UNIVERSITY OF SASKATCHEWAN GE MECHANICS III MIDTERM EXAM FEBRUARY 13, 2008 A. Dolovich & H. Huenison A CLOSED BOOK EXAMINATION TIME: 2 HOURS

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1 UNIVERSITY OF SASKATCHEWAN GE MECHANICS III MIDTERM EXAM FEBRUARY 13, 2008 A. Dolovich & H. Huenison A CLOSED BOOK EXAMINATION TIME: 2 HOURS LAST NAME (printed): FIRST NAME (printed): STUDENT NUMBER: EXAMINATION ROOM: SIGNATURE: INSTRUCTIONS For Marker s Use Only 1) The examination consists of 10 questions. 1. Answer all TEN questions. The exam is out of a total of 100 marks. 2. The marks for each question are given in brackets beside the question. 3. PRINT YOUR NAME AT THE TOP OF EACH PAGE. 4. 2) This is a closed book exam. 5. No Walkmans, Discmans, IPODs or similar devices allowed. No PDAs or laptops allowed. 6. No cell phoned allowed. Calculators are permitted. 7. A list of formulas will be provided separately. Photo ID must be placed on your desk while you write ) SHOW YOUR WORK AND ANSWERS CLEARLY. 10. 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 numerical answers. Total: The back of each page may be used as a continuation sheet if required.

2 GE 226 Midterm Exam 2008 Name: Page 2 of 11 (10) 1. At the instant shown, the crank CD of the pump jack has a constant rotation of 6 rad/s CCW causing links CB and BE to rotate at ω r CB = 0.3 rad/s CCW and r ω BE = 2 rad/s CW respectively. Determine the acceleration of point H at this instant.

3 GE 226 Midterm Exam 2008 Name: Page 3 of 11 (10) 2. The wheel rolls on its hub without slipping on the horizontal surface. If the velocity of the r center of the wheel is v C = 2 ft/s to the right, using the vector method of analysis shown in class, determine the velocities of point A and B at the instant shown.

4 GE 226 Midterm Exam 2008 Name: Page 4 of 11 (10) 3. The mechanism used in a marine engine consists of a single crank AB and two connecting rods BC and BD. Using the IC method shown in class, determine the velocities of pistons C and D at the instant the crank is in the position shown and has an angular velocity of 5 rad/s clockwise.

5 GE 226 Midterm Exam 2008 Name: Page 5 of 11 (10) 4. At the given instant, the cables supporting the pipe have the motions shown. If the pipe r ) also has an angular velocity ωpipe = 0.25k rad/s, determine the angular acceleration, α r r pipe, of the pipe and the acceleration, a B, of point B located on the pipe.

6 GE 226 Midterm Exam 2008 Name: Page 6 of 11 v B (10) 5. The semi-circular member shown is rigid and connected to a roller in a horizontal slot at B and another roller in a vertical slot at A. If point B has a constant velocity, r, of 2 m/s to the right and θ = 30, determine both the angular velocity and angular acceleration of the semi-circular member at this instant. Use the vector method of analysis shown in class.

7 GE 226 Midterm Exam 2008 Name: Page 7 of 11 (10) 6. Determine the angular acceleration, α r AB, of link AB at the instant shown if link CD has an angular velocity of ωr = 2kˆ CD rad/s, an angular acceleration of α r CD = 4kˆ rad/s 2, and links BC and AB have angular velocities of ω r r = 3kˆ rad/s and ω = 6kˆ rad/s, respectively. BC AB

8 GE 226 Midterm Exam 2008 Name: Page 8 of 11 (10) 7. Gear C rotates with an angular velocity of 2 rad/s clockwise, while the connecting link AB rotates counterclockwise at 4 rad/s, as shown. Using the vector method of analysis shown in class determine the angular velocity, ω r D, of gear D at this instant. Note: Points A and B are not fixed. (DO NOT arbitrarily assume that any velocities are zero.)

9 GE 226 Midterm Exam 2008 Name: Page 9 of 11 (10) 8. At the instant shown, the ball is located at the bottom of the circular track and has an angular velocity of ω r Ball = 2kˆ rad/s. If the ball also has an angular acceleration, α r Ball, of 3 rad/s 2 clockwise and a velocity, v r B, of 0.2 m/s to the right, determine the acceleration of r point A, a A, located at the bottom of the ball, at this instant. The track has a radius R = 1 m and the ball has a radius r = 0.1 m.

10 GE 226 Midterm Exam 2008 Name: Page 10 of 11 (10) 9. If the slider block A is moving downward at v A = 4 m/s, determine the velocities of blocks B and C at the instant shown. Use the IC method of analysis shown in class. v A

11 GE 226 Midterm Exam 2008 Name: Page 11 of 11 (10) 10. In class, we showed that a rigid body in 2-D is governed by r r F = ma where G is the center of gravity of the body. In the space provided below, show that this equation is still valid for 3-D. Start your derivation with Newton s 2 nd Law for a particle. G End of Exam