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.