Re: L2-"Negotiating" a curve.

[Hugh Haskell <haskell@ODIE.NCSSM.EDU>]

> At the risk of this list petitioning to have my physics teaching
> license removed
> I'll continue.
>
> Hugh Haskell wrote:
>
> >
> > This statement is exactly why it is dangerous to allow beginning
> > students to think in terms of "centripetal force" rather than
> > centripetal acceleration. NSL is a statement of cause and effect.
>
> snip...  I don't know what "NSL" means, and I'm not sure what you
> mean about the
> "cause and effect".

NSL = Newton's Second Law

> > The
> > left hand side, the "net force," is the cause part, and the right
> > hand side, the "ma," is the effect part.
>
> snip...  This is something I've seen here before (and only here) - what is the
> left side/right side stuff?  If you're talking about the equation you're using
> algebra that I've never been taught.  My understanding is that acceleration is
> caused by force (a=F/m or F/m=a if you prefer) not that acceleration causes a
> force.

Your understanding is correct, and that is what my statement said.
That is the "cause and effect" relation of Newton's Second Law. Since
it is normally written F = ma, I take the left hand side to be the
"cause" side, and the right hand side to be the "effect" side. But
this idea gives Newton's second standing as more than just another
equation. It is truly a statement about the real world as we know it.
It is important that students not get the idea that this is just
another equation to memorize, so I insist that in solving this type
of problem the left side of the equation be reserved for all of the
actual forces acting on the object in question, and that only "ma" in
whatever form is appropriate go on the right side. That keeps them
thinking in terms of real forces. Then when they get all the forces
written, they combine them into the "net force" and then and only
then can they do the manipulation of the resulting equation needed to
solve for whatever is not known.

> > In the case of circular
> > motion, that part of the acceleration that is directed centripetally,
> > is entirely due to forces being applied by outside agents--strings,
> > gravity, wing lift, magnetic fields, etc., etc. There is no single
> > force that can properly be named "the centripetal force," since that
> > is the resultant of all the other forces. There is no "centripet"
> > that exerts a centripetal force. Such a force should never appear on
> > a free-body diagram, since it is (at least part of) the net force
> > which causes the right hand side of NSL to be what it is. Allowing
> > students to think about a centripetal force can get them in all sorts
> > of problem-solving trouble
>
> snip...  so we should allow them to continue to think about
> centrifugal forces?  I
> would be willing to bet (and I don't even go to the casinos) my next
> paycheck that
> if you asked all of the high school seniors at my school to sketch a
> diagram of an
> object going around a curve and then to put an arrow on that object
> for each of
> the forces the vast majority would have NO force going to the center
> of the curve.

Not at all. We do not even allow our first-year students to use the
word "centrifugal" and when they try to put an outward force on an
orbiting object they are immediately asked how that force can make
the object go in a circle. They are required to show all the actual
forces and then distill them to a net force, which, in the case of
uniform circular motion is, of course, radially inward.

> > , because they try to include it with all
> > the other forces and then cannot understand why they get crazy
> > results. I have seen experienced HS physics teachers get in trouble
> > with this.
> >
>
> snip...This is one HS physics teacher that plans to continue unless
> I see a better
> way.
>
>
> >
> > We all know that if we are willing to use an accelerated reference
> > frame (rotating),
>
> snip...  I have enough problems teaching about constant velocity
> reference frames
> in high school, I'm not about to start with noninertial frames.

As I said, this aspect is limited to advanced students only, not ever
first-year students. We do everything but wash their mouth out with
soap if they so much as use the term "centrifugal."

> > then there appears a centrifugal force that can
> > properly be incorporated in the force diagram, and advanced problem
> > solvers use this technique to simplify the solution of certain types
> > of problems all the time. But for beginning students they should be
> > strictly limited to talking about centripetal acceleration, and the
> > forces that give rise to that acceleration, none of which is properly
> > called a centripetal force.
>
> snip... you acknowledge the centripetal acceleration.  Where does centripetal
> acceleration come from?  Centrifugal force?  Gravitational
> acceleration comes from
> gravitational force, net acceleration comes from net force, if there is a
> centripetal acceleration = v^2/r then what do you call mv^2/r other than
> centripetal force?

What I call mv^2/r is the net force in uniform circular motion. Or
"mass times centripetal acceleration."

> > In this sense, I think that Hewitt did
> > indeed "blow it" on his example.
> >
> > >In other words, just like mg causes a horizontal force on an
> inclined plane
> > >(=mgsin(angle) for the force *along the plane*, part of this is
> > >horizontal {too
> > >many angles and forces to describe without sketches}) it will also cause a
> > >horizontal force in the circular motion.  Remember centripetal
> force in this
> > >case *IS* the net force.  The net force causes uniform circular
> motion and is
> > >directed to the center of the circle (if we are using the
> "standard" earth as
> > >the frame of reference).
> >
> > As noted above, the comparison between mg and the net force making an
> > object go in a circle is not valid. Gravity has a readily
> > identifiable origin that is outside of the context of the system
> > under investigation. Centripetal force does not, and always ends up
> > being the resultant of other forces.
> >
> > In the case of a ball being twirled in a vertically oriented circle,
> > mg provides part of the force that makes it go in a circle, part of
> > the time, but is trying to make it do other things during the rest of
> > the circle. But if one looks at the (vector) sum of mg and the
> > tension in the string, and equates that sum to the "ma" on the right
> > hand side, then there will be a component of "a" that will have the
> > form "v^2/r", and can be called the centripetal acceleration. Its
> > magnitude will vary depending on the point the ball is in its circle,
> > being a maximum and the bottom and a minimum at the top. If you add
> > to these two forces a centripetal force, then try to get a sensible
> > answer. It can't be done.
>
> Why would you add these two forces?  Centripetal force IS the net force (in
> uniform circular motion), the sum of all forces.  The centripetal
> force would be
> the sum of the tension on the string and the gravitational force.
> The centripetal
> force is the same at the bottom and at the top, it is the tension on
> the string
> that is the maximum at the bottom and minimum at the top.
>
>
> >
> >
> > Since centripetal forces are always made up of forces applied by
> > other sources, it makes no sense to include them at all.
>
> snip... so then what do you call it?  How do you get students out of
> the idea that
> circular motion is caused by an outward force that they call
> centrifugal force and
> get them to see that the force is toward the center along with the
> acceleration?
> Is not the net force directed toward the center?  Is it not in the
> same direction
> as the centripetal acceleration?  Is it not equal to mv^2/r?  What
> is this force
> if not centripetal force?

It is a "net force." There is always a net force in Newton's second
law problems. Why introduce a special name for one kind of net force?
Why not just call it net force and leave it at that?

> > Just use the
> > actual forces and let the centripetal part be associated with
> > acceleration. Pedagogically, this makes so much sense that I cannot
> > understand why anyone does it any other way.
> >
>
> Because then my students will continue to believe that the force in uniform
> circular motion is toward the outside of the circle.  They might be
> able to crunch
> problems but if you ask them sketch a diagram with forces they will label the
> force causing circular motion going out from the circle.  And if you
> told them to
> sketch what happens if a string swinging a rubber stopper suddenly breaks they
> will sketch the rubber stopper going out from the circle instead of
> tangentially
> to the circle.

Sorry, but this can be demonstrated easily by spinning a ball slowly
in a circle and then letting go of it. If it is going slowly enough,
they can see that it leaves tangentially. Get them to confront their
pre-conception by insisting that they show where every force they
want to include comes from. Ask them how a string can push the ball
outward when it spins. Ask them what direction the acceleration of
the ball is when it is moving in a circle. Ask them what forces act
on a ball spinning in a circle (all of them--tension, air resistance,
gravity) and make them show you what is causing the "centrifgual"
force you find them wanting to include. Point out that as you spin
the ball, there is a force on your hand that is directed toward the
ball (i.e., centgrifugally), and that it is equal and opposite to the
tension in the string pulling the ball in (Newton's third law). Point
out that when they are the orbiting (or turning) body, that they are
no longer in an inertial reference frame and so they feel forces on
them that feel like they are being pushed outward. but they can put
themselves in a turning car and ask them what the forces are that the
acutally feel--the seat and the door pushing on them toward the
inside of the circle, and if those force were taken away, which way
would they move, etc. etc. There are hundreds of ways to show
students that the centrifugal force is fictitious without inventing
an unnecessary new force that will be just as confusing.

It is clear to me that there is no disagreement among us on the
physics, only in pedagogical style. We probably won't resolve that.

Hugh


Hugh Haskell
<mailto://hhaskell@mindspring.com>

Let's face it. People use a Mac because they want to, Windows because they
have to..
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