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ES226 Exam 2 Study Guide Page 1 ES226 Engineering Mechanics: Statics Spring 2013 Lafayette College Engineering Division Exam 2 Study Guide Exam 2: Wednesday, February 27, 2013, in class Exam Format: 50 minute time limit. Closed book. Students are allowed to have a calculator, , pencils, etc. Students may also bring a protractor and ruler, but this is not essential. Exam Coverage: Lessons 7 through 12: Lesson 7 Concurrent Systems in 3D Lesson 9 Moments and the Principle of Moments Lesson 10 Moments in 3D Lesson 11 Moment Couples Lesson 12 Simplification of Force/Couple Systems Given Formulae (provided on the exam): Sine Law: A B C [Cc, Bb, Aa] B c sin a sin b sin c A a Cosine Law: C b C A 2 B 2 2 AB cos c [SAS] Sample Problems – Categorized by Lesson Objectives FOR ADDITIONAL PROBLEMS, SEE HIBBELER Lesson 7 Concurrent Systems in 3D Compute the unknowns (forces, angles, distances, spring extensions) for three-dimensional concurrent statics problems Recommended Hibbeler Problems (12th Edition): 3-55, 3-59, 3-78 1. (35 points) Determine the magnitude of P and the tension in each cable. A cylinder of weight W=650N is supported by two cables AC and BC, which are attached to the top of vertical posts. A horizontal force P, perpendicular to the place containing the posts, holds the cylinder in the position shown. 2. (35 points) Determine the magnitude of force acting along the axis of each of the three struts AB, AC, and AD and specify whether this force is positive (tension) or negative (compression). Given: the chain supports a 500-kg block. (Ans: FB=-19.2 kN, FC=10.4kN, FD=6.32kN) ES226 Exam 2 Study Guide Page 2 3. (45 points) Three cables are connected at A. If the tension in cable AD is 305N, determine P (Ans: 960N) Lesson 8 Moments and the Principle of Moments Compute the moment of a force about a point in a plane by breaking the force into its Cartesian components and/or moving the vector to a more computationally-convenient position. Recommended Hibbeler Problems (12th Edition): F4-5, 4-5, 4-7, 4-9, 4-23 4. (25 points) Determine the direction (0° ≤ ≤ 180°) of the force F = 40 lb so that it produces a) the maximum magnitude of moment about point A and b) the minimum moment magnitude about point A (hint: maximum moment will occur if the perpendicular distance from the force to A is maximum). Compute the resultant moment of a system of planar forces on a point. 5. (25 points) Determine the resultant moment of the three forces with respect to point A. ES226 Exam 2 Study Guide Page 3 6. (30 points) If is known that a moment of 960 N-m about D is required to straighten the fence post CD, determine the tension that must be applied in the cable winch puller AB to create the required moment. Given: d = 2.80m. 7. (10 points) Determine the moment of the 100-lb force about point A. 100-lb 45° 5 ft A 5 ft Specify the direction and sense of a moment using the right-hand rule. Lesson 9 Moments in 3D Compute the moment of a force about a point in space with and without the cross product. Suggested Hibbeler 12th edition problems: F4-11, F4-12, 4.42, 4.43 8. (25 points) Determine the three Cartesian components of the moment of the 39-lb force about point A. ES226 Exam 2 Study Guide Page 4 9. (25 points) Determine the moment of the force about point O. Given: F = -50i. Note: Yes, the answer will be a vector! Compute the resultant moment from a system of forces in space with and without the cross product. 10. (25 points) Determine the resultant moment couple if d=0.4m. Solution: Lesson 11 Moment Couples Show that a couple is a free vector. Suggested Hibbeler 12th edition problems: F4.23, F4.24, 4.97, 4.101 11. (10 points). Show that the couple is a free vector. 100 lbs. A C E B D 10 ft. 10 ft. 10 ft. 10 ft. 100 lbs. Compute the moment of a couple. 12. (20 points) Determine the magnitude of F so that the resultant couple moment is 450 lb-ft counterclockwise 13. (25 points) Determine the magnitude F of the vertical force applied to each wrench if the couple moment acting on the pipe has a magnitude of 400 N-m (Ans: 992N) ES226 Exam 2 Study Guide Page 5 Determine the resultant of moment couples and specify magnitude and direction angles. 14. (25 points). Specify the resultant moment couple in vector notation (ans: 52.0i +50j+30k) Given: Applied moment couples M1 and M2, with orientations shown. 15. (25 points). Specify the resultant moment couple in vector notation. Given: Four applied moment couples with orientations shown. Lesson 12 Simplification of Force/Couple Systems Replace a 2D or 3D system of forces and couples with an equivalent system, consisting of a single resultant force and moment at a point 16. (30 points) Replace the system of forces and moments with a resultant force and moment acting at point O. ES226 Exam 2 Study Guide Page 6 17. (20 points). Replace the system of forces with a resultant force and moment acting at point A. 18. (40 points) Replace the forces and couples that are applied to the pipe assembly with a single resultant force and couple moment at point O, specifying the resultant force and moment as a Cartesian vector. Replace a 2D system of forces and couples with an equivalent system, consisting of a single resultant force and specify the location of the force. 19. (20 points) Replace the three forces acting on the shaft with a single equivalent resultant force, specifying where the force acts, measured from end B. ES226 Exam 2 Study Guide Page 7 20. (30 points) Replace the loading on the frame with a single force. Specify the angle this resultant force makes with respect to the horizontal and determine where its line of action intersects member CD, measured from side C. 21. (30 points) Replace the loading on the frame with a single force. Specify the angle this resultant force makes with respect to the horizontal and determine where its line of action intersects member AB, measured from side A. Exam 2 Study Guide Answers 1. FA=FB=575N; P=300N 2. FB = -19.2 kN, FC = 10.3 kN, FD = 6.34 kN 3. FB = 447N, FC = 342N, FD = 305N, P=960N 4. Moment is 0 at 166 degrees. Max Moment is 330 ft-lbs at 76 degrees 5. -2530 N-m 6. F=1225 N 7. M=0 8. <96,84,-180> 9. <0,-51.2,35.4> 10. 11. Moment about A is the same with the set of forces at C,D as when they are at B,C 12. F=139 lbs ES226 Exam 2 Study Guide Page 8 13. F=992 N 14. Resultant M = <51.96,50,30> 15. Resultant M = <85,40,0> 16. FR = <0 0 -500>, MR = <-650,462,28> 17. FR = <-40, -60, -80>, MR = <720, 0, 480> 18. FR = <141, 100, 159>, MR = <127, 0, -27> 19. FR = <-300, -740, 0> @ 6.57 feet 20. Resultant magnitude is 991 N at 117 degrees wrt to +x, at 2.8 meters from C. 21. Resultant magnitude is 922 lbs at 102.5 degrees wrt to +x, at 3.56 feet from A.