Video Transcript
๐ด๐ต๐ถ๐ท is a square with sides of
length 28 centimeters. Two forces of magnitude 117 newtons
act along ๐ด๐ต and ๐ถ๐ท. And two other forces of magnitude
177 newtons act along ๐ด๐ท and ๐ถ๐ต, as shown in the figure. Find the algebraic measure of the
moment of the resultant couple.
Given the four forces that are
acting, one on each side of this square, we want to solve for the moment of the
resultant couple. Weโll call that moment capital
๐. To start solving for the moment ๐,
weโll consider these pairs of forces as pointing to the corners of our square, ๐ต
and ๐ท. Regardless of which of these two
corners we look at, we see thereโs an opposition of forces going on. In each case, thereโs a force of
177 newtons that tends to make our entire square rotate clockwise. And there are opposing forces of
117 newtons which tend to make the square rotate counterclockwise.
If the opposing forces were equal
in magnitude, we would experience no net moment for this object. But because they are not equal, we
do have a net moment ๐. At both corners, ๐ต and ๐ท, the net
force resulting from the opposition of the forces pointing into that corner is equal
to 177 newtons minus 117 newtons, or 60 newtons. We could redraw our diagram to
reflect this net force reality, where now weโve eliminated the 117 newton forces
acting counterclockwise and only show the remaining net forces that act
clockwise.
To solve for the moment ๐, we want
to take our net force and multiply it by a distance ๐, where ๐ is the
perpendicular distance between the lines of action of our net or resultant
forces. In our exercise setup, weโre told
that the length of the sides of the square is 28 centimeters. Thatโs ๐. So weโre now ready to plug in for
๐น net and ๐ and solve for ๐. There is one last factor to
include. And thatโs the fact that weโre told
in our diagram that counterclockwise rotation of our shape is considered rotation in
the positive direction. Our net forces, however, tend to
rotation in the clockwise direction. That means weโll experience
rotation in the negative direction. So weโll include a minus sign in
our calculation of ๐.
When we multiply these two numbers
together, we find that ๐ is negative 1680 newton centimeters. Thatโs the moment of this force
couple.
