Determine the tension in each of the three ropes supporting the 800-lb crate.

Q: Expert Answer

To determine Tension in each rope. Explanation Given Information: 800-lb crate is supported by three ropes as shown in following figure: Calculation: Draw free body diagram of as shown in following figure: Force vectors are, T → B = T B ( 6 i ^ − 6 j ^ − 10.5 k ^ 6 2 + ( − 6 ) 2 + ( − 10.5 ) 2 ) = T B ( 0.46 i ^ − 0.46 j ^ − 0.81 k ^ ) T → C = T C ( − 6 i ^ − 3 j ^ − 10.5 k ^ ( − 6 ) 2 + ( − 3 ) 2 + ( − 10.5 ) 2 ) = T C ( 0.5 i ^ − 0.25 j ^ − 0.87 k ^ ) T → D = T D ( 2.4 i ^ + 6 j ^ − 10.5 k ^ 2.4 2 + ( 6 ) 2 + ( − 10.5 ) 2 ) = T D ( 0.2 i ^ − 0.5 j ^ − 0.87 k ^ ) W → = − 800 k ^ Take equilibrium of forces as, ∑ F → = 0 ⇒ T → B + T → C + T → D + W → = 0 ⇒ T B ( 0

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4th Edition

Andrew Pytel And Jaan Kiusalaas

Publisher: CENGAGE L

ISBN: 9781305501607

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International Edition---engineerin...

4th Edition

Andrew Pytel And Jaan Kiusalaas

Publisher: CENGAGE L

ISBN: 9781305501607

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To determine

Tension in each rope.

Explanation of Solution

Given Information:

800-lb crate is supported by three ropes as shown in following figure:

Calculation:

Draw free body diagram of as shown in following figure:

Force vectors are,

T→B=TB( 6 i ^ −6 j ^ −10.5 k ^ 6 2 + (−6) 2 + (−10.5) 2 )=TB(0.46i^−0.46j^−0.81k^)T→C=TC( −6 i ^ −3 j ^ −10.5 k ^ (−6) 2 + (−3) 2 + (−10.5) 2 )=TC(0.5i^−0.25j^−0.87k^)T→D=TD( 2.4 i ^ +6 j ^ −10.5 k ^ 2.4 2 + (6) 2 + (−10.5) 2 )=TD(0.2i^−0.5j^−0.87k^)W→=−800k^

Take equilibrium of forces as,

∑F→=0⇒T→B+T→C+T→D+W→=0⇒TB(0

Determine the tension in each of the three ropes supporting the 800-lb crate.

International Edition---engineerin...

Solutions

International Edition---engineerin...