MECHANICS 1 â MECH 210-001 FINAL EXAMINATION
McGill University, Faculty of Engineering, Department Mechanical Engineering
MECHANICS 1 – MECH 210-001 FINAL EXAMINATION Thursday December 19th 2002, 14:00-17:00 (3 hours) Examiner: Prof. Pascal Hubert Associate Examiner: Prof. Andrew Higgins • • • •
Total 100 points. Questions are weighted differently. Answer to all 7 questions. An 8 1/2”x 11” information sheet and a faculty-standard calculator are allowed.
. Question 1 (10 points) The mechanism shown is a modified Geneva drive. The input couplemoment is 120 N·m. For the position shown, compute the contact force at B and the magnitude of the bearing reaction at A. Neglect friction and the weight of the member.
Question 2 (20 points) The bent rod is supported by a ball-and-socket joint at O, a cable at B, and a slider bearing at D. Neglecting the weight of the rod, calculate the tension in the cable and the magnitude of the bearing reaction at D. Note: The bearing at D has no moment reactions and no force reaction in direction x.
Question 3 (15 points) a) Identify zero force members. b) Determine the force in members BG, BC and HG of the truss and state if the members are in tension or compression. Note: Support A is a pin connection and G is a roller support.
Question 4 (15 points) Draw the shear force and bending moment diagrams for the beam and determine the magnitude and location of the maximum bending moment. Note: Support A is a pin connection and D is a roller support.
Question 5 (10 points) The 3 ft wide rectangular gate is pinned at its center C. Determine the torque M that must be applied to its center shaft in order to open the gate. Note: (ρg)water = 62.4 lb/ft3. 12 ft
3 ft
Question 6 (15 points) The pin-connected mechanism is constrained by a pin at A and a roller at B. Using the principle of virtual work, determine the force P that must be applied to the roller to hold the mechanism in equilibrium when θ = 30°. Note: The spring is unstretched when θ = 45°. Neglect the weight of the members.
Question 7 (15 points) The uniform beam AB weighs 100 lb. If both springs DE and BC are unstretched when θ = 90°, determine the angle θ for equilibrium using the principle of potential energy. Investigate the stability at the equilibrium position. Both springs always act in horizontal position because of the roller guides at C and E. Note: The spring stiffness is expressed in lb/in. More than one equilibrium position may be possible.
MECHANICS 1 – MECH 210-001 FINAL EXAMINATION Thursday December 19th 2002, 14:00-17:00 (3 hours) Examiner: Prof. Pascal Hubert Associate Examiner: Prof. Andrew Higgins • • • •
Total 100 points. Questions are weighted differently. Answer to all 7 questions. An 8 1/2”x 11” information sheet and a faculty-standard calculator are allowed.
. Question 1 (10 points) The mechanism shown is a modified Geneva drive. The input couplemoment is 120 N·m. For the position shown, compute the contact force at B and the magnitude of the bearing reaction at A. Neglect friction and the weight of the member.
Question 2 (20 points) The bent rod is supported by a ball-and-socket joint at O, a cable at B, and a slider bearing at D. Neglecting the weight of the rod, calculate the tension in the cable and the magnitude of the bearing reaction at D. Note: The bearing at D has no moment reactions and no force reaction in direction x.
Question 3 (15 points) a) Identify zero force members. b) Determine the force in members BG, BC and HG of the truss and state if the members are in tension or compression. Note: Support A is a pin connection and G is a roller support.
Question 4 (15 points) Draw the shear force and bending moment diagrams for the beam and determine the magnitude and location of the maximum bending moment. Note: Support A is a pin connection and D is a roller support.
Question 5 (10 points) The 3 ft wide rectangular gate is pinned at its center C. Determine the torque M that must be applied to its center shaft in order to open the gate. Note: (ρg)water = 62.4 lb/ft3. 12 ft
3 ft
Question 6 (15 points) The pin-connected mechanism is constrained by a pin at A and a roller at B. Using the principle of virtual work, determine the force P that must be applied to the roller to hold the mechanism in equilibrium when θ = 30°. Note: The spring is unstretched when θ = 45°. Neglect the weight of the members.
Question 7 (15 points) The uniform beam AB weighs 100 lb. If both springs DE and BC are unstretched when θ = 90°, determine the angle θ for equilibrium using the principle of potential energy. Investigate the stability at the equilibrium position. Both springs always act in horizontal position because of the roller guides at C and E. Note: The spring stiffness is expressed in lb/in. More than one equilibrium position may be possible.
