PURPOSE: To illustrate linear kinematics in a possibly counterintuitive way.
DESCRIPTION: When the two balls are launched from one end of the track with the same velocities, what will happen: (a) the ball on the straight track arrives at the other end first, (b) the ball on the track with the dip arrives at the other end first, or (c) the race is a tie - both balls reach the other end at the same time? Click your mouse on the photograph above to see an mpeg video of the action. To view the center segment of the race in slow motion click here.
SUGGESTIONS: Ask the class to vote before doing the experiment.
Note that the only conditions required for this result are that the tracks be frictionless and the slope no greater than that of a rolling brachistochrone, which translated to English means:
(1) no friction (very nearly the case),
(2) the slope of the track cannot be so great that the ball leaves contact with the track, and
(3) the track cannot have any loop-the-loops.
See Question of the Week #2 for information on using this demonstration to enhance class involvement.
A very interesting set of JAVA applets examining aspects of this demonstration has been developed by Tom Thaden-Koch, Bill Leonard, Bill Gerace, Bob Dufresne, Jose Mestre at the University of Minnesota, and is described in the Ph. D, thesis of Tom Thaden-Koch. The motion of the ball on the dipped track has been "adjusted" so that it arrives earlier, later, and at the same time as the ball on the flat track. These applets are on line at a web site they call Two-tracks animations.
Here are the three short videos showing these three situations:
REFERENCES: Available.1D15.20) See the Demonstration Reference File for several very interesting papers on this apparatus and variants thereof. Click for a Racing Balls applet, one in the NTNU Virtual Physics Laboratory series produced by Prof. Fu-Kwun Hwang of the National Taiwan Normal University.
Click here for a mechanical drawing of the apparatus.
EQUIPMENT: Track assembly with two-ball launcher and two pool balls, as photographed.
SETUP TIME: 10 min.