Question Video: Determining the Arm of the Couple Equivalent to a System of Two Forces Mathematics

If the norm of the moment of a couple is 750 N⋅m and the magnitude of one of its two forces is 50 N, determine the length of the moment arm.

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Video Transcript

If the norm of the moment of a couple is 750 newton meters and the magnitude of one of its two forces is 50 newtons, determine the length of the moment arm.

It’s worth recalling what we mean by the norm of the moment. The norm of the moment is simply the magnitude of that moment. And so we’re given information about the norm of the moment and the magnitude of one of its two forces. And so we can link these by using the formula that determines the magnitude of the moment of a couple. It’s the product of the magnitude of either of the forces in the couple and 𝑙, the length of the moment arm. In this case, we’re told that the norm of the moment or its magnitude is 750 newton meters. And the magnitude of one of its two forces is 50 newtons. We can therefore substitute everything we know about the moment of this couple into the formula, and we get 750 equals 50 times 𝑙.

To solve for 𝑙, we divide both sides of this equation by 50. So 𝑙 is 750 divided by 50, or 15. And since we’re dividing newton meters by meters, the units for our length are simply meters. And so the length of the moment arm in this case is 15 meters.

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