Force versus weight, or weight versus force, is a force a weight, is a weight a force? Hopefully this screencast will answer some of those questions.
And we'll start with a tree, an apple tree specifically because we know that
the apple tree started this whole endeavor when an apple fell on
a sleeper's head. It just so happens that that apple has some kind of mass to it,
we're going to say "m" of an apple
and that fell with some type of acceleration. And that mass times acceleration is the force.
This mass--let's say some amount of kilograms--
fell at some acceleration in meters per second squared,
so that when we get a force, it's going to have
units of kilogram-meter per second squared.
Now because of the person that this apple fell and hit, we now call this a "Newton"
pretty selfish, I would say, but regardless
that one Newton is equal to 1 kg-m/s^2.
Alright, if we refer to the acceleration here
as a centimeter per second squared and the mass in terms of grams,
then we refer to this as a "dyne".
Now American engineers decided to take a pound-mass and multiply it by a foot per second squared.
and we would get pounds-mass feet per second squared.
Now what's this equivalent to? Well, this is where it comes in,
American engineering scientists decided to take that acceleration due to gravity
that is 32.174 ft/s^2
and this would equal one "pound-force", so they didn't try to get
clever or any new names for it; they just decided to use
acceleration due to gravity.
So you can see that the major difference is that the American engineering units use gravity
but the SI units just use 1 m/s^2, not 9.8 m/s^2,
which is the acceleration due to gravity in SI units.
Therefore, when we convert between Newtons and pounds force, it's important to use the proper conversions:
One pound force is equal to 32.174 pounds mass feet per second squared.
this if you convert this part into SI units,
ends up becoming about 4.45 Newtons,
so it's important to use these conversion factors--
or at least you should unless you want a space craft to just randomly crash into planets.
Alright, so let's do a little exercise: we have a ball,
and we will work with SI units and American engineering units.
and we'll see that, say we picked a mass of 1 kilogram for this ball,
and we try to accelerate it at 10 meters per second squared.
well that's pretty straightforward, that needs 10 Newtons of force.
When we do the American engineering system,
if we pick 1 pound and try to accelerate it at
10 feet per second squared, this does NOT equal 10 pounds of force.
What this does equal is 10 pounds-mass, foot per seconds squared.
So if we were to do a dimensional equation,
and we wanted this to be in pounds-force,
we need to put pounds-mass foot, and seconds squared here, and pounds-force up here,
and that one pound-force is equal to 32.174 pounds-mass feet per seconds squared.
So, we would divide the 10 by the 32.174,
and see that we have about point 3 pounds of force,
so it's important to take into consideration that conversion factor
when you're working with American engineering units.
Weight is the force exerted on an object by gravitational attraction.
So the ball in this case,
one kilogram ball subjected to gravitational acceleration of 9.8 meters per second squared.
It has a force--or weight--of 9.8 Newtons. You could end up converting this to pounds-force but I'll leave that for your own exercise.
So let's say you're trying to determine the weight of one Liter of water.
The mass of the water can be determined using the
conversion factor of density: we know that one Liter of water
around room temperature is going to be 1 kilogram of water,
the density of water being 1 gram per milliliter.
This, times gravity, gives 9.8 Newtons.
If we want it in American engineering, then
1 kilogram of water is about 2.2 pounds of water, again that's mass.
We're going to then multiply this by gravity's acceleration that's 32.174 feet per second squared,
and then what we're going to do is convert this to the pounds-force
so use the conversion factor "g"
32.174 pounds-mass foot per second squared.
That's one pound force, so when we do that
we see that that cancels that, and we're left with 2.2 pounds of force.
So hopefully you see the difference between what we did prior to this to calculate force
and what we're doing now to calculate a weight.
A weight is due to gravitational acceleration.
This 32.174 that we used over here is our conversion factor to get to our pounds of force.
when we refer to the weight of the object, typically one pound-force
will equal one pound-mass if you're on earth.
Now, this might change if the gravitational constant "g" changes
and that might change with the distance between the center of earth and where you're at--
so, if you are trying to do this for space applications,
or on the moon where "g" is definitely not going to be equal to 32.174,
then that will NOT be true
Otherwise it's a pretty good estimation if you are on earth.