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Getting the Feel for Vector Addition of Forces
Christopher Bracikowski, P. Joseph Garcia, and David J. Harper, Physics Department, Bloomsburg
University, Bloomsburg, PA 17815; brac@planetx.bloomu.edu
O
ne of our goals when
constant forces in constant directions
The student selects two of the three
teaching physics to eduof their own choosing. The forces
force vectors and, using a protractor,
cation majors is to proneed not have the same magnitude. It
adds them using the parallelogram
vide them with laboratory experitakes a little practice to hold the
method of vector addition. Reences that require relatively simple
forces and directions constant. With a
member, the resultant vector is along
equipment and involve the students
pencil, the fourth student makes a
the diagonal of the parallelogram. The
actively in the experiment. We hope
mark on the paper at the point exactstudent measures the length of the
that through these experiences the
ly under the knot (see Fig. 1) and also
resultant force vector and determines
students will not only learn physics,
makes one mark under each string at
the magnitude of the corresponding
but also how to teach it. We describe
points well spaced from the knot. The
force using the scale defined earlier.
here just such an experiAfter comparing the resulment in which students
tant force vector obtained
actively participate in the
graphically with the third
vector addition of forces.
force vector used in the
In this experiment, stuexperiment, the student will
dents create a situation in
conclude that they have
which three forces act on a
(approximately) the same
point in equilibrium. That
magnitude and are (approxis, three forces act on the
imately) 180o apart.
point, however, the net
The use of 20-N spring
force (the vector sum of
scales is not crucial to the
these three forces) is zero
physics of this experiment.
such that the point remains
However, our experience is
at rest. Therefore, the rethat if smaller spring scales
sultant of any two of these
are used, students pull so
force vectors must be
hard as to wrap the indicaequal in magnitude and Fig. 1. Experimental arrangement that allows students to feel vector addition of tor on the scale once or
forces.
opposite in direction to the
more around the scale. This
third force vector.
causes them to record
This experiment is very similar to
fourth student also records the magincorrect values for their pulling
ones described in references 1 and 2
nitudes of the pulling forces as indiforces. Therefore, we recommend 20(and many others). However, in those
cated by the spring scales. The proceN spring scales.
experiments the spring scales are
dure is repeated, using different
References
connected to the lab table and are not
pieces of paper and different forces in
1. C. E. Dull, H. C. Metcalfe, and
held in place by the students. By a
different directions until each student
J. E. Williams, Laboratory Exsimple modification, we can cause
has a unique set of data.
periments in Physics (Henry
the student to go from being a passive
On his or her own sheet of paper,
Holt and Company, Inc.),
observer to an active participant.
each student carefully draws in with a
1960), p. 19.
Students work in teams of four.
ruler the three lines along which the
2. N. H. Black, Laboratory ExFirst, they tie strings together and
forces act through their respective
periments in Elementary
arrange the three 20-N spring scales3
marks on the paper. Using a convePhysics, rev. ed. (Macmillan,
as shown in Fig. 1. Three students
nient scale, the student draws the
New York, 1950), p. 79.
hold the assembly horizontally over a
force vectors along these lines, and
3. Dial Spring Balance, 20 x 0.25
large piece of 24- by 36-in newsprint
using a protractor, measures the
N, (FO2128), available from
Frey Scientific, Mansfield, OH;
and pull on the spring scales with
angles between the force vectors.
800-225-FREY.
114
THE PHYSICS TEACHER
Vol. 36, Feb. 1998
Getting the Feel for Vector Addition of Forces