So far, as I said, we're going to start this course
with a mechanics introduction, with a lot of examples
and ways to think about the world that we'll be using
when we get to some very practical things
in terms of fluid flow and gas expansion and things like this.
We're partway through our forces.
We've talked about the equations of motion,
how things move on their own
whether it's in one or two dimensions.
We've also introduced forces and how forces
and force problems work in both one and two dimensions.
Now, we're going to introduce some key forces, actual physical forces,
where they come from and when you'll use them.
So, we're gonna introduce some of those important forces now.
We'll start with gravity and what we call the normal force.
Because they're so tied, we'll introduce them together
in this list of five forces that we have here.
First, let's go back and look at something that Isaac Newton came up with.
Many people think that Isaac Newton saw an apple falling
and discovered gravity by seeing this apple falling to the ground
and that this was his great revelation.
But actually we have a correction to this
which is that this was not his great discovery
for which he was so well known.
What in fact, Isaac Newton did was to see an apple falling
and think maybe this is the same force
that's bringing it to the ground
that keeps the moon in orbit around the earth
and keeps the earth in orbit around the sun and so on.
So to tie a force that makes things fall to the ground
to the same thing keeping all the heavenly bodies, as they call them,
floating around in space and orbiting each other,
was the key innovation,
to think that these might be coming from the same thing.
And, in fact, he was right, and he called this force gravity.
And so this gravitational force, as I've shown it here,
is Newton's law of gravitation.
What the letters mean in this equation are G,
the force of gravitation is equal to G,
which is just a universal constant, it's a number,
so you can always look this up or will be given to you.
It's just some number, it's not a variable.
It won't change problem to problem.
And then we multiply by the two masses that are attracting each other,
whether it's the earth and the moon
or the earth and the sun or any two things,
and then we're going to divide by the distance between those masses,
that's what the r is, squared.
So, we have G times the product of the two masses
divided by the distance between those two masses squared.
Now this distance, if we're talking about heavenly bodies,
will actually be the distance between the center of the two objects.
So, these heavenly bodies,
like the earth or the moon or anything in space,
we consider the distance from the center of one object
to the center of the other object if it's a perfect sphere.
What this means is that if the two bodies we're considering
are the earth and you on the surface of the earth,
we consider the distance to be
the distance between you and the center of the earth.
The really interesting thing here
is that if you're on the surface of the earth,
if you climb all the way to the top of a very high mountain like Mount Everest
or if you go all the way down to the bottom of the ocean floor,
on this map where we're showing the entire earth,
the distance between those two is pretty well imperceptible
relative to the radius of the earth which is a huge number.
What this means is that for anything happening
on or near the surface of the earth,
certainly anything we would be interested in, in our day-to-day life,
what we would consider the distance between us
and the center of the earth will pretty much be a constant
and that constant will be the radius of the earth.
Looking at the force equation that we have,
what we can do then is take anything in this equation that is constant,
plugging in values for something near the surface of the earth.
So, for example we have the gravitational constant, G.
We also have the mass of the earth if the earth is one object
and little m is the mass of another object on the earth like you.
And then the distance between you and the center of the earth
will be just the radius of the earth,
and then, of course, we square that distance according to our equation.
Now, that we have this force equation, what we can do as I said,
is factor out any quantities that are constant,
anything that's not changing, because what this means
is that for anything happening on the surface of the earth
or near the surface of the earth,
this equation will have many numbers
that will not be changing from problem to problem.
So, we group all these numbers together,
G isn't changing, the mass of the earth isn't changing, and the radius,
the distance between you and the center of the earth is also not changing,
and so we take all these numbers, treat them as a constant,
and call that constant g, little g.
And this little g letter is actually defined to be
these numbers that I've shown you here.
As we've said, the value of g near the surface of the earth
is about 9.8 or 9.810 meters per second squared.
So for anything happening near the surface of the earth,
what we'll have is a gravitational force of m,
your mass or the mass of any object on the earth times g,
this number that's defined like this, downwards.
For many problems you'll just be able to use the number 9.8
and you certainly won't need to keep appealing to this derivation of the letter g.
But it is important that you are able to remember
both expressions for the force equation for gravity,
both this very long one that we started with at the top
as well as the reduced one which is m times g
and understand which one is which and when they each apply.