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### Course: MCAT > Unit 9

Lesson 4: Vector analysis and forces acting on an object- Normal forces questions
- Force of tension questions
- Forces on inclined planes questions
- Balanced and unbalanced forces
- Normal force and contact force
- Normal force in an elevator
- Slow sock on Lubricon VI
- Normal forces on Lubricon VI
- Inclined plane force components
- Ice accelerating down an incline
- Force of friction keeping the block stationary
- Correction to force of friction keeping the block stationary
- Force of friction keeping velocity constant
- Introduction to tension
- Introduction to tension (part 2)
- Tension in an accelerating system and pie in the face
- Intuition on static and kinetic friction comparisons
- Static and kinetic friction example

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# Normal forces on Lubricon VI

Explore the intriguing world of Lubricon VI, a fictional non-rotating planet, and its unique physics! Understand the forces acting on a stationary frozen banana and a perpetually orbiting frozen sock. Delve into the concepts of gravity, normal force, and centripetal acceleration in this engaging thought experiment. Created by Sal Khan.

## Want to join the conversation?

- Isn't the force of gravity equal to the force normal in both cases?

Let's say that the moving block did have the same magnitude for both forces in the y direction, if it's true that the block would just leave the surface, then the block would no longer have a normal force. So wouldn't the force of gravity pull it back down to the surface?

I agree that the object does not have a net force of 0 because the initial force push (the one that set it into motion) is continuing to act on the object due to the frictionless nature of lubricon.

But why does the force normal not equal the force of gravity?(53 votes)- You're correct in thinking the block would no longer have a normal force and gravity would pull it back down if it left the surface. But the block doesn't have to entirely leave the surface for the normal force to decrease. It can decrease at a very small scale since the surface is slightly curved and the block keeps wanting to continue in a straight path and leave the surface. It just isn't quite as dramatic as the block flying off the surface and being pulled back down, but more subtle like the feeling you get when driving a car over a rolling hill. In that case, the normal force on you decreases, and there is a net force pulling you down the hill and you can feel it in your stomach. The net force on the block is at a much smaller scale than this because the curvature is that of the entire planet (and not just a hill).

As far as the initial force goes, after the force has been applied to get the object moving, it goes away. Afterwards, the only forces involved are from gravity and the normal force.(72 votes)

- At1:44, he says that the banana has no tangential velocity, and that the sock will retain it's velocity (which, actually, should be speed, since its direction changes as it orbits). Would the banana and the sock not have a gravitational effect on each other, causing them both to accelerate towards each other?(68 votes)
- They would have an acceleration of of G*m1*m2/d^2/m1 and G*m1*m2/d^2/m2 or a total speed towards each other of (G*m1*m2/d^2/m1 + G*m1*m2/d^2/m2) * t

G = gravitational constant = 6.67*10^-11

This means that if the distance between the two objects was 1 km (d = 1000), m1 = 1 kg and m2 = 2 kg, the speed after 10^8 years would be 0.421m/s

I might be totally off though :)(14 votes)

- Why can't a non-rotating planet have an equator?(17 votes)
- The equator is defined to be perpendicular to the axis of the planet. If the planet is not spinning, then there is no axis. If a planet does not have an axis, then we cannot define the equator either.(40 votes)

- If the planet were rotating, what effect would that have on either block? Would it make a difference if the sock were going around the equator or the poles?(18 votes)
- No effect, since there is no friction. However, there is the problem of the relative speed. When we say moving at one km per hour in the East, is that relative to the planet's surface or to an observer in space? If it were relative to the surface, and the planet was rotating at 2 km per hour to the East (measured at the surface), then the object would be moving 3 km per hour to the East.

tldr:

No effect(23 votes)

- I"m completely confused. The sock is traveling at a constant velocity, not accelerating. Why is there any tangential force?(11 votes)
- The sock's speed is constant, but it's velocity isn't.

Yes, it's moving at 1km/h, but it's direction is constantly changing. For the sock to circle around the planet (which, in this case, would be the same as orbit around it), it needs a centripetal acceleration curving it's movement inwards, keeping it from flying away.

If it's velocity were constant, the sock would move tangentially away from Lubricon VI and into deep space.(32 votes)

- How is there gravity? Doesn't the planet need to be rotating inorder to be able to have a gravitaional force? Or is this just theoretical gravity?(14 votes)
- The planet doesn't have to be rotating to have gravitational force.Gravitational force is the force between any 2 objects in the universe.Anything in this universe that has mass, would bend space, which results in gravity.Gravity acts between any 2 bodies in the universe (including you and me, but its magnitude would be very very small).So, a planet doesn't have to be rotating to have gravity, as long as it has mass, it would have gravity(5 votes)

- 6:30If the frozen sock block's movement comes Fg being greater than Fn, why does the sock block move around the planet instead of sinking into the center of the planet (the direction of the net force unbalance.(6 votes)
- The movement of the sock is not caused by the force Fg.

That motion has been caused by some other means that we have not been told about. We do know that it was a force with a component TANGENTIAL to the surface of the planet.

The sock is now travelling with constant speed around the friction-less planet

He is saying that Fg must be greater than Fn because there is a centripetal acceleration (that the banana does NOT have) simply keeping the sock moving in a circular path and nothing else and that Fg is providing this centripetal force

Hope that helps

IM(4 votes)

- Is the force of gravity 'round'? That is, would an object with mass, hence gravity, get formed into a sphere? Why not a square planet? I assume the roundness is due to rotation, and a non rotating planet might lose its roundness....(3 votes)
- Gravity tends to shape large objects into a spherical shape because it is a central force. A point mass produces a gravitational field that extends radially from the point, and this type of field will try to redistribute all mass into a spherical shape. Keep in mind, though, that this is true if the object has enough mass. Many asteroids and some moons are not massive enough to have a spherical shape, and they are just lumps of rock. For instance, think about Phobos and Deimos, the moons of Mars.(7 votes)

- I didn't really understand how force of gravity is more than normal. I thought the reason it stays on the surface is because maybe it left the surface by really small amounts and at that moment there was no normal force and only gravitation force due to which it was pulled down again.(3 votes)
- The normal force must be less than the force of gravity or else the object would not accelerate toward the center. Imagine the process that you are describing happening instantaneously and continuously, and averaging out. Doesn't it average out to normal force that is less than force of gravity? It must, since in your reasoning the normal force is sometimes zero.(3 votes)

- Is gravitational force not equal to normal force even on earth?And why do they dont cancel each other in case of sock?(1 vote)
- Yes, even on earth, and on any spherical body. However Earth is HUGE and also has friction, so these effects will never be noticeable in day-to-day life, and it can be assumed that Fn = Fg even if the object is moving.(1 vote)

## 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?