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Re: positive and negative work



On 11/11/01 10:30 AM, "Brian Whatcott" <inet@INTELLISYS.NET> wrote:

At 09:45 AM 11/11/01 -0500, Carl Mungan wrote:
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.

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
not work on it.

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.

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.

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 *
* 301 Constitution Blvd. *
* Kutztown, PA 19530 *
* (610) 683-3597 home *
* emosca@ptd.net *
**************************