Name: Exam 04: Chapters 08 and 09 Select and solve four of the following problems to the best of your ability. You must choose two problem from each column. Please notice that it is possible to select problems adding up to more than 100 points. It is also possible to select problems adding up to fewer than 100 points. Your discretion. If you have the time and/or the inclination, you may solve a fifth problem for additional credit. Indicate below which problems you wish to have graded. If you do not explicitly mark a problem to be scored, it will not be scored. If you have worked on more than five problems, select only five to be graded. I will not choose for you. Choose At Least Two Grade this one? Score Choose At Least Two Grade this one? Score Problem 01 /25 Problem 05 /30 Problem 02 /30 Problem 06 /20 Problem 03 /20 Problem 07 /20 Problem 04 /15 Problem 08 /25 You have 50 minutes in which to complete this exam. No one will be permitted extra time. You may use your calculator and textbook. Read and follow the directions carefully. Solve using the method required by the problem statement. If you are not explicitly required to use a specific technique, please be sure to show sufficient work so that your method is obvious. Show all your work. Work as neatly as you can. If you need scratch paper, blank sheets will be provided for you. It is permissible to use your calculator to solve a system of equations directly. If you do, state this explicitly. Express your answer as directed by the problem statement, using three significant digits. Include the appropriate units. EXAM 04! PAGE 1
Problem 01 The uniform rod has a mass m = 15 kg, and length L = 0.5m. It is supported by the smooth (assume frictionless) ring at B. If, at the 30 angle shown, the rod is on the verge of slipping, determine the coefficient of static friction µs between the rod and the floor at point A. NB mg fa NA EXAM 04! PAGE 2
Problem 02 The two blocks used in a measuring device have negligible weight. The spring has constant k = 20 lb/in, and is compressed 5 in. when in the position shown. The end of the screw is smooth and the coefficient of static friction at all other points of contact is µs = 0.3. (Hint: This is a wedge problem, not a screw problem.) A. Draw the free body diagrams for blocks A and B. B. Determine the minimum horizontal applied force P required to move block B to the right (and downward). kx µn3 N3 N2 µn2 N2 P µn2 µn1 N1 EXAM 04! PAGE 3
Problem 03 The square-threaded bolt is used to join two plates together. If the bolt has a mean diameter of d = 20 mm and a lead of l = 3 mm, determine the smallest torque M required to loosen the bolt if the axial tension in the bolt is W = 40 kn. The coefficient of static friction between the threads and the bolt is µs = 0.15. EXAM 04! PAGE 4
Problem 04 The 100-lb boy at A is suspended from the cable that passes over the quarter circular cliff rock. What horizontal force must the woman at B exert on the cable in order to let the boy descend at constant velocity? The coefficient kinetic friction between the cable and the rock is µk = 0.35. (Hint: TA = T2) B TB π/2 TA EXAM 04! PAGE 5
Problem 05 Locate the x-coordinate of the centroid of the area shown. Use direct integration. (Hint: da = ydx is the easier differential element to use. Remember that the centroid of that differential element will be (x, y/2)!) EXAM 04! PAGE 6
Problem 06 Use the method of Pappus and Guldinus to calculate the volume of concrete needed to construct the 30 curb shown on the right. EXAM 04! PAGE 7
Problem 07 A rack is made from roll-formed sheet steel and has the cross section shown. Determine the location (x, y) of the centroid of the cross section. The dimensions are indicated at the center thickness of each segment. Segment Length (mm) x (mm) y (mm) 1 15 7.5 0 2 50 0 25 3 15 7.5 50 4 30 15 65 5 30 30 80 6 80 45 40 7 15 37.5 0 EXAM 04! PAGE 8
Problem 08 The semicircular tunnel passes under a river which is 9 m deep. Determine the horizontal resultant hydrostatic force Fx acting per meter of length along the length of the tunnel. The tunnel is 6 m wide; ρw = 1.0 Mg/m 3. (Hint: We set this up on the board with a constant (rectangular) distributed load and a linearly increasing (triangular) distributed load.) y1 = 6m F1 y2 = 3m F2 EXAM 04! PAGE 9