ) rel + ω ( ω r B/A ) ê i = ω ê i F = m a T 1 + V 1 + U nc 1 2 = T 2 + V 2 m 1 v 1 + F dt = m 2 v 2 Exam 2 Page 10 of 10

Exam 1 September 11, 2013

Exam 1 September 11, 2013 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