Explanation Given information: The tension ( T A C ) in the cable AC is 544 lb. Calculation: Draw the free body diagram of point D of a crate as in Figure (1). The force applied at the point D is T A B , T A C , T A D , and W . Write the weight of the crate in vector as below: W = − W j Express the vector A B → as below: A B → = − ( 36 in . ) i + ( 60 in . ) j − ( 27 in . ) k Calculate distance of the member DA as below: A B = ( − 36 ) 2 + 60 2 + ( − 27 ) 2 = 1296 + 3600 + 729 = 75 in . Calculate the unit vector ( λ A B ) using the relation: λ A B = A B → A B Substitute − ( 36 in . ) i + ( 60 in . ) j − ( 27 in . ) k for A B → and 75 in . for AB . λ A B = − ( 36 in . ) i + ( 60 in . ) j − ( 27 in . ) k 75 = − 0.48 i + 0.8 j − 0.36 k Calculate the tension force ( T A B ) in cable AB using the relation: T A B = T A B λ A B Substitute − 0.48 i + 0.8 j − 0.36 k for λ A B . T A B = ( − 0.48 i + 0.8 j − 0.36 k ) T A B Express the vector A C → as below: A C → = ( 60in . ) j + ( 32in . ) k Calculate distance of the member AC as below: A C = ( 60 ) 2 + ( 32 ) 2 = 3600 + 1024 = 68 in . Calculate the unit vector ( λ A C ) using the relation: λ A C = A C → A C Substitute ( 60in . ) j + ( 32in . ) k for A C → and 68 in . for AC . λ A C = ( 60in . ) j + ( 32in . ) k 68 in . = 0.8824 j + 0.4706 k Calculate the tension force ( T A C ) in Cable AC using the relation: T A C = T A C λ A C Substitute 0.8824 j + 0.4706 k for λ A C . T A C = ( 0.8824 j + 0.4706 k ) T A C Substitute 544 lb for T A C . T A C = ( 0.8824 j + 0.4706 k ) × 544 = 480.0256 j + 256.0064 k Express the vector A D → as below: A D → = ( 40 in . ) i + ( 60in . ) j − ( 27in . ) k Calculate distance of the member AD as below: A D = ( 40 ) 2 + ( 60 ) 2 + ( − 27 ) 2 = 1600 + 3600 + 729 = 77 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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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 2.5, Problem 2.105P

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Vector Mechanics for Engineers: Statics and Dynamics

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The weight ( W ) of the crate.

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