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Re: When Physical Intuition Fails



I don't understand Bob Sciamanda's statements about different coefficients of friction being needed when calculating frictional
forcce and frictional dissipation.

I am not sure about Bob's later statement about energy dissipation in non-kinetic forms. I was saying that myself, but now I am
less sure if that is correct for this problem.

I buy John Mallinckrodt's calculation of the dissipation from a power perspective. He said the key is the "relative slipping
velocity." I agree that is one way to look at it, and it indeed helped me see what I was looking for. Relative slipping velocity
is the right thing to use in a power calculation, but there ought to be something appropriate for finding dissipation as F*delta-D.
I can now see that it should be the *relative slipping distance.*

I had calculated the heat from mu*m*g*delta-x, and delta-x was the linear distance it took the center of mass to reach its final
velocity. I now see that was incorrect because the distance the tire and pavement slip past each other is more than this. If
delta-theta is the angular displacement of the wheel (from when it hits the pavement until it reaches the final velocity), then
R*delta-theta is the tangential displacement of the tire. That means the relative displacement between the tire and the pavement is
(R*delta-theta) minus (delta-x).

Since John's power calculation gives a correct result by the usual friction force of mu*normal-force, I presume
mu*m*g*(R*delta-theta - delta-x) ought to work for calculating the dissipation without having to do a power calculation. My problem
is that I have worked through the algebra a couple times and it didn't come out right. In fact, I didn't get the same result the
two times I tried it, and at this point I have put off grading my lab reports long enough..

Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Chair of Sciences
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.