Re: positive and negative work

[Brian Whatcott <inet@INTELLISYS.NET>]

At 10:18 AM 11/12/01 -0500, Gene Mosca wrote:

I first need to thank Gene for not visibly noticing that I was
addressing the wrong person.

> >> Brian Whatcott wrote:
> >>
> >>> We use Professor Leigh's favorite model: the car rolling on an incline.
> >>> Let us suppose that Michael is sitting in this car, which has started
> >>> to roll backwards, downhill. He wants to proceed slowly astern,
> >>> so he applies a little throttle while he is in a forward gear.
> >>> This prevents the car from careering away.
> >>>
> >>> The work done by the car, we say, is negative.   There is no
> >>>discussion, no debate.     [!!!]       This is the convention.
> >>
> >> I disagree.  The car exerts a force on the road surface, which is
> >> stationary, and the tire is rolling so the frictional force is static, not
> >> kinetic.  It seem to me that the car is not doing any work on the road
> >> surface.  Is there anything else the car is doing work on?
> >>
> >> Gene
> >>
> >> --
> >> Eugene P. Mosca
> >> 301 Constitution Blvd.
> >> Kutztown, PA 19530
> >> (610) 683-3597
> >> emosca@ptd.net
> >
> >
> > Hmmmm...we agree that a car would accelerate down an incline,
> > if a force acting 'uphill' were not holding its speed steady.
>
> I agree.  That would be the force exerted on the tire tread by the road
> surface.
>
> >   We see that this retarding force varies with the throttle so we are
> > confident that the car is supplying this retarding force.
>
> I disagree.  The acceleration of the car is proportional to the sum of the
> external forces acting on it.  The car can push the road harder down the
> slope.  According to Newton's third law the road will simultaneously push
> the car up the slope harder.


I can agree with you, but STILL I can say that the car is controling the
retarding force - if  "supplying the force" makes you uncomfortable.
That's what drivers do, after all!


> > We see that this force acts opposite the motion, so we say by convention
> > the work is negative.
>
> The definition of work I am using is:  Work is the integral of F dot v dt,
> where v is the velocity of the point of application of the  force.  You
> stated:
> >>> The work done by the car, we say, is negative.
> Since we are talking about the work done "by" the car, I presume we are
> talking about the work done by the forces exerted by the car on its
> surroundings.  The force the car exerts on the stationary road surface does
> no work on it.


Yes, I understand now that saying that the car is retarded does not mean
that the CAR is doing negative work - in this point of view. I think you
too will agree that we are applying a force to the road surface which
contributes to accelerating the Earth's  movement in the direction of the
car's movement.
So here, I should say that the car's tires are doing work on the Earth.

Can you agree with this?


> > But this is another way of saying that if the car's
> > work on the road is negative, the road's work on the car is positive.


Now, to reverse my assertion: if the braked tires are doing positive work
on the Earth, then the Earth is doing negative work on the car. The Earth
is reacting a force uphill, while its point of application is moving down hill.
   Does this now seem like a sensible physics model for negative work?


> Perhaps you are referring to center-of-mass work (pseudowork). Pseudowork is
> the integral of F dot v_cm dt, where v_cm is the velocity of the center of
> mass of the system the force acts on.

I can assure you that no concept of pseudowork or quasi work entered my
thoughts.

> > Carl's model does not seem to offer a mechanism. Would it be clearer if
> > the tires were locked, and the car were slowly skidding down hill?
> >
> > Perhaps not. What if the car were stationary, and the road were a
> > treadmill running uphill? The treadmill is then applying a force in the
> > direction
> > of its motion at a given velocity. This seems to describe a rate of
> > [positive] working.
> >
> > What did I miss?   :-)
>
> It seems to me you neglected to define work.  It appears there are several
> working definitions of work, and I have defined two here.
>
> Gene
>
>
>
> **************************
> * Eugene P. Mosca   x


<smile>    Gene, I don't think I'm smart enough to be choosing between
viable alternative models for a physics concept. I usually satisfy myself with
supposing that I can find a useful product of force and displacement acting
in the same direction as a measure of positive work.

But this leads to some curious speculations wherein I see that the sign of
the work changes from place to place inside the object of intrerest - the car.

I expect that this is why there is a natural urge expressed on the list to
stick with particles - they don't reverse in this disconcerting way.

Thank you for patiently rehearsing the usual arguments.
 Would you say you are orthodox, in this respect?





Brian Whatcott
  Altus OK                      Eureka!