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Re: [Phys-l] check your work (and kinetic energy)



On 01/07/2012 08:08 PM, curtis osterhoudt wrote:
how is the ground NOT doing work on the car to slow it down if the brakes are applied?

In addition to my previous answer, here is another line of
reasoning that leads to the same conclusion ... and doesn't
involve strings.

Although it often goes unstated, many of our most basic ideas
about Newtonian mechanics, work, and energy apply only to a
structureless point particle. You can generalize them to an
extended object, but this involves additional effort, including
additional concepts.

One such additional concept is _the point of application_ of
a force. For a pointlike particle the point of application
is obvious, but for an extended object maybe not.

For example: The "basic" definition of work (for a pointlike
particle) is:

work = integral F dot dx [1]
integrated along some path

The generalized definition is:

work = integral F dot dx [2]
integrated along the path of
*the point of application*
of the force

Obviously equation [1] is a corollary of equation [2], but
the converse does not hold. You can't get from [1] to [2]
without some additional cogitation.

So ... in the case of the car, you cannot simply talk about
"the" speed of the car and "the" force on the car. You have
to talk about the point of application of the force. Normally
this is the point of contact between the tire and the road,
and the speed of this part of the car is normally zero, even
when "the" car as a whole is moving.

Note that even among professional physicists, the concept of
force is not super-clearly or super-rigidly defined:
A) Some people insist that a physics force is a vector, with
a direction and magnitude, period.
B) Some people, especially in the engineering community but
also sometimes in the hard-core physics community, have a
notion of something they call "force" that has a direction
and a magnitude *and* a point of application.

Personally I prefer version (A) but I'm not prepared to get
dogmatic about it.

In any case, the laws of physics require "something" that has
a direction and a magnitude *and* a point of application. I
prefer to call this some sort of combination, combining the
force with the point of application. If we are not going to
call this combination a force, perhaps it would be smart to
coin a name for it. It's important enough to deserve a name
IMHO. Any suggestions?