During the session on “Introductory College Physics Textbooks” at the 2007 Summer Meeting of the AAPT, there was a brief discussion about whether introductory physics should begin with one-dimensional motion or two-dimensional motion. Here we present the case that by starting with two-dimensional motion, we are able to introduce a considerable amount of physics even before discussing the constant acceleration formulas or Newton's laws.
REFERENCES
1.
We used this graphical approach in both Huggins, Physics 1, (W.A. Benjamin Inc., New York, 1968), and Physics2000 at http://www.physics2000.com.
2.
One of the convenient features of this graphical approach is that for motion with constant acceleration, and for uniform circular motion, the acceleration vector you calculate is independent of the time step Δt that you use. That is why we could use a long time step for Glenn's orbit and get an accurate result.
3.
This strobe photograph was taken with archaic but effective equipment: a strobe, Tri-X film, and a darkroom enlarger. With NTSC video, we could not measure the air resistance acceleration with sufficient accuracy. Perhaps HDTV will be adequate. For tracking motion, various systems are available, including Alberti's Window, Videopoint, and Innovision System's MaxTRAQ. Laboratory exercises using these systems can be found at http://www.albertiswindow.com/cirriculum.htm;http://www2.vernier.com/manuals/video_and_logger_pro.pdf. http://www.pasco.com/products/software/videopoint http://www.innovision-systems.com/products-MaxTRAQ.aspx The labs discussed, focus on having the computer break 2d motion into its 1d components for analysis. This obscures the vector nature of the object's acceleration.
4.
A search under “air resistance” in The Physics Teacher Online brings up 15 articles, most of which deal with air resistance acting on falling balls, including Styrofoam ones. In all cases, the emphasis is on the formula for the magnitude of the air resistance. We found no studies of the changing direction of the air resistance force vector. Perhaps the most comprehensive analysis of the air resistance force will be found in the paper by
Margaret Stautberg
Greenwood
, Charles
Hanna
, and Rev. John W.
Milton
, “Air resistance acting on a sphere: Numerical analysis, strobe photographs, and videotapes
,” Phys. Teach.
24
, 153
(March 1986
).5.
Jeffrey
Prentis
, Bryan
Fulton
, and Carol
Hesse
“Elliptical orbit ⇒ 1/R2 force
,” Phys. Teach.
45
, 20
–25
(Jan. 2007
). In this cover article, the authors describe another approach to graphical analysis, with interesting reference to Newton's work.
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© 2009 American Association of Physics Teachers.
2009
American Association of Physics Teachers
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