Main content

## Slow sock on Lubricon VI

Current time:0:00Total duration:7:12

# Normal forces on Lubricon VI

## Video transcript

Let's continue with our study
of the planet Lubricon VI. Now the one thing I did not
tell you in the last video is that Lubricon VI is
not rotating at all. And because it's
not rotating, it can really not have an equator. So when we talked about in
the path of this frozen sock, instead of saying it's
traveling across an equator, I should say it's traveling
along a great circle. If you assume that
earth is a sphere-- and it's not a perfect
sphere-- but if you assume it's a sphere, our equator
would be a perfect sphere. But in order to have an equator,
you need to have some rotation. This right over
here, we'll just say it's traveling along the
largest possible circle that it can travel along. It's traveling along one of the
great circles of this sphere, this block of sock
right over there. And now that we know
it's not rotating, I want to enter another
thought experiment. Because this little frozen block
of sock is not the only thing that's on the surface
of Lubricon VI. Over here-- we were
viewing it at a distance-- but right over there,
if we were to zoom in, you would see sitting on
the surface of Lubricon VI-- so once again, that's the
surface-- is a frozen banana. So this right over
here is a block of ice. And in that block of
ice we have a banana. It's a frozen banana. So that's my best attempt
at drawing our banana. And this relative to the
surface of Lubricon VI is absolutely stationary. It has absolutely no tangential
velocity like this block had and will continue to
have for all eternity. This has absolutely no
tangential velocity. And so my question
for you, if we think about what are the
forces acting on this? Well, we have the
force of gravity towards the center
of Lubricon VI. So we have the force of gravity. And I'm drawing all the
forces from the center of mass of this block of banana. So once again, let me
draw that same color. We have the force of gravity
acting radially inward. And then we know that
this banana is not plummeting straight into
the center of the Earth. There must be some other force
that is keeping it stationary. And that force is the
force of the surface of Lubricon VI on the banana or
on this block that's keeping it from plunging towards
the center of the planet. So that, in this case,
is the normal force. And my question to you
is, are these two things equal in the case of the banana? Well, as far as we
can tell, this banana is completely at rest. This planet right over here, at
least relative to the planet, this planet right here has
absolutely no rotation. And this banana has no relative
motion towards the planet. It is not accelerating in
absolutely any direction. And if it's not accelerating
in any direction, the net forces on
it in any dimension must all or must be 0,
or all of the forces must cancel out with each other. So in the case of this banana,
the normal force exactly cancels out the
force of gravity. These two things,
the normal force is exactly equal to the
inward force of gravity. Or I guess we should
say that they add to 0. They're going in
opposite directions. So I should say the normal
force plus the force of gravity are going to be equal 0. They have the same
exact magnitude. They're going in
opposite directions. So when you add them together,
they are going to cancel out. Now, with that little thought
experiment out of the way, let's return to the frozen sock. The frozen sock, as
we already learned, is orbiting around this
planet at a altitude of 0 for all eternity at
1 kilometer per hour. And we know that
the force of gravity is acting on it towards
the center of the planet and there is a
normal force that's keeping it from
plummeting, from spiraling towards the center
of the planet. But my question to you is, in
the case of the frozen sock right over here,
are these two forces equal like they
are for the banana? So in the case of the
frozen sock, the traveling, orbiting sock, if these two
forces had the same magnitude, but just going in opposite
directions the way we've drawn it right over here,
it would completely cancel out. And then we would
have no net force. So let me make it clear. If the normal force plus
the force of gravity canceled out with each
other, if this equalled 0, then we would have
absolutely no net force and the object would not
accelerate in any direction. An object in motion
will stay in motion. So this one right
over here, if it had no net force
acting on it, it would not stay on the
surface of the planet. It would just travel
in a straight line, in a tangential line from where
it happens to be at this moment forever. So if it was right over here--
I know this isn't the path, it would just keep
traveling forever off the surface of the planet. We know that clearly is
not what's happening. It is orbiting
around the planet. It has a circular path. And since it has
a circular path-- so if I were to draw a
cross-section of its-- if I were to look at
its path from the side, it has a circular
path like that. It is going like that. It is constantly being
accelerated inward. There is some
centripetal acceleration going on, inward acceleration. So in order for that inward
acceleration to be going on, there must be some
net inward force. So in this situation, in the
situation for the stationary banana, these two guys
cancelled each other out. But for the case of the moving
frozen sock, the sock that is orbiting for all of
eternity, it is in orbit. It has a circular path. So there are centripetal motion. There is some net inward
force going on here. So In this situation, the magnitude
of the force of gravity is going to be greater than the
magnitude of the normal force. So we don't have this situation. In that situation,
you wouldn't orbit. We have the situation
where you do have some net centripetal force. The force of gravity,
the magnitude of it, is slightly larger than the
magnitude of the normal force. And an interesting
thing to think about, and we might address it
in a future tutorial, is what would happen if this
started going faster and faster and faster, if the frozen
sock were to accelerate. What then? How would the relationship
between these two things potentially change,
if they change at all?