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Final_F09_v3 - Name(Last(First ME 270 – Fall 2009 Final...

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Unformatted text preview: Name (Last) (First) ME 270 – Fall 2009 Final Examination Please Circle Your Instructor’s Name Jones Li Murphy Nauman Krousgrill INSTRUCTIONS Begin each problem in the space provided on the examination sheets. If additional space is required, use the yellow 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. Problem 1 ________ Problem 2 ________ Problem 3 ________ Problem 4 ________ Problem 5 ________ Total ____________ Name (Last) (First) Problem 1a (4 points) Please denote all the ZERO‐FORCE members in the truss below: Zero‐Force Members are: Problem 1b (6 points) Please state Newton’s Laws in order as succinctly as possible: Newton’s First Law Newton’s Second Law Newton’s Third Law Name (Last) (First) Problem 1 C (5 points) Please determine the maximum height a ball thrown vertically will achieve if it has an initial velocity of 60 ft/s and the time it will take to reach the maximum height. Max. Height = Time to reach max height= Problem 1 D (5 points) Please determine the maximum weight that can be held in place by a 100‐lb tension if the coefficient of friction μ=0.3. Note that the cable does not wrap all the way around the stationary cylinder. 30º 100‐lb W W = Name (Last) (First) 2. The mechanism below is a model of a can crusher built by students in a basic mechanisms class. The slider mechanism is constructed with link ABC connected to link BD at a pin joint. A slider is attached at point D and slides along the horizontal surface with negligible friction. The force to crush a can is represented by force P (the force the can pushes back on the mechanism). The input to crush the can is force F = 40 lb which acts horizontal to the plane of mechanism. Please show all your work. i. (2 points) Please list all (if any) two‐force members here . ii. (3 points) Provide a free‐body diagram for the entire mechanism (please use the figure provided on the next page). iii. (5 points) Provide a free‐body diagram for the broken‐up mechanism (please use the figure provided on the next). iv. (10 points) Please determine the reactions at A, and the reaction P for the 40 lb input at the angles shown. Please provide answers here: a. Ax = b. Ay = c. MA= d. P = Name (Last) (First) Please show work for Part ii here Please show work for Part iii here Name (Last) (First) 3. A car, currently at point C, is driving on a circular track. At the position shown, its velocity is v = ‐(40 ft/s)j. In addition, we know that its rate of change of speed is +10ft/s2. Part 3A. Sketch the unit vectors et and en on the figure below. (3 points) 400 ft r θ Part 3B. Determine the components of the acceleration in i and j coordinates. (5 points) a = Part 3C. We will use cylindrical coordinates to describe the motion from point O. Sketch the er and eθ unit vectors on the figure above. (2 points) Name (Last) (First) Part 3D. Determine θ, r , and θ . (5 points) Part 3E. Determine r , and θ . (5 points) Name (Last) (First) 4a. Consider the picture of Iron Man below. The maximum thrust each boot jet can generate is Tmax. Iron Man (person + armor) has a weight of 425 lbs. and he can hover in the air using only 1% of Tmax in each boot. Draw a free body diagram of Iron Man hovering in the air below. You may model him as a particle. (3 points) Draw free body diagram here 4b. Determine the value of Tmax. (3 points) Name (Last) (First) 4c. If Iron Man needs to move straight up and decides to initiate maximum thrust in each boot, what will his acceleration be? (6 points) 4d. If Iron Man starts at rest (at 0 height) and accelerates at the maximum rate found in 4c, at what height will he achieve a speed of 300 ft/s? (8 points) Name (Last) (First) 5. Please read all parts of the problem before you start. The goal of this problem is to determine the geometry of the triangular dam required to prevent the dam from slipping or tipping. Assume the height of the water (and the dam) is 3m and the distance into the page is 4m. If the water has a density of 1000 kg/m3 and the concrete has a density of 2400 kg/m3, what value of a is required to prevent the dam from slipping or tipping? The coefficient of static friction between the ground and the dam is 0.9. (20 points) a) Determine the resultant force from the water and its point of application from the bottom of the dam. (3 points) b) Determine the weight of the concrete block (in terms of dimension a) and its center of mass from point C (in terms of dimension a). (3 points). Name (Last) (First) c) Draw the free-body diagram for the case of impending tipping and determine the value of dimension a to prevent slipping (6 points). Name (Last) (First) d) Draw the free-body diagram for the case of impending slipping and determine the value for a to prevent tipping (6 points). e) What value of dimension a is required to prevent the dam from slipping or tipping? (2 points) Name (Last) (First) ...
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