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2008F_Test1_solutions

2008F_Test1_solutions - EM 306 Statics TEST 1 Fall 2008...

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EM 306 – Statics TEST 1 Fall 2008 - Kontsos Name : ___________________________________ EID: ___________________________________ Unique Number : ___________________________ Instructions: This is a closed book, closed notes test. You are allowed to use calculators. The duration of the test is 1 hour . Problem 1 (50 points): Two forces are exerted on the crankshaft by the connecting rods as shown in Figure 1. The direction cosines of F A are cos θ x = - 0.182 , cos θ y = 0.818 , and cos θ z = 0.545 , and its magnitude is 4 kN . The direction cosines of F B are cos θ x = 0.182 , cos θ y = 0.818 , and cos θ z = -0.545 , and its magnitude is 2 kN . (i) [10 points] Draw a diagram where you clearly show the points of application of the two forces and the two forces. (ii) [30 points] Given the two forces in the figure, compute a single force R and a moment M O acting at the origin O . Draw R and M O on the diagram you presented in (i). (iii) [10 points] If the system of forces that you computed in (ii) should be represented by a single force acting at some point in space, show how you would compute the coordinates of this point by deriving a system of equations (you are not required to solve it).

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2008F_Test1_solutions - EM 306 Statics TEST 1 Fall 2008...

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