Last Name, First Name. I have not received unauthorized aid in the completion of this exam.

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1 ME 270 Spring 2013 Examination No. 2 Please read and respond to the following statement, I have not received unauthorized aid in the completion of this exam. Agree Disagree Signature INSTRUCTIONS Begin each problem in the space provided on the examination sheets. If additional space is required, use the 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. Please circle your instructor s name: Nauman Silvers Chagdes Problem 1 Problem 2 Problem 3 Total

2 PROBLEM 1 (Short Answer) The following sub-problems labeled 1A to 1D are worth 5 points each for the correct answer and zero points for the wrong answer (no partial credit, no matter how trivial the mistake). 1A. Determine the area and the x- component of the centroid for the object below. (5 points, no partial credit)

3 Last Name, First Name 1B. On the figure on the right, draw the equivalent force (located at the appropriate point) for the distributed load. Make sure to label the magnitude and position of the equivalent force. (5 points, no partial credit) 1C. The hinged gate ABC closes an opening of width b (perpendicular to the paper) in a water channel. The water, of density, has free access to the underside as well as the right side of the gate. Resolve any distributed loads into single forces (located at the appropriate point) and draw a complete free body diagram of the hinged gate ABC when the water level is such that the gate begins to rotate counter- clockwise and begins to open. Neglect the weight of the gate and assume that there is no friction at point A. (5 points, no partial credit) Free Body Diagram:

4 1D. A channel- marker buoy is anchored to the ground. The buoy consists of an 8 ft hollow steel cylinder 1 ft in diameter which weighs 180 lbs. Determine the tension in the cable at high tide when. Assume that the specific weight ( ) of sea water is. (5 points, no partial credit)

5 PROBLEM 2. (20 points) GIVEN: A cabinet weighing 60 lbs rests on the 25 incline shown. A cable attaches to the cabinet at point C, wraps over a fixed drum, and connects to a weight, D. Between C and the drum, the cable has a tension, T. FIND: First, consider just the cabinet. a) Determine the tension, T, required to tip the cabinet up the incline. Your solution must include a free body diagram. (7 pts) b) Determine the tension, T, required for the cabinet to slip up the incline. Your solution must include a free body diagram. (7 pts) c) Will the cabinet tip or slip? (2 pts) Now consider the weight, D, attached to the cable. d) What weight, D, is required to initiate the motion described in part (c)? (4 pts) a) FBD for Tipping case T tip =

6 b) FBD for Slipping case T slip = c) Tip or Slip (circle one) d) Weight, D =

7

8 PROBLEM 3. The scaffolding below is loaded at four points by a force F 1 = 2,000 Newtons. You may assume that L 1 = 3 m and L 2 = 4 m. 3a. In the box below, draw a free body diagram of the entire structure and solve for the reactions at points (a) and (b). (8 points) Free Body Diagram: Reactions:

9 3b. Calculate the forces in links ih, im, and hm. (3 points) F ih = F im = F hm = 3c. Determine the forces in links ad, dc, and ec and note which ones are in tension and compression. (9 points) F ad = F dc = F ec = T or C T or C T or C

10

11 Centroid By Integration Equation Sheet By Composite Parts Special Case: Uniform Density Center of Mass By Integration By Composite Parts

12 ME 270 Exam 2 Solutions for Spring A. Area = mm 2 x = 244 mm 1B. F eq = 1040 lb x = 4.69 ft 1C. FBD 1D. T = 122 lb 2A. FBD for Tipping case T Tip = 46.2 lb 2B. FBD for Slipping case T Slip = 47.1 lb 2C. Tip 2D. Weight, D, = 62.4 lb 3A. FBD A y = -4,500 N A x = 2,000 N 3B. F ih = 0 N F im = 0 N B = 10,500 N y F hm = 0 N 3C. F ad = 6,000 N T F dc = 0 N F ec = 12,000 N C

I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Examination No. 2 Please review the following statement: Group Number: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin

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