Brachistochrones

 

Code Number: 1D15.50

Demo Title: Brachistochrone

Condition: Excellent

Principle: Path Lengths and Velocities

Area of Study: Mechanics

Equipment: 

Brachistochrones.

Procedure:

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.  The standard demonstration has a straight track, a circular track, and a cycloid track.  Using the carbon paper will enable you to show that the balls have the same energy when they leave the track.

References:

  • Yiqi Fang, Xianle Zeng, Rongyu Fan, Zhu'an Chen, Marcelo F. Ciappina, "A Minimization Problem Based on Straight Lines", TPT, Vol. 62, #5, May 2024, p. 387.
  • John A. Milsom, "The Brachistochrone: An Excellent Problem for All Levels of Physics Students", TPT, Vol. 59, #8, Nov. 2021, p. 606.
  • 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.
  • The Queen Catalogues, Catalogue of Physical Instruments, Chapter III, p. 15.

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

1D15.50 - Brachistochrone