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Re: The old loop-de-loop



On 11/15/2003 05:51 PM, I suggested a method for
solving the loop-de-loop problem.

Alas I must have left my brain in my other hat.

The previous method was not at all wrong, but
here's a much nicer method.

The question was asked in terms of forces. But
it is best answered in terms of energy.

First, establish the lemma that a force of
constraint does no work (assuming the constraint
is itself stationary). Proving this should be
no great strain for anybody.

The total energy of the object is constant. So
you can figure out the KE of the object (and
hence the speed) simply as a function of height.

Knowing the shape of the track, and the speed at
which the object moves along the track, you
immediately know the velocity, and from that you
can easily and directly calculate everything else.