Statics S08 Test 1 with Answers

# Statics S08 Test 1 with Answers - Question 1 a the...

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1 Question 1 a) the direction angles β and γ measured from point O for cable OB From the information given, we know that α = 120 degrees, where α is measured from the positive x-axis. In order to use the equation, 1 cos cos cos 2 2 2 = + + γ β α , we must first determine either β or γ. Since we’re told that points A , B , and C are the same height, we can find the height of point C by using the length of the cable OC and the given angle of 70 degrees. () ft C B A ft ft C y y y y 5 . 85 5 . 85 70 cos 250 = = = = = Now, using the height of point B (85.5 ft) and the length of cable OB (171 ft), we can determine the direction angle β. Since the direction angle β is measured from the positive y-axis, () ° = = 60 5 . 85 cos 171 ft ft Solving for γ , ° ° = = + + 135 45 1 cos 60 cos 120 cos 2 2 2 or Since γ is measured from the positive z-axis, γ should be 135 degrees. b) the tension in cables OA and OB Writing the force vectors, [] ()( )() [] () ()( )() () [] kips k j i F kips k F j F i F F kips j ft ft F i ft ft F F OC OB OB OB OB OA OA OA ˆ 50 sin 70 sin 70 ˆ 70 cos 70 ˆ 50 cos 70 sin 70 ˆ 135 cos ˆ 60 cos ˆ 120 cos ˆ 66 . 172 5 . 85 ˆ 66 . 172 150 + + = + + = +
2 Summing the forces in the x, y, and z-directions, () ()( ) () () () ( ) ( ) kips F kips F kips F F W kips ft ft F F F ft ft F F kips F OA OB OB z crate OA OB y OA OB x 66 . 7 26 . 71 0 50 sin 70 sin 70 135 cos 0 0 70 cos 70 66 . 172 5 . 85 60 cos 0 0 66 . 172 150 120 cos 50 cos 70 sin 70 0 = = = + = = + + = = + = c)

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## This note was uploaded on 08/29/2010 for the course EGN 3311 taught by Professor Nohra during the Spring '08 term at University of South Florida.

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Statics S08 Test 1 with Answers - Question 1 a the...

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