Explanation Given: Value of a is 1 ft . Value of b is 12 ft . Concept used: Here, point B is the origin of the given diagram. Write the coordinate of point E as ( 12 , 1 , 0 ) ft . Write the expression for position vector of point E with respect to point B. r → E = ( 12 i ^ + 1 j ^ ) ft Here, r → E is the position vector of point E with respect to point B. Write the coordinate of point F as ( 5.5 , − 5 , 0 ) ft . Write the expression for position vector of point F with respect to point B. r → F = ( 5.5 i ^ − 5 j ^ ) ft Here, r → F is the position vector of point F with respect to point B. Write the coordinate of point G as ( 14.5 , − 3 , 0 ) ft . Write the expression for position vector of point G with respect to point B. r → G = ( 14.5 i ^ − 3 j ^ ) ft Here, r → G is the position vector of point G with respect to point B. Write the coordinate of point H as ( 22.5 , − 5.5 , 0 ) ft . Write the expression for position vector of point H with respect to point B. r → H = ( 22.5 i ^ − 5.5 j ^ ) ft Here, r → H is the position vector of point H with respect to point B. Write the expression for force vector at point E. F → E = − 90 k ^ lb Here, F → E is the force vector at point E. Write the expression for force vector at point F. F → F = − 105 k ^ lb Here, F → F is the force vector at point F. Write the expression for force vector at point G. F → G = − 160 k ^ lb Here, F → G is the force vector at point G. Write the expression for force vector at point H. F → H = − 50 k ^ lb Here, F → H is the force vector at point H. Write the expression for resultant force. R → = F → E + F → F + F → G + F → H ....... (1) Here, R → is the resultant force. Write the expression for moment due to force F → E about point B. M → E = r → E × F → E ....... (2) Here, M → E is the moment due to force F → E about point B. Write the expression for moment due to force F → F about point B. M → F = r → F × F → F ....... (3) Here, M → F is the moment due to force F → F about point B. Write the expression for moment due to force F → G about point B. M → G = r → G × F → G ....... (4) Here, M → G is the moment due to force F → G about point B. Write the expression for moment due to force F → H about point B. M → H = r → H × F → H ....... (5) Here, M → H is the moment due to force F → H about point B. Write the expression for net moment about point B. M → = M → E + M → F + M → G + M → H ....... (6) Here, M → is the net moment about point B. Write the expression for moment due to resultant force R → about point B. M → R = r → × R → ....... (7) Here, M → R is the moment due to resultant force R → and r → is the position vector of resultant force. Write the expression for position vector of resultant force with respect to point B. r → = x i ^ + y j ^ + z k ^ ....... (8) Here, x , y , z are the coordinates of location of resultant force vector. Moment due to resultant force is equal to net moment, M → R = M → ....... (9) Calculation: Substitute − 90 k ^ lb for F → E , − 105 k ^ lb for F → F , − 160 k ^ lb for F → G and − 50 k ^ lb for F → H in equation (1) R → = ( − 90 k ^ ) + ( − 105 k ^ ) + ( − 160 k ^ ) + ( − 50 k ^ ) = − 405 k ^ lb Substitute ( 12 i ^ + 1 j ^ ) ft for r → E and − 90 k ^ lb for F → E in equation (2) M → E = ( 12 i ^ + 1 j ^ ) × ( − 90 k ^ ) = ( − 90 i ^ + 1080 j ^ ) lb

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 3.4, Problem 92P

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The magnitude of resultant force and its location.

Solution Summary: The author explains the magnitude of resultant force and its location. Point B is the origin of the given diagram.

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