Re: Automobile tires and friction

[Michael Bowen <fizzbowen@MINDSPRING.COM>]

At 05:57 2002/02/25, Ludwik Kowalski wrote:

> What does your friction lab consist of? The activity which
> comes to my mind is to measure static friction on the inclined
> plane (mu=tanA, where A is the angle at which the object
> starts sliding). I would ask the student to prepare several
> wooden sliders which have different widths and to explore
> the effect of the width on the angle A. I would suggest to
> use sliders whose masses are identical. Yes the mass is not
> expected to be important but one should not lean on
> expectations, if possible. It would be a good idea to explore
> the effect of the mass as well. I would also try at least two
> very different materials. Why not?
> <snip>
> Please share your findings with the rest of us.

It's very basic; we measure static and kinetic mu for wooden blocks sliding
on a horizontal wooden surface (a smooth oak plank, to be specific). To
measure frictional force, we tie one end of a string to an eye bolt that is
screwed into one end of the block. The string extends horizontally from the
eye bolt over the top of a small wheel that is clamped to one end of the
plank. The string wraps 90 degrees around the top of the wheel, as a small
mass is suspended vertically from the string's other end. To the extent
that the pulley may be considered frictionless, the tension in the string
should be equal to the suspended mass, given that the block is either
stationary or moving with constant velocity. In principle, this should also
be equal to the force of wood-on-wood friction under the same
circumstances. Normal force is simple; it's simply the weight of the block
(plus extra weights we add to give additional trials).

We get static mu by loading the suspended mass as heavily as possible
without allowing the block to slide. As the planks are not uniformly
smooth, mu varies a bit from place to place, so the students obtain
multiple measurements for a given value of normal force. The normal force
is also varied using extra weights, which allows a scatterplot to be made
of the relation between normal and frictional forces; the nominal slope of
the plot is of course mu. Kinetic mu is similar except now the suspended
mass is set so the block moves without accelerating over the plank. The
same weights are used on top of the block as were used for the static case,
enabling a direct comparison of the (maximum) static and kinetic frictional
forces. It is necessary to nudge the block to push it from the static to
the kinetic regime. Experimentally, the suspended mass is usually 10-30%
lower in the kinetic case than in the corresponding static case, which is
significant even with the large error margin associated with this approach.

Kinetic friction is evaluated a second time by removing the string and
letting the block slide down the no-longer-horizontal plank at an incline.
The incline angle (theta) is adjusted until the block slides at constant v.
At this angle, free-body analysis predicts that kinetic mu is equal to
tan(theta). Most students do not understand (until afterward) that one
consequence of the approximate invariance of mu over a wide range of normal
forces is that (theta) is essentially independent of the mass of the load.
During the initial naive phase, they expect to have to adjust (theta) as
the load changes. If by chance they establish an apparent trend of slight
angle changes (either upward or downward) for the first few load values,
they attempt to reinforce that trend for still greater loads by predicting
what the next angle should be. They are deeply puzzled when the system
eventually stops following the "trend" until they realize that they have
been fooled by their initial data and assumptions. They then routinely ask
me whether the angle is "supposed" to increase or decrease. I tell them to
figure that out from the data; which makes them unhappy, as they are much
more accustomed to "cookbook" labs that usually don't leave much room for
actual discovery. The light bulb pops over their heads usually about the
time they finish the last trial. It is an unexpected result for most.

As the blocks are rectangular rather than cubic, I do a quickie demo that
shows the frictional force is the same regardless of which side of the
block (broad or narrow) rests on the plank. I haven't tried this for other
materials. I'll have to do that with the students (a good suggestion), but
I won't have time until next semester.

--MB