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[Phys-L] Re: Quick question on static frictionHi All

• From: "John S. Denker" <jsd@AV8N.COM>
• Date: Fri, 11 Mar 2005 19:28:02 -0500

On 03/11/05 18:28, Aaron Titus wrote:
Probably the best treatment of work and energy of any introductory
textbook is Chabay and Sherwood's Matter & Interactions. The following
analysis is based on that book.

You asked "If I place a coffee cup on a sheet of paper and pull on the
paper gently enough to accelerate the coffee cup without it slipping on
the paper, has the force of static friction done work on the coffee
cup?"

The answer is indeed "no" because the work done by the paper on the
coffee cup is

W_paper = F_paper dot
displacement_through_which_the_force_of_the_paper_on_the_cup_acts

Since the force of the paper on the cup does not act through any
displacement, then the work done by the paper on the cup is zero.

But But But ... that's the wrong answer.

As several people recently pointed out, that violates
conservation of energy. Violations are considered a

1) Whoever is pulling the paper loses energy ... and that
energy has to go somewhere.

2) The cup gains KE in the lab frame. That energy must
have come from somewhere.

I don't have a problem with the _formula_ stated above.
Instead, the problem lies in the assertion that the force
does not act through any displacement.
-- In the lab frame there is clearly a nice big
displacement. This is the traditional and sensible way
of analyzing the situation.
-- In the frame of the cup, you are using an accelerated
reference frame, and most of what you learned in high-
school physics is inapplicable. For starters, even
F=ma is invalid. We have agreed that there is a force
on the cup, but in the frame of the cup the cup is
(obviously) not moving, so it has no acceleration.

It is of course possible to do physics relative to
non-inertial reference frames ... but such techniques
are beyond the scope of the course.

We can discuss the topic if people are interested.
The accelerated cup is not the traditional introductory
example, but I suppose it is as good as any.
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