Hi. It's Mr. Andersen and this AP Physics essentials video 45. It is on calculating
the gravitational force. We all know that there is a force of gravity holding us to
the planet. But an easy question might be, why do you not experience that when you are
in space? Why are you weightless? Some students will tell me it is because there is no gravity
there. But we know that is true, because the moon is held around the earth and we are held
around the sun. There has to be gravity out there. And so Newton explained this years
ago. And so think about it like this. Imagine that we have the earth and we build a giant
mountain on it. And then we put a canon at the top of that mountain. And we launch a
canon ball out at the horizontal. What is going to happen? Well it is going to fall
to earth. There is a gravitational force between the canon ball and the earth. And so it is
going to follow this nice path. Let's say we launch it faster, what is going to happen?
It is still going to fall to earth. We still have that force toward the center of both
objects. Let's say we launch it faster? It is still going to fall to the earth. But if
we launch it fast enough what is going to happen is it is going to fall towards earth
but it just keeps missing it. And so it is going to orbit around the earth. This is how
satellites work. And Newton predicted this years ago. And so what would it feel like
to be inside that canon ball? Well, you would feel weightless. It is not that there is no
gravitational force there. It is just as big as it was before, it is just that as you fall
toward the earth you keep missing it. And so again, Newton's Law of Universal Gravitation
allows us to not only understand this, but to quantify it. To come up with a value for
that. And we are going to do that in this video. So if we have two masses there is going
to be a gravitational force between the two and that is always going to be attractive
with anything in mass. And let's just assume that these are spherically symmetrical objects.
The equation is really really simple. It is simply force is equal to big G, and we will
get to that in a second, times the mass of the two objects divided by the square of the
distance between the two. So you simply calculate the force by multiplying the masses times
this constant. And then you divide it by the center center distance. But you are going
to square that value. Center center distance is always going to go to the center of those
two objects. Or the center of mass. Now on our planet the earth is so big in relation
to us that this gravitational force, or this gravitational acceleration, we will call it
G, is essentially constant. Changes in our distance from the earth are so small and the
mass is so big in relation to our mass that it really does not change much over time.
And so here is our equation. If we have two objects then the force is going to be equal
between the two and it is explained using this equation right here. Where G, we will
refer to it as big G, is a constant. And it is worth memorizing it. It is 6.67 times 10
to the negative 11. And so what else do we have in this equation? It is the mass of the
two objects and then the center center distance. And there is a nice PHET simulation that gets
at that. So if I have two objects like this, and I increase the mass on one, you can see
the force is increasing on both of them. And the force is always going to be equal. Now
if we show the values you will see that those numbers are incredibly small. But what happens
as we move them close to each other? The force gets larger. So we move them apart, it gets
smaller. And we can start to do some actual analysis here. If we make both of their masses
1, to make the numbers easy and then we move them 1 meter apart, you start to see that
gravitational constant come out. It is a really small value. What happens now if we increase
the mass ten-fold, so if I increase this to 10 kilograms you can see the force increases
by 10. What if I increase this mass by 10? We also see a ten-fold increase. But it is
not the same if we are looking at the distance. If I double that we are not just cutting it
in half, we are taking it by a fourth. And that is because we are squaring that distance
between the two. And so if this is our equation let me show you how to solve a simple problem.
And this is what you might see in a physics class. Calculate the gravitational force between
two 3.0 kilogram masses that are 2.0 meters apart. And so this is going to be you know,
a really small value hopefully when you get it. And so we know the gravitational constant
is 6.67 times 10 to the negative 11. I am given the masses and the center center distance.
And so it is really easy to solve that. I have gotten my constant G. Then I am going
to multiply my two masses on the top. And then divide that by my center-center distance
squared. And so if I simplify that a little bit my constant is here. What happened to
these units? Well you can that I have kilograms squared on the top. Kilograms squared on the
bottom here. So those cancel. Meters squared on the bottom, meters squared on the top.
And this is simply 9 divided by 4 which is 2.25. And so what is going to be my force?
1.5 times 10 to the negative 10 newtons. So it is an incredibly small value. Let me give
you a problem that I would like you to answer. So calculate the gravitational force acting
on me standing on the surface of the moon. And so if you were given a problem like this,
what do you have to figure out? Well the gravitational constant is going to be constant. So you already
know that. But what else do you need to know? You need to know the mass of the moon and
the mass of me. And so the mass of the moon is a really large number. And the mass of
me is large, but not that large. What else do we need to know? The center-center distance?
And that is going to be the distance from the center of the moon to the surface where
I am standing. And so what you should do is use this universal law of gravitation to calculate
what that force is. I will put it down below in the video description so you can figure
that out. And if you know anything about Newton's second law of motion, you could simply divide
that force by the mass and it is going to give you the acceleration. And it should be
a sixth of what it is on our planet. Now what is interesting about our planet is the mass
of the earth is so big and the distance is so large that in this narrow band on the surface
of the earth it really does not change that much. And so did you learn to use Newton's
law of gravitation to calculate the gravitational force between two objects? It is pretty straight
forward. Remember gravity does not go away when you are circling the earth. And I hope
that was helpful.