SOLUTIONS MARK DISTRIBUTION Physics 170 Final Exam December 2006 Page 2 of 11 Name: Student Number: Note: Very little credit for correct answers without a clear explanation of reasoning. Question #1: The end of the rope (point-B) is pulled by a student with a force, F , of magnitude 30 N. (a) Express the force, F , in terms of i, j, and k components. (b) Determine the unit vector pointing from point-D to point-C. (c) Determine the moment that the force, F , exerts about point-D. (d) Determine the magnitude of the above moment about the axis going through points D and C. (e) The pole is held in the sidewalk with cement and, thereby, restrained from moving. The mass of the pole is 200 kg. Draw the free body diagram for the pole. (Do not solve for the reaction forces and couples; just give the free body diagram). Mark Distribution 1 30N 1 Part Answer Reasoning a) rs- 12m C 1 1 1 6) 1 1 2. B 6 m F 1.5 m c) 1/2 1 1/2 3 m 4 m D 1) 1/2 1 1/2 7 m e) 2 0 Totals 2 2 2 2 2 /10/
Solution: Question - 1 11/7 a) F = (30 N) [ (4-0) } + (-3-0) } + ( 1.5 - 12) = ] V(4)2+ (3) + (10.5) 2 = +10.3 2 - 7.741 - 27.14 N b) ûrc = [0] +(0-7)} +(6-0)}] V(0)2+(7)3+(1)2 V 02 -0.759 1 + 0651m = TO DA x F = -7 0 10.3 - 7.74 12 - 27.1 0 -7 10.3 -7.74 = 2836 + 124} + 72.11 N.m d) 1 MDC = mr . upc = ( 283) (0) + (124)(-0.759) + (72.1)(0.651) = - 46.9 N.m ( = 46.9 N.m. Don't worry about sign) 8 Î A c) FSSON 1 B 1 1 .. My 1 200 (9.81) Oy 4 O - 7 My 47M 2 c) ? =
Physics 170 Final Exam December 2006 Page 4 of 11 Name: Student Number: Note: Very little credit for correct answers without a clear explanation of reasoning. Question #2: Replace the three forces (2.5 kN, 1.5 kN, and 3 kN) acting on the beam by an equivalent force and couple moment acting at point-C. Use the x-y-z axes shown < < below to express your final answer in terms of i, j, and k components. 3 kN 7 0.5 m 2,5 KN 30° 5 3 1.5 KN 4 X Z(OUT) B . 2 m- C + 2 m . 4 m -2 m- Mark Distribution Answer Reasoning Totals Resultant Face 2 3 5 = Comple 2 3 5) 10