Exam 3 Instructions: You have 60 minutes to complete this exam. This is a closed-book, closed-notes exam. You are allowed to use a 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 Name: Section (circle): 8:30-9:20 11:30-12:20 2:30-3:20 Exam 3 Page 1 of 8
Problem 1 (20 points): Given: A stepped drum (having a mass of m D and radius of gyration about its center O of k O ) is attached to a smooth shaft passing through its center O. The cable wrapped around the outer radius of the drum is attached to block A. A second cable is wrapped around the inner radius of the drum with this cable pulled over an ideal pulley that is attached to the car with mass m C. Assume that the cables do not slip on the drum. The system is at rest when the car is at height h off the ground. Find: The angular acceleration of the drum immediately after release. Equations approach and write your final answer as a vector. Use the Newton-Euler Use the following parameters in your analysis: m A = 10 kg, m c = 1500 kg, m D = 25 kg, k O = 0.35 m, R = 0.50 m, r = 0.25 m, and h = 1 m. m D m c m A h Exam 3 Page 2 of 8
This page is for extra work related to Problem 1. Exam 3 Page 3 of 8
Problem 2 (20 points): Given: A homogeneous, rigid bar (of mass m and length l) is pinned to the block at O. The block has a mass of 2m. The whole system is released from rest when θ = 0. Find: When the bar reaches θ = 90 : (a) Determine the velocity of the bar s center of mass G. Write your answer as a vector. (b) Determine the velocity of the block. Write your answer as a vector. Exam 3 Page 4 of 8
This page is for extra work related to Problem 2. Exam 3 Page 5 of 8
Problem 3 (20 points): Part A (4 points): Circle ALL of the expressions below that are a correction formulation of the Euler Equation that describes the angular acceleration of the disk with mass center G and geometric center O? (a) ΣM D = I D α (b) ΣM E = I E α (c) ΣM O = I O α (d) ΣM G = I G α Part B (4 points): For the homogeneous disk shown below, G is the mass center, and points A and B are distances a and b from the mass center, respectively. Circle the answer below that correctly relates the mass moment of inertia about A (I A ) to that about point B (I B ): (a) I A = I B (b) I A = I B + ma 2 (c) I A = I B + mb 2 (d) I A = I B + m(a 2 b 2 ) Exam 3 Page 6 of 8
The center of the disk shown below has a downward acceleration. Assume the cable does not slip. Part C (3 points): Sketch a Free Body Diagram of the Disk. Part D (3 points): Circle the answer that most accurately describes the tension in section AB of the cable: (a) The tension in section AB is equal to the tension in section CD. (b) The tension in section AB is smaller than the tension in section CD. (c) The tension in section AB is larger than the tension in section CD. (d) More information is needed to answer the question. Exam 3 Page 7 of 8
Part E (6 points): Particle A strikes particle B with a known speed v A1. The coefficient of restitution is known to be less than one (e < 1). Particle B is attached to a rigid bar which is pinned to ground. Circle all of the responses below that correctly describe the impact of particle A and particle B: For the particle A: (a) Linear momentum of particle A is conserved in the x-direction. (b) Linear momentum of particle A is conserved in the y-direction. (c) Linear momentum of particle A is conserved in the n-direction. (d) none of the above. For the system A+B: (a) Linear momentum of the system A+B is conserved in the x-direction. (b) Linear momentum of the system A+B is conserved in the y-direction. (c) The total energy of the system A+B is conserved. (d) none of the above. Exam 3 Page 8 of 8