Explanation Given information: The length of the vertical rod CD ( l C D ) is 23 inch. The length of the rod AB ( l A B ) is 50 inch. The force ( Q ) is 174 lb. The distance between the points O to B ( x ) is 32 inch. The distance between the points O to A ( y ) is 24 inch. The vertical height of OA ( h O A ) is 30 inch. The vertical height of OH ( h O H ) is 17 inch. The horizontal distance between point O and midpoint C ( d O C ) is 16 inch. The horizontal distance between midpoint C and point G over x axis ( d C G ) is 21 inch. The horizontal distance between point B and midpoint C ( d B C ) is 12 inch. The horizontal distance between midpoint C and point G over z axis ( h ) is 18 inch. Calculation: Calculate the position vector of AB using the relation: A B ⇀ = x i − h O A j − y k Substitute 32 in. for x , 30 in. for h O A , and 24 in. for y . A B ⇀ = 32 i − 30 j − 24 k A B = ( 32 ) 2 + ( − 30 ) 2 + ( − 24 ) 2 A B = 50 in . Calculate the unit vector of AB using the formula: λ A B = A B ⇀ A B Substitute 32 i − 30 j − 24 k for A B ⇀ and 50 in. for AB . λ A B = 32 i − 30 j − 24 k 50 = 0.64 i − 0.6 j − 0.48 k Apply the force Q at the point H . Calculate the position vector of from point H to point B ( r H / B ) using the relation: r H / B = − x i + h O H j Substitute 32 in. for x and 17 in. for h O H . r H / B = − 32 i + 17 j Calculate the position vector of DH using the relation: D H ⇀ = − d O C i − [ ( h O A 2 + l C D ) − h O H ] j − d B C k Substitute 16 in. for d O C , 30 in. for h O A , 23 in. for l C D , 17 in. for h O H , and 12 in. for d B C . D H ⇀ = − 16 i − [ ( 30 2 + 23 ) − 17 ] j − 12 k D H ⇀ = − 16 i − 21 j − 12 k D H = ( − 16 ) 2 + ( − 21 ) 2 + ( − 12 ) 2 D H = 29 in

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 3.2, Problem 3.56P

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Vector Mechanics for Engineers: Statics and Dynamics

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