Explanation Given: Tension in cable AC is 1065 N . Concept used: Write the expression for the position vector for point C with respect to A. d → A C = ( − 900 i ^ + 600 j ^ − 920 k ^ ) mm Here, d → A C is the position vector for point C with respect to A. Write the expression for the magnitude of position vector for point C with respect to A. | d A C | = ( − 900 ) 2 + ( 600 ) 2 + ( − 920 ) 2 = 2016400 = 1420 mm Here, | d A C | is the magnitude of position vector for point C with respect to A. Write the expression for unit vector along line AC. n ^ A C = d → A C | d A C | ……. (1) Here, n ^ A C is the unit vector along line AC. Write the expression for representation of tension in cable AC in vector. T → A C = | T A C | ⋅ n ^ A C …… (2) Here, T → A C is the representation of tension in cable AC in vector and | T A C | is the magnitude of tension in cable AC. Write the expression for moment about x axis due to force exerted on plate at point C. M x = d y ( T A C ) z − d z ( T A C ) y …… (3) Here, M x is the moment about x axis due to force exerted on plate at point C, d y is the distance of point C from x axis along y direction, d z is the distance of point C from x axis along z direction, ( T A C ) z is the z component of tension in cable AC and ( T A C ) y is the y component of tension in cable AC. Write the expression for moment about y axis due to force exerted on plate at point C. M y = d z ( T A C ) x − d x ( T A C ) z …… (4) Here, M y is the moment about y axis due to force exerted on plate at point C, d x is the distance of point C from y axis along y direction, d z is the distance of point C from y axis along z direction and ( T A C ) x is the x component of tension in cable AC. Write the expression for moment about z axis due to force exerted on plate at point C. M z = d x ( T A C ) y − d y ( T A C ) x …… (4) Here, M z is the moment about z axis due to force exerted on plate at point C, d x is the distance of point C from z axis along z direction and d y is the distance of point C from z axis along y direction. Calculation: Substitute ( − 900 i ^ + 600 j ^ − 920 k ^ ) mm for d → A C and 1420 mm for | d A C | in equation (1) n ^ A C = ( − 900 i ^ + 600 j ^ − 920 k ^ ) 1420 = ( − 0

2nd Edition

ISBN: 9780073398167

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David Mazurek

Publisher: McGraw-Hill Education

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Chapter 3.2, Problem 36P

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The moment of force exerted on plate at C about each coordinate axis.

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Chapter 3.2, Problem 35P

Chapter 3.2, Problem 37P

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Statics and Mechanics of Materials

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