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In the figure below, πΉ sub one is equal to three newtons and πΉ sub one and πΉ sub two form a couple.
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Find the algebraic measure of the moment of that couple.
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In order to find the algebraic measure of the moment of the couple, we begin by recalling that if the forces form a couple, then their magnitudes must be equal.
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If we define πΉ sub one and πΉ sub two to be their respective magnitudes, then we can say that πΉ sub one equals πΉ sub two, which equals three newtons.
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Then, to find the magnitude of the moment of the couple, we find the product of the magnitude of one of the forces times sin π and π, where π is the distance between the line of action of each force.
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And π is the angle that each force makes with the line connecting the points that force one and force two act from.
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We see from our diagram that π here is equal to 45 degrees.
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And π, the distance between points π΄ and π΅ here, which are the points where πΉ one and πΉ two act, is equal to seven root two centimeters.
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And so the magnitude of the moment of this couple is three times sin 45 degrees times seven root two.
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Now, of course, sin of 45 degrees is an exact value that we should know by heart.
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Itβs root two over two.
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But of course, the square root of two divided by two times the square root of two is two over two or simply one.
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And so the magnitude of the moment of the couple is three times seven, which is 21 or 21 newton centimeters.
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Since the forces are trying to move the body in a counterclockwise direction, we know that the algebraic measure of the moment is going to be positive.
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So the answer is 21 newton centimeters.