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This applet simulates a force table, a device used to introduce
students to the concept of vectors and vector addition. Vector's are
quantities that have magnitude and direction. With the force table
the physical manifestation of the vectors' magnitudes are the
tensions created by counter weights attched to strings (as seen in
the diagram at right). The directions of the vectors are set by
aligning the pulleys to specified marks on the perimeter of the
force table. The sum of the vectors
corresponds to the net effect of the strings tied to a ring that
loosely fits about a post at the center of the force table. In a
typical student exercise, the students are given a set of vectors to
add. The mass of each counter weight is set to the magnitude of the
corresponding vector or some multiple thereof, as long the same
multiple is used for all vectors. That constant multiple serves as a
scale factor. One additional pulley and counterweight is added,
whose direction and mass are adjusted to exactly balance the
tesnsions of the original vectors. Once balanced (by centering the
ring about the post), the additional tension corresponds to the equilibrant
of the original set of vectors. The equilibrant
is the opposite (or the negative of) the sum
of the vectors, having the same magnitude as the sum
but the opposite (off by 180 degrees) direction. The vector
components of the equilibrant will be
the negative of the corresponding components of the sum.
With this applet you can add 1 to 5 vectors together, optionally
displaying the sum and/or the equilibrant.
You can adjust the vectors individually by dragging the arrow tips
in the lower left window, or you can edit the table items
corresponding to the vector components as well as the vector
magnitudes and directions.
Consider the following:
What conditions are necessary for two vectors to add to zero? How
about 3 or more vectors?
Does it matter what order vectors are added together when
determining their sum?
Under what conditions will the magnitude of the vector sum of
three vectors be equal to the sum of the magnitudes of the
vectors? That is, if R = A + B + C,
when will R = A + B + C?
Input 3 arbitrary vectors. Now add a fourth so and adjust that
fourth vector so that vector sum of all four vectors is as close
to zero as you can get. How does this fourth vector compare the
the equilabrant of just the first three vectors? How does it
compare to the sum of the first three vectors?
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