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: When Physical Intuition Fails



Mike Edmiston wrote:

In response to John Mallinckrodt... I didn't necessarily want to imply
that "no dissipation of energy" is 100% possible. But I was saying this
in the same spirit that we say it when we study "elastic collisions" in
general-physics class. We still do that don't we? I.e. we pretend it
is possible to have an elastic collision, which is defined as one in
which kinetic energy is conserved, even though we know the deformation
of the bodies during impact will result in some amount of thermal
energy.

Is that where we differ, John? Or are you talking about something
else I am not picking up on?

That's not where we differ; it *is* something else.

There is a fundamental difference here that does not arise in
collisions between nonrotating objects that have no frictional
interaction. In the case we are discussing an elastic collision is
strictly impossible even in theory as the Newtonian analysis makes
clear.

Also, what assumptions are being made about I for this wheel. I was
assuming a disk with I = 0.5mr^2. In this case I get v_f =
r*w_0/sqrt(3) if there is absolutely no dissipation, and I get
v_f=r*w_0/sqrt(5) if there is dissipation due to "slippage."

You can check for yourself that my formulas give the same answer that
you just under the assumption of no dissipation, but that I get v_f =
r*wo/3 from the Newtonian (dissipation required) analysis in
agreement also with Oren Quist's formula.

Note that there is no disagreement that mu does not appear, and that
the final velocity is r*w_0 times some factor. We just aren't
agreeing on what that factor is.

Right.

I'm not getting r in this factor, I assume because of my assumption for I.

Right. But it's easy to make the translation as long as you
understand the definition of radius of gyration: R_g = sqrt(I/m)

But also, is there a dimension problem in the results that John
gave? How do the units work out on the factor that multiplies
r*w_o? Doesn't that need to be dimensionless?

As you can see for yourself from the definition I gave for r, it *is*
dimensionless.

--
John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm

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