Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

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