1D15.50 - Brachistochrone

Code Number:
1D15.50
Demo Title:
Brachistochrone
Condition:
Excellent
Principle:
Path Lengths and Velocities
Area of Study:
Mechanics
Equipment:
Brachistochrones.
Procedure:

Video and Editing Credit: Jonathan M. Sullivan-Wood.

The balls will start and end at the same height.  The route is different and hence the time that the ball takes will be different also.  Using the carbon paper will enable you to show that the balls have the same energy when they leave the track.

References:
  • Leonid Minkin and Percy Whiting, "Restricted Brachistochrone", TPT, Vol. 57, #6, Sept. 2019, p. 359.
  • D. Figueroa, G. Gutierrez, and C. Fehr, "Demonstrating the Brachistochrone and Tautochrone", TPT, Vol. 35, #8, Nov. 1997, p. 494.
  • Alan Cromer, "An Unusual Rolling-Sphere Phenomenon", TPT, Vol. 34, #1, Jan. 1996, p. 48.
  • Dale T. Hoffman, "A Cycloid Race", TPT, Vol. 29, #6, Sept. 1991, p. 395.
  • Kevin J. Tillotson, "Who Will Win the Race, II?", TPT, Vol. 28, #8, Nov. 1990, p. 537.
  • Julius Sumner Miller, "Further to the Brachistochrone", TPT, Vol. 24, #5, May 1986, p. 262.
  • R. D. Edge, "The Brachistochrone - Or, The Longer Way Round May be the Quickest Way Home", TPT, Vol. 23, #6, Sept. 1985, p. 372.
  • Thomas B. Greenslade Jr., "Brachistrochrone Demonstration", AJP, Vol. 81, #1, Jan. 2013, p. 19.
  • Thomas B. Greenslade Jr., "Time of Descent Apparatus (Photo)", AJP, Vol. 72, #12, Dec. 2004, p. 1500.
  • S. E. Joens, T. M. Antatnackovic, and M. Dehn, "Remarks on the Brachistochrone with Viscous Friction", AJP, Vol. 56, #8, Aug. 1988, p. 758. 
  • H. A. Yamani and A. A. Mulhem, "A Cylindrical Variation on the Brachistochrone Problem", AJP, Vol. 56, #5, May 1988, p. 467.
  • David G. Stork and Ju-xing Yang, "The General Unrestrained Brachistochrone", AJP, Vol. 56, #1, Jan. 1988, p. 22.
  • David Stork, "Problem: The Unrestrained Tachistos", AJP, Vol. 55, #4, Apr. 1987, p. 296, 376.
  • Ju-xing Yang, David G. Stork, and David Galloway, "The Rolling Unrestrained Brachistochrone", AJP, Vol. 55, #9, Sept. 1987, p. 844.
  • David G. Stork, Ju-Xing Yang, and Chris Stover, "The Unrestrsained Brachistochrone", AJP, Vol. 54, #11, Nov. 1986, p. 992.
  • Daniel T. Giellespie, "Simple Harmonic Motion of a Round Body Rolling on a Concave Curve", AJP, Vol. 52, #2, Feb. 1984, p. 180.
  • P. K. Aravind, "Simplified Approach to Brachistochrone Problems", AJP, Vol. 49, #9, Sep. 1981, p. 884.
  • N. Ashby, W. E. Brittin, W. F. Love, and W. Wyss, "Brachistochrone With Coulomb Friction", AJP, Vol. 43, #10, Oct. 1975, p. 902.
  • Brian Holton, "Go Big or Go Home", PIRA Newsletter, Vol. 11, #1, Oct. 1996, p. 5.
  • Wallace A. Hilton, "M-14a. Conservation of Energy", Physics Demonstration Experiments, p. 31.
  • George M. Hopkins, "Falling Bodies - Inclined Plane - The Pendulum", Experimental Science, p. 38 - 43.
  • R. D. Edge, "Experiment 1.53", String & Sticky Tape Experiments.


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