THE UNIVERSITY OF BRITISH COLUMBIA 2010/2011 WINTER SESSION SESSIONAL EXAMINATIONS PHYSICS 170 MECHANICS I 8:30 am to 11:00 am, Thursday, December 9, 2010 MARKS This exam counts for a total of 70 marks towards your Final Grade for the course. The exam consists of 4 questions worth a total of 70 marks. Questions 1 and 3 are each worth 20 marks. Questions 2 and 4 are each worth 15 marks. Write all work to be marked in the Answer Booklets provided. NUMERICAL ANSWERS You must give numerical answers correctly to three figures and with correct units to get any marks for your numerical answers. No marks are given for correctly solving incorrect equations. CALCULATOR You may use a graphing calculator. INFORMATION SHEET You may consult one 8 1/2 inch by 11 inch hand-written double-sided Information Sheet. Your Information Sheet must not contain any sample problems or solutions to sample problems. Put your name and student number on your Information Sheet. You must hand in your Information Sheet with your Answer Booklet in order for your exam to be marked.
PHYSICS 170 MECHANICS I Sessional Examinations: 8:30 am to 11:00 am, Thursday, December 9, 2010 QUESTION 1 (20 marks) The diagram below shows a uniform rigid body ABCD in equilibrium in the horizontal plane. The weight of ABCD is 2 kN. A force and couple act at point C where F = (31 +4]+5k) kN and M = (-201+24]+8k) kNm where i, j, k are the usual Cartesian unit vectors. ABCD is supported at G by a cable attached to J, and at H by a frictionless hinge. There are no other supports for ABCD. a) Draw a large, clear free-body diagram for ABCD. Show also the Cartesian unit vectors and the numerical values of the coordinates of C, G, H, J and the centre of gravity of ABCD. Make sure that this part of the Question is correct before proceeding to the next parts of the Question. (4 marks) b) Express the force in the cable and the reaction at H as Cartesian vectors. (2 marks) c) Determine the three Cartesian component force equations of equilibrium for ABCD. (3 marks) d) Determine the vector moment equation of equilibrium for ABCD. Take moments about H and use forces at their point of action on ABCD. (4 marks) e) Determine the three Cartesian component moment equations of equilibrium for ABCD. (3 marks) f) Solve the six Cartesian component equations of equilibrium for ABCD to determine the Cartesian components of reaction at H and the magnitude of the tension in cable GJ. (The equations are easy to solve by substitution.) (4 marks) J 6m 7 m 6m $ 4 m H A D TE 4m 4m B 3 m 7 m G A C x
PHYSICS 170 MECHANICS I Sessional Examinations: 8:30 am to 11:00 am, Thursday, December 9, 2010 ANSWERS TO QUESTION 1 b) Force in the cable and the reaction at H F= (!4?!9 ]+ 7k)X F = H i +