Question Video: Finding the Magnitude of a Couple of Two Inclined Forces Acting on Two Ends of a Line Mathematics

In the figure below, 𝐹₁ = 3 N and 𝐹₁ and 𝐹₂ form a couple. Find the algebraic measure of the moment of that couple.

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Video Transcript

In the figure below, 𝐹 sub one is equal to three newtons and 𝐹 sub one and 𝐹 sub two form a couple. Find the algebraic measure of the moment of that couple.

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. If we define 𝐹 sub one and 𝐹 sub two to be their respective magnitudes, then we can say that 𝐹 sub one equals 𝐹 sub two, which equals three newtons. 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œƒ and 𝑑, where 𝑑 is the distance between the line of action of each force. And πœƒ is the angle that each force makes with the line connecting the points that force one and force two act from.

We see from our diagram that πœƒ here is equal to 45 degrees. And 𝑑, the distance between points 𝐴 and 𝐡 here, which are the points where 𝐹 one and 𝐹 two act, is equal to seven root two centimeters. And so the magnitude of the moment of this couple is three times sin 45 degrees times seven root two. Now, of course, sin of 45 degrees is an exact value that we should know by heart. It’s root two over two. But of course, the square root of two divided by two times the square root of two is two over two or simply one. And so the magnitude of the moment of the couple is three times seven, which is 21 or 21 newton centimeters. 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. So the answer is 21 newton centimeters.

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