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On which trajectory the movement will be the fastest? (Brachistochrone curve)
The briefest amount of time
to get from one point to another
is not necessarily the straight line path
connecting those two points.
To be sure,
we cut up
on the top of an electrical wire moulding,
two pieces,
of which one is longer than the other.
For instance,
95 cm and 100 cm
We join the two end of the electrical wire moulding
by gluing or screwing those
on two small pieces of wood
or plastic.
Naturally,
the largest electrical wire moulding must be curved
to make this operation a success.
The two pieces constitute slide rail
in which we can roll the marbles over
starting at the same point
and reaching the same end point,
following two paths
unequal in length.
The slow motion prove
that contrary to what we thought,
the marble place on the curved slide rail
is the first to get at the end point
having, however,
traveled a greater distance
than the other on the straight line trajectory.
This result,
is all the more suprising
as it is easy to demonstrate,
using the conservation of the kinetic energy,
that the two marbles reach the end point
at the same speed.
So what happened?
The observation of the slow motion
at the beginning of the experience,
gives us the answer.
The marble rolling over the curved slide rail
increases its speed quicker
than the other on the straight line trajectory
and then takes the lead.
At the end of the movement,
the speed is barely increasing
but lead taken by the marble is sufficient
to be the first at the end point.
Production: University of Lille 1 - Sciences and Technologies
SEEM Multimedia Service - University of Lille 1
The Online Thematic University for Sciences
Teachers/ Researcher: Jean-Marie Blondeau, Bernard Bonnel
Project coordinator (shooting and editing): Bernard Mikolajczyk
Technician: Gerard Destrun
Voice over: Alain Nempont
Contact: semm@univ-lille1.fr