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8/20/2019 5. Forces System - Couple
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COUPLE
By Rani Rumita
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• Is the moment produced by twoequal, opposite and noncollinearforces
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• Consider the action of two equal andopposite forces F and –F a distance d apart
• These two forces cannot be combined into
a single force because their sum in everydirection is ero! Their only e"ect is toproduce a tendency of rotation
• The combined moment of the two forcesabout an a#is normal to their plane andpassing through any point such as $ intheir plane is the couple %
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• This couple has a magnitude
% & F!'a(d) – F!aor
% & F!d
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• The magnitude of the couple isindependent of the distance a whichlocates the forces with respect to the
moment center $
• The moment of a couple has thesame value for all moment centers
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*ector +lgebra %ethod
% & 'r+ # F) ( 'rB # 'F))
& 'r+ – rB)!F
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• The moment e#pressioncontains no reference to themoment center $ and,
therefore, is the same for allmoment centers
• -e may represent % by a freevector
• The direction of % is normal tothe plane of the couple andthe sense of % is establishedby the righthand rule
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.quivalent Couples
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ForceCouple /ystems
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