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

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9781259639272

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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The weight (W) of the crate.

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Chapter 2.5, Problem 2.104P

Chapter 2.5, Problem 2.106P

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Can you solve it analytically using laplace transforms and with Matlab code as well please. Thank You

Can you solve it analytically using laplace transforms and with Matlab code as well please. Thank You.

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Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

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The weight ( W ) of the crate.

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The weight (W) of the crate.

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