Erik Hofman wrote:
> Jon S. Berndt wrote:
> > Erik Hofman wrote:
> > > Christian Mayer wrote:
> > > > Jon S Berndt wrote:
> > > > > In my mind, mass is in kg. and force is in Newtons.
> > > > That's correct.
> > > Are you sure [...]?
> > See?
> My bad
Oh, dear. Time for the whirlwind tour of unit conventions.
In traditional* mechanics, there are only three measurable quantities
in the universe: mass, length, and time.
[* The various force interactions, like electromagnetism, have units
too. And in relativity, it turns out that length and time are the
same thing. And I'm skipping temperature for simplicity.]
You can move something around, covering some distance in some time.
So we have a derived unit:
velocity = length/time
The velocity can be changing with time, too, so we have another
derived unit:
acceleration = velocity/time = length/time^2
Newton's first law leads us to a wonder "conservation property". It
turns out that if you take the mass of something multiplied by its
velocity, and add up all the mass-times-velocity values in the whole
universe, the sum never changes. Call this wonderful property
"momentum":
momentum = mass * velocity = mass*length/time
It is possible to move momentum between objects, by delivering some
amount per time. This is called a force:
force = momentum/time = mass*length/time^2
There's another great conservation law, too. When you apply a force
for a given distance (by lifting it, or by compressing a spring) it
turns out that you are trafficing in another conserved quantity. All
the force-time-distance you put in can be "gotten back out" later on
by reversing the action*, and in fact all the force-times-distance in
the whole universe stays constant with a little accounting magic. We
call this nifty bit:
energy = force * distance = mass*length^2/time^2
[* Although it doesn't always come out in quit the way you want;
c.f. the third law of thermodynamics.]
What does this all have to do with units, you ask? Well, wouldn't it
be nice if we could pick units where all of these relationships worked
automatically without the need for "conversion" factors? That is,
wouldn't it be nice if one unit for energy was equal to one unit of
length time one unit of force? If we could get a velocity by dividing
a distance by a time?
Well, fear not, there is. This magical unit world is called "SI", and
it works like this:
mass: kilogram
length: meter
time: second
velocity: m/s
acceleration: m/s^2
momentum: kg*m/s
force: newton, or kg*m/s^2
energy: joule, or kg*m^2/s^2
And there are other units in there too: pressures of one "pascal" are
the result of one newton of force acting over a square meter, etc...
This doesn't hold for the blasphemous "engineering" units. How many
pounds of thrust are required to accelerate an aircraft with a mass of
3000 pounds by one foot per second per second? I dunno. Trying this
in SI: How many newtons of thrust are required to accelerate an
aircraft with a mass of 1500 kg by one m/s^2? The answer, immediate
and obvious, is 1500.
To be fair, SI isn't the only system that has this property. There is
another metric system that goes by "cgs" (for centimeter/gram/second
-- the basic units) with the same property. Those folks talk about
force in "dynes" and energy in "ergs".
Andy
--
Andrew J. Ross NextBus Information Systems
Senior Software Engineer Emeryville, CA
[EMAIL PROTECTED] http://www.nextbus.com
"Men go crazy in conflagrations. They only get better one by one."
- Sting (misquoted)
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