As physics instructors, we try to help our students
learn physics. But most of us begin to realize that our
students are not learning as much as we hope they
would. As we listen to our students, we begin to see some of
their difficulties. Some of their difficulties are expected, but
some are unexpected. One such difficulty is drawing the force
diagram, or free-body diagram (FBD). Knowing the importance of being able to draw correct FBDs, we try to help our
students by presenting the necessary steps clearly. Unfortunately, many times, what seemed clear to us isn’t as clear to
our students. So, how can we help our students draw correct
FBDs? In this paper, we present an approach we used in lectures to help our students draw FBDs correctly. We also present some encouraging preliminary results from a comparison
study of two introductory physics classes. As you will see in
the discussion of our approach, we will be highlighting a few
things, so in this paper we will refer to our approach as “the
highlight approach.”
The highlight approach
Student difficulties with drawing correct FBDs are as varied as students themselves. So it is not surprising to find that
many physics instructors already have shared various helpful
approaches, including several sets of exercises,1-5 suggestions,5-16 and warnings about FBDs.17 The highlight approach
shares many of the features discussed in these papers.But the
highlight approach also has a few features not mentioned in
these papers.
The main goal of using the highlight approach was to make
sure that our students can account for all the contact forces.
So we highlight the fact that in order for contact forces to exist, there must be a physical contact. This naturally led us to
talk about forces in terms of contact forces and noncontact
forces as we started to draw the FBDs. We will illustrate the
highlight approach by using an example: Two blocks, block A
and block B, shown in Fig. 1, are placed in contact with each
other. A hand is pushing block A with a horizontal force to the
right. We will show the steps taken to produce two separate
FBDs: one for block A and another for block B.
Step one: Sketch the figure
First, we represent the problem/situation as a simple drawing, as done in Fig. 1. But sometimes, a drawing such as Fig. 1
is already given. In that case, we go to Step Two.
Step two: Choose and isolate
Next, we choose one object for which the FBD will be
drawn. We also remind the students that we need a separate
FBD for each object. Here we will draw the FBD for block
A first. So we start a new drawing with block A in isolation.
Then, with dotted lines, we draw everything that is making
physical contact with block A, as in Fig. 2. It might be helpful to remind the students that each object should be drawn,
as in Fig. 2, rather than be represented as a point, so that the
contact points and/or surfaces can be clearly identified and
indicated.
Step three: Find and highlight
We find all the contact points and/or surfaces that block A
is making with other objects. Then, we highlight all the contact points and surfaces for block A. Figure 3 shows what this
would look like.
Step four: Identify and label
At each contact point/surface, we identify what contact
forces are being exerted on block A. For example, as we point
to the surface of contact with block B, we ask which object is
exerting a contact force on block A. Students would respond,
“block B.” If they struggle, then we ask what is touching block
A at that surface. We ask what would this contact force, exertFig. 1. A simple drawing of the problem/situation of the two
blocks, block A and block B, being pushed across a frictionless
table by a hand to the right. mA is the mass of block A and mB is
the mass of block B.
Fig. 2. Block A is drawn with solid lines. Other objects that are
making physical contact with block A are drawn with dotted
lines. The hand is pushing block A and making a physical contact
with block A. The frictionless table is making a physical contact
with block A. Block B is making a physical contact with block
A. Therefore, the hand, the table, and block B are all drawn with
dotted lines.
Helping Students Draw Correct FreeBody Diagrams
Albert Lee, California State University, Los Angeles, Los Angeles, CA
486 THE PHYSICS TEACHER ◆ Vol. 55, November 2017
contact force acts on block A. A few students might respond,
“gravitational force.” We then ask which object is exerting the
gravitation force on block A. Students would respond, “the
Earth” and “toward the Earth.” After we finish all the contact
forces, we finally draw the noncontact force that is being exerted on block A by the Earth as shown in Fig. 5. Our finished
FBD includes all the places of physical contact highlighted
and corresponding contact forces, and noncontact forces.
For block B, we repeat these steps to produce the FBD for
block B, shown in Fig. 6. Some students might be concerned
with the hand that is pushing block A. Again, we highlight
the fact that the hand does not make a physical contact with
block B, thus no place of contact is highlighted in the drawing. Therefore, a force exerted by the hand cannot appear in
the FBD for block B.
The impact of the highlight approach
We used the highlight approach during the lectures of a
college course in introductory calculus-based physics offered
at a large master’s-granting public university. This course
covered mechanics, which was the first course of a year-long
sequence of courses in introductory physics. This course
was taken mainly by students majoring in engineering and
physical sciences. To try to answer the question of whether
the highlight approach helps students, we compared student
performances on exam problems, and the preliminary results
are encouraging.
ed by block B, try to do to block A. Students would eventually
respond, “push it away, to the left.” We ask what we should
call this force. Students would respond, “the normal force.”
We draw the force vector and label explicitly which object
is exerting the force on which object. (In labeling the forces,
we followed the convention used in the textbook, where Fab
means “the force exerted by a on b.”18 To make this more explicit, we added “by” and “on” above the ab in our labels.) For
example, the contact force that block B exerts on block A at
the contact surface would be written as shown in Fig. 4 (a).
The force vector is drawn with the tail starting at the contact
surface. Then, we ask if another contact force would be exerted on block A at the contact surface. If the answer is yes,
we would then draw and label the force vector. We repeat this
process for all the contact points and surfaces. The resulting
force vectors are shown in Fig. 4 (b).
Step five: Draw the noncontact forces
Once we finish with all the highlighted surfaces and
points, we move on to noncontact forces. We ask what nonFig. 3. All the places of contact for block A are highlighted in
pink. The point of contact with the hand (finger), the surface of
contact with the table, and the surface of contact with block B
are all highlighted.
Fig. 4. (a) shows the normal force exerted by block B on block
A. The force vector is drawn with the tail starting at the contact
surface between block A and block B. (b) shows all the contact
forces exerted on block A at the point of contact with the hand
(finger), at the surface of contact with the table, and at the surface of contact with block B.
Fig. 5. This is the final FBD drawn for block A. It includes all the
places of physical contact highlighted and corresponding contact forces, and noncontact forces.
Fig. 6. This is the final FBD drawn for block B. It includes all the
places of physical contact highlighted and corresponding contact forces, and noncontact forces.
THE PHYSICS TEACHER ◆ Vol. 55, November 2017 487
4. James E. Court, “Free-body diagrams revisited – II,” Phys.
Teach. 37, 490–495 (Nov. 1999).
5. L. C. McDermott, P. S. Shaffer, and the Physics Education
Group, Tutorials in Introductory Physics, 1st ed. (Prentice Hall,
2002).
6. David P. Maloney, “Forces as interactions,” Phys. Teach. 37,
386–390 (Sept. 1990).
7. Brian Lane, “Why can’t physicists draw FBD’s?” Phys. Teach.
31, 216–217 (April 1993).
8. Louis G. Mathot, “Free-body diagrams,” Phys. Teach. 31, 390
(Oct. 1993).
9. Brian Lane, “Response to Mathot,” Phys. Teach. 31, 390 (Oct.
1993).
10. Lou Turner, “System schemas,” Phys. Teach. 41, 404–408 (Oct.
2003).
11. Mark Mattson, “Getting students to provide direction when
drawing free-body diagrams,” Phys. Teach. 42, 398–399 (Oct.
2004).
12. Paul Wendel, “Adding value to force diagrams: Representing
relative force magnitudes,” Phys. Teach. 49, 308–311 (May
2011) and references therein.
13. Ronald Newburgh, “Force diagrams: How? and why?,” Phys.
Teach. 32, 352 (Sept. 1994).
14. Willard Sperry, “Placing the forces on free-body diagrams,”
Phys. Teach. 32, 353 (Sept. 1994).
15. Avinash Puri, “The art of free-body diagrams” Phys. Educ. 31,
155–157 (May 1996).
16. Ed van den Berg and Cor van Huis, “Drawing forces,” Phys.
Teach. 36, 222–223 (April 1998).
17. Andrew F. Heckler, “Some consequences of prompting
novice physics students to construct force diagrams,” Int. J. of
Sci. Educ. 32, 14, 1829–1851 (Sept. 15, 2010).
18. The textbooks used were the 7th edition and the 8th edition of
Physics for Scientists and Engineers with Modern Physics by R.
A. Serway and J. W. Jewett, Jr. There were some additions and
deletions of end-of-chapter problems between the editions.
However, there was no significant difference between these
editions to give one class advantage over the other class.
19. David Hestenes and Malcolm Wells, “A Mechanics Baseline
Test,” Phys. Teach. 30, 159–166 (March 1992).
20. View supplementary material under the “Supplemental” tab at
TPT Online, http://dx.doi.org/10.1119/1.5008345.
21. L. C. McDermott, P. S. Shaffer, and the Physics Education
Group, Instructor’s Guide for Tutorials in Introductory Physics,
1st ed. (Prentice Hall, 2003).
Department of Physics and Astronomy, California State University,
Los Angeles, 5151 State University Drive, Los Angeles, CA 90032-
8206; albertlee.calstatela@outlook.com
Class F was taught following the steps outlined in this paper, but without the “highlight” portion of Step Three. Class
G was taught with the highlight approach. Both classes were
taught by the same instructor, who covered the same topics.
Both classes used the textbook18 by Serway and Jewett. The
majority of assigned end-of-chapter homework problems
were common to both classes. A t-test on the pre-test scores
on the Mechanics Baseline Test19 (MBT) for these two classes
indicates that they were statistically similar (p-value = 0.096),
with the average pre-test score of about 25% for 71 students in
Class F and 27% for 110 students in Class G, as shown in the
two figures available online (Figs. 8 and 9).20
Both classes had midterm exam problems that asked them
to draw three FBDs. The problem used is very similar to the
Sample Examination Question 7a21 for Tutorials in Introductory Physics.5 Students were asked to draw three separate
FBDs, for blocks A, B, and C shown in Fig. 7.
For this study, we regraded each of the three FBDs as
either “completely correct” (1 point) or “not completely correct” (0 point). (However, partial credits were given to students for their FBDs on their exams.) For example, extra force
vectors, wrong vector directions, missing force vectors, missing labels, or wrong labels would make the FBD be “not completely correct” (0 point) for this study. Different but valid
label formats were all regarded as correct. For example, labels
in Figs. 4, 5, and 6, as well as NbyBonA, NBonA, NBA, etc. were all
counted as correct. A total score of three points indicates that
the student drew all three FBDs correctly. The result is summarized in an online table (Table II).20
Chi-square test was used to determine if this was statistically significant. Each class was subdivided into two categories, as shown in Table I: “All Correct” if the total score was
3 and “Not All Correct” if the total score was 0, 1, or 2. Only
about 10% of the students in Class F were able to draw all
three FBDs correctly. For Class G, which used the highlight
approach, about 22% of the students were able to draw all
three FBDs correctly. This was statistically significant with a
p-value of 0.037.
We hope that the highlight approach outlined in this paper
can play a positive role at making improvements here and
where you work possible.
References
1. James E. Court, “Free-body diagrams,” Phys. Teach. 31, 104–
108 (Feb. 1993).
2. James E. Court, “Free-body diagrams revisited – I,” Phys. Teach.
37, 427–433 (Oct. 1999).
3. Kurt Fisher, “Exercises in drawing and utilizing free-body dia