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Re: Centripetal Force--was part of L2-"Negotiating" a curve.

Arlyn,

The question here is one of nomenclature and pedagogy.

We invent no special name for the net force that causes an object to speed
up or to slow down. We simply say that a = (net F)/m either along the
direction of motion or opposite the direction of motion. Of course, we have
no special names for these accelerations either. Now with uniform circular
motion we have a problem. The acceleration points towards the center of the
motion but is always changing direction from a Cartesian point of view. It
is difficult to constantly describe this situation in full, so we use the
nomenclature 'centripetal acceleration' to make communication 'easier'.
Once we've done that, then it is tempting (and has become conventional) to
call the NET FORCE that causes such an acceleration the centripetal force.
This does balance the more commonly used (outside of physics) term
centrifugal force, but from the non-accelerating frames you wish to use (and
I agree you should) such a thing as centrifugal force is non-existent, at
least in most of the cases where it is usually invoked.

OK, so what's the problem? First, you need to dissuade students of the
notion that there are 'real' centrifugal forces acting. (Again, so Leigh
doesn't jump on me, we are considering the normal HS approach of considering
only inertial frames.) Is it helpful to replace the centrifugal forces with
centripetal forces? That has been the common pedagogy, but what many of us
have discovered is that when we do so, students then think of the
centripetal force AS A FORCE OF NATURE. That is, if you ask them to draw a
force diagram for the person on the Ferris Wheel at the upmost position,
they would draw THREE forces--the weight of the person pulling down, the
chair pushing up, AND the centripetal force pulling down. That is, they
don't understand that the weight force is greater than the chair force such
that the net force downwards provides the necessary centripetal
acceleration.

In order to address this pedagogical problem, the suggestion has been that
we NOT use the term centripetal force, but rather the somewhat more
cumbersome 'net force that causes the centripetal acceleration'. Doing
such, at least with introductory students, might prevent the common problem
detailed above.

I hope this clarifies the 'controversy' surrounding 'centripetal force'.

Rick


----- Original Message -----
From: Arlyn DeBruyckere <arlynd@HUTCH.K12.MN.US>
To: <PHYS-L@lists.nau.edu>
Sent: Friday, November 05, 1999 7:42 AM
Subject: Re: L2-"Negotiating" a curve.


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".


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.


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.



, 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.


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?

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?


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.



Hugh

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

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

At least we agree on something :)



******************************************************

--
Arlyn DeBruyckere
Hutchinson High School