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**Problem 3.152 y The frame ACD is hinged at A G**

z x 0.875 m 0.75 m 0.5 m 0.35 m 0.925 m A B O C D P H G The frame ACD is hinged at A and D and is supported by a cable which passes through a ring at B and is attached to hooks at G and H. Knowing that the tension in the cable is 450 N, determine the moment about the diagonal AD of the force exerted on the frame by portion BH of the cable.

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**Solving Problems on Your Own**

z x 0.875 m 0.75 m 0.5 m 0.35 m 0.925 m A B O C D P H G Solving Problems on Your Own The frame ACD is hinged at A and D and is supported by a cable which passes through a ring at B and is attached to hooks at G and H. Knowing that the tension in the cable is 450 N, determine the moment about the diagonal AD of the force exerted on the frame by portion BH of the cable. Problem 1. Determine the moment MOL of a force about a given axis OL. MOL is defined as MOL = l . MO = l . ( r x F ) where l is the unit vector along OL and r is a position vector from any point on the line OL to any point on the line of action of F.

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**TBH = ( 0.375 i + 0.75 j _ 0.75 k ) MAD = l AD . ( rB/A x TBH )**

y z 0.875 m 0.75 m 0.5 m 0.35 m 0.925 m A B O C D P H G TBH lAD rB/A x Problem Solution Determine the moment MAD of a force about line AD. MAD = l AD . ( rB/A x TBH ) Where lAD = (4 i _ 3 k) rB/A = (0.5 m ) i 1 5 dBH = ( )2 + ( 0.75 )2 + ( _ 0.75 )2 = m TBH = ( i j _ 0.75 k ) = ( 150 N) i + ( 300 N) j _ ( 300 N) k 450 N 1.125

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**MAD = lAD . ( rB/A x TBH ) TBH lAD 4 0 _3 MAD 0.5 0 0 1 MAD =**

y z 0.875 m 0.75 m 0.5 m 0.35 m 0.925 m A B O C D P H G TBH lAD rB/A x Problem Solution Finally: MAD = lAD . ( rB/A x TBH ) MAD = 1 5 _3 _300 1 5 = [(_3)(0.5)(300)] MAD = _ 90 N.m

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