Re: [Phys-L] friction

[John Denker <jsd@av8n.com>]

On 09/25/2017 12:31 PM, Anthony Lapinski wrote:
> Kinetic friction does negative work on a sliding book, which makes it stop.
> And static friction moves us forward when we walk. But there is no
> slipping, so static friction does no work on us. Yet we move forward. How
> can this be explained to kids in terms of work and energy?

The short answer is, I wouldn't explain it that way.

If I were explaining it to the kids in the introductory course,
in September, I would analyze the situation in terms of momentum,
as Paul Fedoroff and others have suggested.  Then (if required)
the energy can be obtained via p^2/2m.

Analyzing it in terms of pseudowork is pretty much the same
thing;  anything you can do in terms of pseudowork you can
do in terms of momentum and vice versa.  I find the momentum
approach (not bothering with pseudowork) to be more direct,
since it reduces the number of concepts I have to deal with.

The concepts of energy and work can always be applied, but
they are not always convenient and not always informative.
In the walking situation, the work is zero and the energy
transfer across the earth/person boundary is zero.  That is
the right answer;  it's just not very informative.

The zero-work result may be counterintuitive if you confuse
pseudowork with work ... so don't do that.

This is a teachable moment, pertaining to the topic of ill-posed
questions.  The first rule is, when given a question, always
start by asking how badly ill-posed it is.  We can apply that
to the present case as follows:  before asking yourself "how"
you would explain the phenomena in terms of work and energy,
start by asking /whether/ you should do it that way.
  https://www.av8n.com/physics/ill-posed.htm

=========================

If we want to look at this in more detail, we run into the
fundamental pedagogical dilemma:
 -- You can't teach everything at once, but
 -- you have to start somewhere.

AFAICT the only way out of this dilemma is the spiral approach.
Depending on where your kids are along the spiral, the topic of
sliding friction might or might not be within reach.

The typical pedagogical sequence starts with a very small subset of
the relevant concepts, and then applies it to an artfully-selected
of physical situations.  That's fine as a starting point, but if
there is no follow-up then students come away thinking they understand
more than they do.  In particular, sliding friction violates many of
the simplifying assumptions on which the usual starting point depends.

Let's look at the sliding book from the non-simplified viewpoint,
and inventory a few of the physics concepts that are relevant:
 *) energy
 *) energy conservation
 *) energy transfer
 *) work (not the same as energy transfer)
 *) kinetic energy
 *) pseudowork
 *) momentum
 *) momentum conservation
 *) momentum transfer
 *) macroscopic versus microscopic
 *) single particle versus extended rigid body versus continuous media
 *) bilinear (not the same as linear)

++ For starters, the pseudowork/KE theorem is not the same as 
 conservation of energy.  It's not even particularly closely
 related.  It looks like it should be, but it isn't.

++ The expression
    work = ∫F⋅dx					[1]
 is bilinear in F and dx.  That means you can write the
 average work as
    ⟨work⟩ = ∫⟨F⟩⋅dx         for any particular dx	[2]
 or you can write
    ⟨work⟩ = ∫F⋅⟨dx⟩         for any particular F	[3]
 but you cannot combine the two 
    ☠ ☠  ⟨work⟩ = ∫⟨F⟩⋅⟨dx⟩  ☠ ☠                 	[4]

 If you multiply out the RHS of equation [4], you get some
 terms that look like equation [3] or [2] ... plus other
 terms, i.e. the cross terms, which don't.  The physics of
 dissipation is hiding in the cross terms.

+ As a generalization of the previous item, note that Newton's
 laws in their simplest form apply to point particles.  That
 is fine as a starting point, but it's not the whole story.
 If you want to analyze extended and/or nonrigid objects,
 you have to do a whole lot more work.  You can't naïvely
 extrapolate the microscopic laws to the macroscopic world.

 This is directly relevant to the question that was asked,
 because the whole idea of energy dissipation is incompatible
 with the assumption of pointlike (or even rigid) bodies.

+ In addition to the necessary pedagogical simplifications,
 there are outright blunders.  The concept of energy is
 all-too-often misdefined as "the ability to do work", which
 is simultaneously unclear, unduly complicated, and unphysical.

+ The concept of conservation is also all-too-often misdefined.

+ Work can be confused with pseudowork.

+ The law of conservation of energy is always valid, but it
 can be hard to keep track of all the energy when there is
 dissipation.  (Conservation of momentum is easier to apply,
 because momentum can't be hidden.)

There's a lot more that could be said, but I have to run
off now, so I'll leave it there.