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Re: Friction



I've found this discussion stimulating as it reveals that we can't always put
observations into nice little analytical packages. In first approaching
force, I make it clear that Fnet = ma is a definition. It is something we
are all going to agree on. (Actually, I prefer Fnet = delta(p)/delta(t ).
It seems to me that velocity should be introduced followed immediately by
momentum. Then acceleration and net force can be defined as the slopes of
the velocity and momentum graphs respectively.)

Prior to discussing friction, I'll digress and explain my approach building
up to force and friction.

I always emphasize my simplified version of the scientific method which is:

1. Observe.
2. Model.
3. Test the model.

And, I stress that we start with simple models. If these don't work well
enough, then we can always look for better ones. But, we must always test
any model to see how good it is!

Since I use a lot of video analysis, I next define the positive and negative
directions on the computer screen. If an object is moving right, then it is
moving in the positive x direction. If it is moving left, then it is moving
in the negative x direction, and similarly for the positive and negative y
directions. Again, these directions are something we are all going to agree
on. Are they arbitrary? Yes, but we have to start at some point of mutual
agreement.

Then we start observing many cases of constant velocity. Cars, bicycles, air
pucks, etc. that are moving across the computer screen. Using video
analysis, positions versus times are marked and visual observations are made.
What is the direction(s) of motion? Positive x or negative x? Positive y
or negative y? What can you say about the spacing of the data points? Draw
the general shape of the position (x and/or y) versus time graph. Will it
have a positive or negative slope? Why? Will it be a straight line? Why?
What visual observations tell you these things? What will the velocity(s)
versus time graph look like? What will its slope be? What visual
observations tell you this? What are the meanings of the slope and
intercepts for the various graphs? What variables do we use for the slopes
and intercepts? Can you write an equation that describes the graph? Given
the graph, can you get numerical values for the slope and intercept? Can
you check the equation and see if it does correlate with the object's motion?
Does our model work?

When approaching acceleration, I first define acceleration as the slope of a
velocity versus time graph. Then I show a video of a falling object, mark
positions versus times and ask for visual observations. How are these
observations different? Will this affect the shape of the position and
velocity versus time graphs? What will they look like? What observations
tell you they will look different? Can we still use the same equations
(models) to describe these graphs? How might we change them so they more
accurately correlate with our observations? What units does the area of the
velocity versus time graph have? Can we find this area by adding a rectangle
and a triangle? How well does this model work?

I continue with more dropped objects, objects thrown straight up,
projectiles, inclines, etc.

End of digression and on to forces and friction.

Using Fnet = ma, I stress that whatever direction the acceleration is in,
this is the same direction the net force must be in. Why? Because we all
agree on the definition. (Please, no negative mass here.) I also stress
that not all the forces acting on the object must be in the direction of the
acceleration. And, it is the physicist's job to identify which forces are
important and in which directions they are acting on the object.

I then immediately discuss some forces in mechanics and demonstrate their
properties . These include weight, normal, tension, air resistance, pushes,
pulls and friction.

To demonstrate friction, I start with a video of a chair being pushed and
then released. What are your visual observations? If the pushing force were
the only force, then what would the velocity versus time graph look like
during the push? What would it look like after the push? Is there another
force present? Why? What observations tell you this? Which direction does
this force act in? What observations tell you this? How would you write
Fnet = ma when the pushing force is acting? How would you write Fnet = ma
after the push? Is this second equation good for all time after the push?
How do you find Fnet using the velocity versus time graph? How do you find
Fnet using the momentum versus time graph? What do you expect these graphs
to look like?

Now for the kinetic frictional force model, uN. If I introduce it, and this
depends on the level of physics, I stress that it is a simple model. What
does the model say? For a sliding object, what will a plot of the friction
versus normal magnitudes look like? What is the slope of this plot? If this
plot results in a straight line, what does this mean? If it is not linear,
then what? What happens if it doesn't fit a nice analytical curve, then
what? How could we test the model with the pushed chair? Does the model
have a contact area dependence in it? Should there be? How might we test
this? If the pushed chair experiment validates the model, within
experimental error, then should we extrapolate this result to all sliding
objects?

I apologize for being so long winded, if you've read this far. The point I'm
trying to make is that I tell my students to pretend they're all from
Missouri. To me, physics is the study of nature and an attempt to model it.
Only use the model when it works, and look for a better one if it doesn't.
But always check the model and know its limitations.

rac

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Robert A. Carlson raacc@aol.com

Visit World-in-Motion, a physics video analysis program, at:

http://members.aol.com/raacc/wim.html

Visit the World-in-Motion AVI MOVIE DATA BASE at:

http://members.aol.com/raacc/data.html

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