Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin each problem in the space provided on the examination sheets. If additional space is required, use the white lined paper provided to you. Work on one side of each sheet only, with only one problem on a sheet. Each problem is worth 20 points. Please remember that for you to obtain maximum credit for a problem, it must be clearly presented, i.e. The coordinate system must be clearly identified. Where appropriate, free body diagrams must be drawn. These should be drawn separately from the given figures. Units must be clearly stated as part of the answer. You must carefully delineate vector and scalar quantities. If the solution does not follow a logical thought process, it will be assumed in error. When handing in the test, please make sure that all sheets are in the correct sequential order and make sure that your name is at the top of every page that you wish to have graded. Instructor s Name and Section: Sections: J. Silvers 8:30-9:30am B. Hylton 2:30-3:20pm J. Jones 11:30am-12:20pm J. Seipel 12:30-1:20pm M. Murphy 9:00-10:15am E. Nauman 9:30-10:20 am K. Li 1:30-2:20pm J. Jones Distance Learning Problem 1 Problem 2 Problem 3 Total
PROBLEM 1. (20 points) The truss shown below is loosely modeled after the Wabash River Bridge on State Route 316 in Wells County Indiana. Images taken of the Wabash River Bridge on State Route 316 just to prove that it does exist and uses giant pins at the joints. The real part of the problem starts below. GIVEN: Our model of this truss is shown below. The height, H, is 12 ft., and there are 7 panels, each with length 8 ft. so that the total length of the span, L, is 56 ft. Each force, F = 2,000 lbs.
1a. List as many 0 force members as possible. You do not need to provide the reasoning for your choices. (2 points) 1b. On the truss below, draw a free body diagram and solve for the reactions at points (a) and (j). (7 points)
1c. Calculate the forces in links (op), (fg), and (pq). Make sure you include the appropriate free body diagrams. Indicate whether the links are in tension or compression. (11 points)
PROBLEM 2. (20 points) GIVEN: A crate weighing 220 lbs is resting on a 40 degree incline as shown. A rope is attached to the crate at point C, wraps part way around a fixed drum, and is pulled by a 180 lb man. FIND: First, consider just the crate. a) Determine the minimum tension, T c, to prevent the crate from tipping. Your solution must include a free body diagram. (6 pts) b) Determine the minimum tension, T c, to prevent the crate from slipping. Your solution must include a free body diagram. (6 pts) c) When the crate begins to move, will the crate tip or slip? (2 pts) Now consider the 180 lb man at the top of the incline and the friction between his shoes and the ground, μ!. d) Assuming that the man is pulling horizontally on the rope, what is the maximum force with which the man can pull? (3 pts) e) Considering the required tension, T m, to hold the crate in equilibrium - can the man support the crate, or will the crate begin to move? Include any necessary calculations to support your answer. (3 pts) a) FBD for Tipping case
T tip = b) FBD for Slipping case T slip = c) Slip or Tip (circle one) d) T max,man =
e) Yes or No (circle one)
PROBLEM 3. (total: 20 points). NO PARTIAL CREDIT. PLEASE WRITE ANSWERS IN THE LOCATION PROVIDED. Part a). Given: A ship with dimensions below and a weight of 1,000,000 N. (Water density is 1000kg/m^3.) 50 m long 5 m 3 m 4 m 10 m (3 pts) Write the volume of the ship here: (2 pts) Will the ship float or sink? (circle one here) Part b) Given: The frame shown below with an applied torque. The locations of each joint are labeled in meters using (x,y) notation. Assume all joints are pinned, and masses are negligible. D ( 2.5, 1.5 ) B ( 0.5, 1 ) 10 Nm applied torque y x C ( 1, 0.5 ) E ( 2, 0 ) A ( 3, 0.5 ) (4 pts) List any two-force members (using AB notation): (3 pts) Is the member AE in tension or compression? (circle one here).
Part c). Given: The gate below is pinned to ground and the water depth is 3 meters. (water density is 1000kg/m^3.) Assume that the water extends 1 meter into the page. Water surface 20,000 N y x Water depth: 3 m 2 m pin-joint (3 pts) Write the equivalent force magnitude (3 pts) Write the distance of the equivalent force from the pin joint (2 pts) Will the gate swing to the left, swing to the right, or be in equilibrium? (circle one here).
ME 270 Exam 2 Equations Buoyancy FB gv Fluid Statics p gh F p Lw eq avg Belt Friction TL T S e
ME 270 Exam 2 Solutions for Fall 2013 1A. Zero Force Members: ri, kb, ij, hi, ab, and bc 1B. FBD 1C. F fg = 9333 lbs/ tension F op = -10,670 lbs/ compression F pq = -9337 lbs/ compression 2A. FBD for Tipping case T Tip = 45.72 lbs 2B. FBD for Slipping case T Slip = 107.7 lb 2C. Slip 2D. T max,man = 99 lbs 2E. Yes 3A. 3,550 m 3 Float 3B. Two-Force Members: DB (or BD), CB (or BC), EA (or AE) Tension 3C. approximately 45,000 N Approximately 1.0 m Swing to the right