THE UNIVERSITY OF BRITISH COLUMBIA 2010/2011 WINTER SESSION Physics 170 Mechanics I Final Exam 3:30-6:00PM, Tuesday, April 19, 2011 Please write your name, student number, and course Section num- ber on the exam answer booklet which is provided. Write all work to be marked in the answer booklet. This is a closed book exam. You are allowed to use writing and drawing instruments, a calculator (without internet connection ca- pability) and an 82 x 11-inch handwritten, double sided formula sheet with no mechanical printing or reduction. You must hand in BOTH your formula sheet and your Answer Booklet in order for your exam to be marked. The exam consists of four questions. Please attempt all of them. The four questions are weighted equally. Within each question, marks are given as indicated. over > 1
1. The diagram below shows a bent rod in equilibrium in the horizontal plane. The rod is supported by a ball and socket joint at D, a cable at B and a smooth journal bearing at A. The bearing is in proper alignment and only exerts force reactions on the rod. The collar at E exerts a couple moment of Mo = 800Nmj on the rod. The weight of the rod may be neglected. 0.2 m C 1 m A 0.6 m 0.3 m B Mo z 0.5 m E 0.5 m D y x 100 kg over -> 2
0.2 m 1. C A 1 m 0.6 m 0.3 m B Mo IV 0.5 m E 0.5 m D y x 100 kg (a) Draw a large, clear free body diagram for the rod. Draw and label the coordinate axes and indicate the forces and label the coordinates of the points at which the forces act. (4 marks) (b) Find the three force component (scalar) equations of equi- librium. (7 marks) (c) Determine the vector moment equation of equilibrium. Take moments about the point D. (5 marks) (d) Determine the three scalar moment equations of equilib- rium. (3 marks) (e) Solve the six scalar equations of equilibrium to find the tension in the cable and the Cartesian components of the reactions at A and D. (6 marks) over > 3