Re: Energy, etc

[Robert A Cohen <bbq@ESU.EDU>]

See my response below...

On Thu, 5 Aug 1999, Brian McInnes wrote:

>  Robert A Cohen wrote (inter alia)
> >   As such, I prefer to say that an object's kinetic energy increases
> > because some force does work on the object
>
> I think we should be careful here in the use of the word object.
>
> The statement is necessarily true for a particle but it is not
> necessarily true for an extended object. Extended objects are real,
> particles are not.
>
> Suppose the object was a person wearing a pair of roller skates,
> standing on a polished floor and pushing against the wall of a room.
> The object's kinetic energy increases there is no work on the object
> by any force.  An object's kinetic energy can increase without work
> being done on it!

I think this is misleading.  As far as I can tell, an object won't speed
up unless there is a net force acting in the direction of the object's
displacement.  In other words, an object's kinetic energy can only
increase when there is work done on it, where I define work as

     dW = F dot dx = m d(v^2) / 2

In this expression, F is the net force on the object, the same F as in
F=ma. "dx" is the displacement of the object that is being accelerated
(not the force, as if anyone can define the displacement of a force). If
the object speeds up, then there must be a net force in the direction of
the object (and thus F dot dx must be positive).

Just as F=ma can be applied to extended objects, so can dW=dK.  If the
extended body's KE changed, there must've been work on on it (i.e., there
must be a net force in the direction of the motion, as in the case of the
skater pushing off the wall).  Now, how one identifies *what* did the work
can be a point of debate (or preference), which I'll get to in a little
bit...

On Fri, 6 Aug 1999, Brian McInnes wrote:

[snip]
> It is apparent that the walker's kinetic energy increases.  What is
> the source of this increase? Muscular contractions and extensions -
> associated with some of those many internal forces - have resulted in
> a decrease of the body's chemical energy.

Again, I think this is misleading, as it ignores the force of the floor
(friction), which is crucial for the walker to speed up.  A decrease in
chemical energy will occur even if the walker attempts to walk on a
frictionless surface, yet there will be no increase in the translational
kinetic energy.

So...the question is "what did the work on the skater pushing against the
wall?"  After all, the normal force cannot do work, can it?

I answer it thusly...

As the skater pushes against the wall, it makes more sense to consider the
arm and wall as one system and the rest of the skater as another.  The
arm/wall exerts a force on the skater's body, which experiences a
displacement.  The arm/wall does work on the skater's body, much as a
spring does work.  As the arm "detaches" from the wall, the body does work
on it as the arm experiences a displacement in the direction of the body.

The work/energy theorem doesn't break down as far as I can tell. [thank
goodness!]

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| Robert Cohen               Department of Physics       |
|                            East Stroudsburg University |
| bbq@esu.edu                East Stroudsburg, PA  18301 |
| http://www.esu.edu/~bbq/   (570) 422-3428              |
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