Re: [Phys-l] Action

[Carl Mungan <mungan@usna.edu>]

> For a simple high school level Action problem, see page 76, problem 15 at:
> <http://www.sci-ed-ga.org/modules/driving/parts/StayingAlive.pdf>
>
> Larry Woolf

I looked at this problem with interest.

But somehow I feel it's incomplete or at least unsatisfying in its 
present form. Surely a particle can take *any* of the four paths. For 
example, to take path B, start the particle moving at 10 m/s and 
provide a bumper that it runs into at the 1 m mark. I don't see 
anything wrong with that!

At minimum you've underspecified the constraints on the possible 
motions of the particle. If bumpers aren't allowed, what in the 
problem specifies that? If the particle can only start at certain 
speeds (apparently 1 m/s), what requires that? I think the problem 
needs to say that no external forces act on the particle between the 
instant after it starts until (hmm until what in fact? 10 seconds 
elapse? it reaches the 10 m mark? are we or are we not allowed to 
stop the particle when it reaches the 10 m mark?).

I understand the spirit of the problem. But how do we fix it up? 
Maybe we can't. With only KE involved, it seems to me path A may be 
the *only* allowed path once the problem is properly qualified, even 
without considering action at all.

Sorry to rain on a nice attempt to construct a high-school-level problem, Carl
--
Carl E Mungan, Assoc Prof of Physics  410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu     http://usna.edu/Users/physics/mungan/