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Using a Ternary Diagram to Display a System's Evolving Energy Distribution
2.The value of 0.89 is found in K. C. Maynes, M. G. Compton, and Blaine Baker, “Coefficient of restitution measurement for sports balls: An investigative approach,” Phys. Teach. 43, 352–354 (Sept. 2005).http://dx.doi.org/10.1119/1.2033520
2.A nice approach to measuring elastic energy can be found in Eric Gettrust, “The energetics of bouncing (revisited): A quantitative demonstration of energy conservation during bouncing,” Phys. Teach. 44, 428–429 (Oct. 2006).http://dx.doi.org/10.1119/1.2353581
3.Ruth Chabay and Bruce Sherwood, “Computational physics in the introductory calculus-based course,” Am. J. Phys. 76, 307–313 (April 2008).http://dx.doi.org/10.1119/1.2835054
4.Mark Nagurka, “Aerodynamic effects in a dropped Ping-Pong ball experiment,” Int. J. Eng. Educ. 19 (4), 623–630 (2003).
5.Abigail R. Daane, Lindsay Wells, and Rachel E. Scherr, “Energy Theater,” Phys. Teach. 52, 291–294 (May 2014) andhttp://dx.doi.org/10.1119/1.4872412
5.Leslie J. Atkins et al., “Animating energy: Stop-motion animation and energy tracking representations,” Phys. Teach. 52, 152–156 (March 2014). There are also PhET simulations relevant to the roller coaster and LRC circuit.http://dx.doi.org/10.1119/1.4865517
6.We attempted to use data from a real roller coaster, acquired with a Vernier WDSS system during Six Flags Physics Day. However, the altimeter measurements have relatively low precision, a somewhat slow response rate, and hysteresis, as described in the WDSS spec sheet, which is available from the Vernier website. Cellphone data seem to have some of the same issues—see R. Vieyra and C. Vieyra, “Analyzing forces on amusement park rides with mobile devices,” Phys. Teach. 52, 149–151 (March 2014).http://dx.doi.org/10.1119/1.4865516
6.Although the simulated coaster's track shape differs from the real roller coaster analyzed in Alberghi et al., “Is it more thrilling to ride at the front or the back of a roller coaster?” Phys. Teach. 45, 536–541 (Dec. 2007), our primary motivation here is not to attempt to develop the most accurate model coaster, but rather to demonstrate energy transformations on ternary diagrams.http://dx.doi.org/10.1119/1.2809145
7.Air resistance generally is described as being proportional to velocity at low velocities and proportional to velocity squared at higher velocities—e.g., see J. Varriano, “Energy diagrams with drag forces,” Phys. Teach. 34, 546–548 (Dec. 1996).http://dx.doi.org/10.1119/1.2344563
8.Ternary diagrams could nicely complement the energy flow diagrams described by A. Hobson, “Energy flow diagrams for teaching physics concepts,” Phys. Teach. 42, 113–117 (Feb. 2004), which also can be used as power diagrams.http://dx.doi.org/10.1119/1.1646488
9.This approach is analogous to the “half-step integration method” described by Norris W. Preyer, “The coupled harmonic oscillator: Not just for seniors anymore,” Phys. Teach. 34, 52–55 (Jan. 1996).http://dx.doi.org/10.1119/1.2344340