UNIVERSITY OF SASKATCHEWAN GE 226.3 MECHANICS III FINAL EXAM APRIL 18, 2011 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS LAST NAME (printed): FIRST NAME (printed): STUDENT NUMBER: EXAMINATION ROOM: SIGNATURE: INSTRUCTIONS 1) The examination consists of 5 questions. Answer all five questions. All five questions are of equal value. PRINT YOUR NAME AT THE TOP OF EACH PAGE. 2) This is a closed book exam. A list of formulas will be provided separately. Calculators are permitted. No IPODs or similar devices allowed. No PDAs or laptop computers allowed. No cell phones allowed. Photo ID must be placed on your desk while you write. For Marker s Use Only 1. 2. 3. 4. 5. Total: 3) SHOW YOUR WORK AND ANSWERS CLEARLY. All forces in your equations should also be shown in clearly drawn free body diagrams. Give all final numerical answers to 3 significant figures. Give your solutions in the space below the question. Neatly place a box around your final answers. Continuation sheets have been provided within the exam paper. In addition, the back of each page may be used as a continuation sheet if required.
GE 226 Final Exam - Winter 2011 Name: Page 2 of 11 1. Two slender rods, AB and BC, are pin connected at B. Each rod has a mass of 3 kg and a length L = 250 mm. The rods are released from rest in the position shown, with AB perpendicular to BC. At the instant the rods are released, a horizontal force P = 100 N is applied to the center of mass of AB as shown. Determine the initial angular acceleration of link AB and the initial angular acceleration of link BC just after release. L/2 P A B L C L
GE 226 Final Exam - Winter 2011 Name: Page 3 of 11 Continuation Sheet - Problem 1
GE 226 Final Exam - Winter 2011 Name: Page 4 of 11 2. The assembly shown is released from rest when θ = 30. The slender link BC weighs 2 lb and has a length of 1.25 ft. The disk weighs 12 lb and has a radius of 0.25 ft. The slider weighs 4 lb and slides without friction along the fixed vertical post. Link BC is pin connected to the center of the slider at C, and to the center of the disk at B. The disk rolls without slipping. Using the work-energy method, determine the angular velocity of link BC when θ = 15. C post slider θ link A B disk
GE 226 Final Exam - Winter 2011 Name: Page 5 of 11 Continuation Sheet - Problem 2
GE 226 Final Exam - Winter 2011 Name: Page 6 of 11 3. The spool has a mass of 40 kg, an inner radius r 1 = 0.4 m, an outer radius r 2 = 0.8 m, and a radius of gyration k G = 0.65 m, where G is the center of mass. The spool sits on a flat plate, and the plate sits on a horizontal frictionless surface. The plate has a mass of 10 kg. The coefficients of static and kinetic friction between the spool and the plate are, respectively, μ s = 0.6 and μ k = 0.4. A torque T = 50 N m is being applied to the spool. Determine the angular acceleration of the spool. T frictionless surface spool r 2 B G A r 1 cord plate
GE 226 Final Exam - Winter 2011 Name: Page 7 of 11 Continuation Sheet - Problem 3
GE 226 Final Exam - Winter 2011 Name: Page 8 of 11 4. A uniform plate BC of mass 20 kg is pin-connected to slender links AB and DC. Each of the links AB and DC has a length of 350 mm and a mass of 4 kg. A spring of stiffness k = 2 kn/m is attached between the pins at D and B. A horizontal force P = 750 N is applied to the plate such that it acts through B and C, as well as through the plate s center of mass G. When θ = 25, the spring is unstretched and link AB has a clockwise angular velocity of 10 rad/s. Use the work-energy method to determine the angular velocity of link AB when θ = 45. 400 mm A D L AB = L CD = 350 mm θ k θ B G* C P 400 mm
GE 226 Final Exam - Winter 2011 Name: Page 9 of 11 Continuation Sheet - Problem 4
GE 226 Final Exam - Winter 2011 Name: Page 10 of 11 5. The car illustrated below has rear-wheel drive and is travelling over a rough road. Without its wheels, the car weighs 3500 lb, has center of gravity G, and has radius of gyration k G = 3.0 ft. Each of the four wheels has negligible weight and a radius of 1.2 ft. At the instant shown, the dashed line between A and B is horizontal, the road is flat and horizontal at the rear wheels, and the shape of the road is the same for both front wheels (i.e., the shape of the road into the page is constant). Also at this instant, the shape of the road at the front wheels may be approximated as circular with a radius R = 0.9 ft, and the bottom of each front wheel is at the top of the circular bump. At the instant shown, the rear wheels have a clockwise angular velocity of 5 rad/s and a clockwise angular acceleration of 0.5 rad/s 2. All four wheels are rolling without slipping. For each of the four wheels, determine the normal force and the friction force applied by the ground to the wheel at this instant. Determine also the torque delivered to each rear wheel at this instant. front B G A 1.3 ft R 4 ft 2 ft
GE 226 Final Exam - Winter 2011 Name: Page 11 of 11 Continuation Sheet - Problem 5