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*From*: Aaron Titus <titus@MAILAPS.ORG>*Date*: Fri, 11 Mar 2005 18:28:12 -0500

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

adopt their book.

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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