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

["John S. Denker" <jsd@AV8N.COM>]

On 03/10/05 09:55, rlamont wrote:
> 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? One of the homework problems in Serway (Physics for
> Scientists and Engineers) implies that no work is done by the
> static frictional force because there is no actual displacement
> of the cup relative to the paper. I don't find that very
> satisfying because the cup still gains kinetic energy and the
> only force acting horizontally on it is the static friction.

I agree with what several others have said.

Let me thrown in an additional cent or two:

1) Analyzing this situation in the accelerating frame
  of the paper is not a good way to go.  I'm not saying
  that it can't be done ... I'm just saying it's beyond
  the scope of the course.  It converts a HS kinematic
  problem into a general relativity problem ... probably
  not what you wanted.

  This is conceptually slightly -- very slightly --
  tricky, since you want to use the accelerated frame long
  enough to observe that the fricion is indeed _static_
  in that frame.  Then you want to use an unaccelerated
  frame for calculating the energy budget.

  Tangentially relevant reference: "What makes the car go?"
    http://www.av8n.com/physics/car-go.htm

2) It's not wrong to say that the hand does work on
  the paper ... but this does not exclude the possibility
  that the paper is doing work on the cup.

  Here is an important conceptual point:  energy obeys
  a local conservation law, which is conveniently
  expressed in terms of a conserved flow.

   http://www.av8n.com/physics/conservative-flow.htm

  In this case, energy flows from the hand to the paper,
  and thence most of it flows into the accelerating cup.
  (Some of it is used to accelerate the paper itself,
  and presumably some of it is dissipated at the
  paper/table interface.)

3) The following has a wide applicability, not limited
  to just friction, and may be a contributing issue here:
  Many people have learned the theorem that a force of
  constraint does no work.  But that's wrong;  the real
  theorem says that a *stationary* constraint does no
  work.  If you have a moving constraint, all bets are
  off.  For example, suppose we have some water that is
  constrained by the walls of a ladle.  For a nonmoving
  ladle, these are clearly conservative forces i.e.
  the derivative of a potential.  But if I'm allowed
  move the ladle, I can easily schlep water from a
  lower bucket to a higher bucket, doing as much work
  as I like.

  This may sound like a triviality;  you may be wondering
  how anybody could be so dumb as to mis-state that
  theorem ... but I've seen it done.  I've seen Ivy
  League professors get flummoxed by this.
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