Rate of free fall vs Acceleration of free fall

On Sat, 20 Sep 2003 20:42:50 GMT, "Donald G. Shead"
wrote:


"ghytrfvbnmju7654" wrote in message
om...
"Donald G. Shead" wrote in message
. com...
"ghytrfvbnmju7654" wrote in message
...
"Donald G. Shead" wrote in message
om...
Metric mass [a gram or kilogram] is nothing more than a unit of
inertia;
like the slug is a unit of inertia: A measure of "quantities of
matter".
Length; Force and Time are the fundamental units of measu Mass is
a
"derived unit"!

Bah. All of these units are arbritrary.

The fundamental units can be, and are arbitrarily chosen, and named; but
then must be consistently applied: Like for speed we can choose to use
either meters per second, or feet per second; but then we must use the
chosen units to express acceleration: Either as 9.81 meters/sec², or 32
feet/sec². Nor can we stop the Inertia isn't an arbitrary unit that
we
can just grab onto out of thin air!

Ha. Watch me. I arbitrarily define a unit of mass, units of distance
and time, and units of force. Then I write Newton's second law as:

F=kma

Newton's second law says that the acceleration [a] of an object; body or
mass [m] of matter is directly proportional to the net force [f] causing it:
Therefore m = f/a, and/or w/g; So by transposition, f = (m)a = (f/a)a, and w
= (m)g = (w/g)g! Like the song says you've got to 'know when you can hold
'em, and know when you can throw them away'....

where k is the "inertial constant."

and where did you get k?

Less convenient, but still consistent with Nature.

All units are human conventions and are arbitrary.

In a pig's eye: One gram is one _unit of mass_ because it's a ratio [f/a = 1
dyne divided by 1 cm/sec²] = [w/g = 980 dynes divided by 980 cm/sec²]!

Inertia is a ratio of the (net) force divided by the acceleration that
it
causes, which is a quantity measure of the amout of matter in an object;
body or mass of matter: We can use either the newton of force with the
meter/sec²; so that the kilogram is ONE unit, or we can use the pound
with
the foot/sec²; so that the slug is ONE unit. We can call these by other
names, but the principle (concept) will not change.

In particular we can't choose the rate at which bodies free fall in
vacuum:
That's whatever mother nature; or God requires it to be!

Yes, we can; we can add more mass to the object it's falling towards.
Not easy to do, but not strictly impossible.

Oh yes it is.

The calculus is just a fancy way of
stretching out _averaging_, to make it
look like plotting data on coordinates
is something very mathematically
sophisticated.

Calculus, Donald, is a way of getting exact formulas that can greatly
simplify calculations, where numerical calculations could have yielded
only approximate results. Calculus is used to make problems simpler.

Don't you wish(;^! Slide rules make problems simpler, and numerical
calculations will yield whatever precision we can handle; up to and
including umpteen decimal place accuracy. Now cut the crap, will you
Spiral?

Here's a problem that should be easy for you, since calculus makes
things more complicated:

Determine the average value of sin(x) from x=0 to x=theta,
where theta could be any value from 0 to pi.
Show all work.

When you are done, I can show you the calculus way, and we can
compare to see which is simpler.

I've got a better idea Spiral: You show me the calculus way first, and why
stop at pi? Let theta, whatever the heck that is, vary from zero to 360
degrees:

_Then_ we'll see which is simpler.

The difficulty remains about the same with calculus, Dense Donny.
Your buddy with the unpronounceable name was just trying to make it
easier for you, by making sure you didn't have to average in any
negative numbers.

So lets make it even simpler, Donald. I'll specify the top end, too.
Find the average value of sin(x) from x=0 to x=1.25 pi = 225 degrees.

Gene Nygaard
http://ourworld.compuserve.com/homepages/Gene_Nygaard/

"Donald G. Shead" wrote in message om...
"ghytrfvbnmju7654" wrote in message
m...
Ha. Watch me. I arbitrarily define a unit of mass, units of distance
and time, and units of force. Then I write Newton's second law as:

F=kma

Newton's second law says that the acceleration [a] of an object; body or
mass [m] of matter is directly proportional to the net force [f] causing it:
Therefore m = f/a, and/or w/g; So by transposition, f = (m)a = (f/a)a, and w
= (m)g = (w/g)g! Like the song says you've got to 'know when you can hold
'em, and know when you can throw them away'....

where k is the "inertial constant."

and where did you get k?

Oh, come on. Don't be dense. Here, let me show you by an
example. We'll use newtons for force, meters/sec^2 for
acceleration, and fizzles for mass.

Then k = 1 newton*time^2/(meter*fizzle) = 1 kilogram/fizzle

There are other equations in physics where there are or could
be constants like that, and we can always either choose to set
the constant to 1 to make things simpler, or choose our units
without regard to the relationship. In some cases we throw
in a constant; in others, we don't. It's an arbitrary choice.

Here's a problem that should be easy for you, since calculus makes
things more complicated:

Determine the average value of sin(x) from x=0 to x=theta,
where theta could be any value from 0 to pi.
Show all work.

When you are done, I can show you the calculus way, and we can
compare to see which is simpler.

I've got a better idea Spiral: You show me the calculus way first, and why
stop at pi? Let theta, whatever the heck that is, vary from zero to 360
degrees:

_Then_ we'll see which is simpler.

I was making it easier for you, because if theta could be
anything, you would have to make me an awfully big table of
numerically calculated values. Since I'm using calculus,
I'm automatically going to get a general formula, so that
restriction didn't make squat easier on my side.

Since you insist, here is the calculus way:

theta
/\
\
\ sin(x)dx
\/
0
------------
theta - 0

theta
|
| -cos(x)
|
0
= -----------
theta

( -cos(theta) ) - ( -cos(0) )
= -----------------------------
theta

= (1 - cos(theta))/theta

Waiting for your answer.