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Carl Mungan, United States Naval Academy
There are five platonic solids. If we draw a straight line passing through any vertex of such a solid and the geometric center of the solid, that line will intersect another vertex of the solid in 4 out of these 5 solids. Which is the exception and what does that have to do with the challenge question related to the cover picture of the February 2015 issue of The Physics Teacher? Also be sure to check out the incredible photograph of a balanced tower of rocks on the back page of the March issue!
An article on page 110 of the February 2015 issue of the American Journal of Physics considers a remarkable variation on Newton’s cradle. Suppose a traditional cradle has 3 equal-mass balls. If ball 1 is pulled aside and released, ball 3 will come off the end of the chain with the incident velocity of ball 1. That happens because ball 1 makes 1 elastic collision with ball 2 transferring all its momentum to it, and likewise ball 2 makes 1 collision with ball 3. One can instead reduce the mass of ball 2 to √5 – 2 = 23.6% of balls 1 and 3. The cradle will now function as before. This time it happens because ball 1 makes two elastic collisions with ball 2, to end up at rest, and likewise ball 2 makes two collisions with ball 3. The paper similarly finds the “magic mass ratio” of 11.0% for Newton’s cradle to operate where ball 2 makes three elastic collisions with each of balls 1 and 3. A general formula is found for any integer number of collisions with each end ball. See a quicktime movie linked to Fig. 6 of the paper. Next, Bertrand’s theorem states that only forces that vary linearly or with the inverse square of the distance from a point can yield closed orbits. Proofs of this theorem are generally not simple. However, an elementary derivation is provided on page 320 of the April issue. Incidentally, the book review of “A Student’s Guide to Entropy” on page 383 of the same issue motivated me to buy that well-written text. Finally, Craig Bohren’s article on page 443 of the May issue makes it clear that the difference in thermal conductivities is not the only reason that aluminum feels colder to the touch than does paper in the Veritasium video.
Page 329 of the May 2015 issue of Physics Education has a detailed study of the sliding motion of a ladder leaning against a wall, where friction with both the floor and wall is considered. Video analysis is used to compare the theory with experiment, including the loss of contact between the ladder and wall at a sufficiently small angle of inclination. Also be sure to read about David Featonby’s surprising experiment showing the difference in behavior of a spinning top on an inclined plane coated with sandpaper depending on whether the base of the top is rounded or pointed on page 391 of the same issue. Turning to the European Journal of Physics, article 028001 in the March 2015 issue calculates the length of a heavy cable spanning two fixed points that minimizes the tension at the highest end. Article 035027 in the May issue uses high-speed cameras to investigate the flickering of incandescent and fluorescent lamps. Both journals are accessible at http://iopscience.iop.org/journals.
Page 643 of the April 2015 issue of the Journal of Chemical Education at asks what produces the thick white fog seen when dry ice is dropped into water? The answer is not condensation of atmospheric water vapor onto the cold CO2 gas subliming away.
Article 010101 in Physical Review Special Topics — Physics Education Research compares student performance in adding and subtracting vectors graphically versus algebraically. The authors conclude that optimal learning occurs if students are introduced to both methods concurrently and that it is important for students to practice the graphical approach for arrows drawn in a variety of different orientations.