On 5 Oct 2003 07:45:54 -0700, jim rozen wrote:
Kinetic energy of a moving object and the work
done to produce that motion are defined as the
same thing - and yes the units are the same
as they should be. This comes under the general
heading of 'conservation of energy.'

But we have just been told (in the parts you snipped) that
work is w = mv^2 and kinetic energy is Ke = (mv^2)/2. So
they aren't the same, by a factor of 2. If both equations
are correct, we need an explanation for the factor of 2
difference.

(Explanation of that could go a long way toward resolving
this issue.)

But back to the original question, why is mechanical work
calculated with the dot product w = F dot D instead of the
cross product w = F X D? I've heard some handwaving
about the conservation laws (and I'm a firm believer in
them), but no specific derivation which requires dot over
cross for this calculation.

However, I did a bit of digging and came up with another
defining equation for mechanical work in Van Nostrand's
Scientific Encyclopedia. (Sorry for the kludged nomenclature,
I don't have an integral sign on this keyboard.)

W = [definite integral from a to b] F cos(theta) ds

Were W is work, a and b are the endpoints for the
distance over which work is done, F is force, cos(theta)
is the angle of the force with the direction of work (ie
yields the component of the force in the direction work is
being done), and s is unit displacement.

Note that W is capitalized, which is the normal way to
denote a vector when an over-arrow is not available in
the typeface used. Note also that an integral is really
a repeated sum taken to a limit. The sum of any number
of vectors is still a vector.

So, while I *know* energy isn't supposed to be a vector
quantity, though an energy flux *is*, I still don't have a
satisfactory mathematical answer why mechanical work,
which certainly has to have a direction while it is being
done, is not.

Note, I *believe* it to be true that work is not a vector
quantity, what I'm asking for is some form of at least
semi-rigorous derivation showing why that must be so.

The dog ate my homework is not a satisfactory response.

Gary