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

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.

If you consider the cup of coffee as a point particle, then

W_by_net_force_through_cm_displacement = Delta K_cm

Thus,

Fnet dot Delta r_cm = Delta K_cm

(F_grav+F_paper) dot Delta r_cm = Delta K_cm

But since the gravitational force is perpendicular to the
center-of-mass displacement, then

F_paper dot Delta r_cm = Delta K_cm

While this equation alone may look like the work done by paper, it is
not. It is in fact the work done by the net force acting through the
center of mass displacement.

Chabay's and Sherwood's textbook teaches application of conservation of
energy to the "real system" and the "point particle system" more
clearly than any book I've ever seen. This was a major reason for me to

Aaron

On Mar 10, 2005, at 9:55 AM, rlamont wrote:

Hi All,

I have a quick question related to static friction that came up
in class today - and I just don't have time today to search the
archives - so forgive me if I'm traveling an old path here.

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.

Help!

Bob at PC

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