HOST: So, apparently, ice blocking is a thing.
You put a towel on top of a block of ice and slide
down that on a grassy hill.
And it's so ridiculously fun.
And as a 31-year-old child, I visited a park recently
to try it out and ended up with grass in more places
than I imagined.
But it motivated today's lesson, because I tried
the same scooting with just a towel and no ice.
And no matter how hard I scooted, of course
it didn't work.
But why?
Well, that's the whole point of today's lesson.
Hello, and welcome to lesson 6
of Dianna's Intro Physics Class,
also known as AP Physics 1 Review,
also known as Physics by Dianna.
Today's lesson is about friction.
Part of the lesson, we'll be working
with problems that involve slopes or inclined planes.
Some people say these problems are the coolest we've done yet,
and I'm "inclined" to agree with them.
Today's theme is slipping and sliding.
You can try to hit me in the face.
[LAUGHTER]
Today's theme is slipping and sliding.
[LAUGHTER]
Whether you're into water slides or snowboarding,
friction and slopes are key to all sort
of slippery shenanigans.
Friction is super important.
Without it, we would be slipping and sliding everywhere
all the time.
That might sound fun, but imagine
trying to get anything done when you're constantly sliding off
your chair or shooting down a slightly tilted sidewalk
in directions that you don't want to go.
By the end of today's video, we'll know what friction is,
what causes it, and how to calculate
how much friction there is in some certain scenarios.
So what is friction really?
You might have a general idea that friction
is something that resists slipping or sliding,
or something that comes from rubbing, like when
you rub your hands together and they feel warm.
Well, there's something happening there
that's resisting the motion.
That's what friction does.
Friction exerts a force in the direction
opposite of the motion.
There's other kind of friction that
happens when things aren't moving,
and we'll get to that in a minute.
But where does friction come from?
Think about floating in space.
Is there any friction to slow you down?
No, there's effectively none.
There's like 1 atom in every cubic meter.
That's crazy.
It's slightly more in the space around our solar system,
and there's a lot less in the space between galaxies,
but there's, like, no friction.
So friction comes from something.
It comes from the interaction between things,
specifically between surfaces.
So no friction in space.
But if I'm sliding across the kitchen floor in my socks,
well, it's slippery, but there's still friction,
and I'm still slowing down.
But why?
No, really, why do two surfaces rubbing on each other
have friction?
Because the surfaces are rough--
blah, blah, blah.
Yes, that's part of the answer.
But even when something feels really smooth,
like glass, or like a smooth tabletop,
or like a waxed surface, or like a book,
even those are bumpy when you get down
to a small enough level.
But why do these bumpy surfaces resist sliding?
Well, Dianna, you say, because the bumps catch on each other.
OK, but why?
Why did they catch? Why do they stick?
If the surfaces are rough, it means that they're only
touching at certain points, and why would those contact points
catch on each other?
The answer is actually kind of from chemistry.
Those tiny little bumps, those tiny points,
are made up of molecules.
And those molecules like to stick.
Maybe from chemistry class you remember
learning about forces between molecules--
the intermolecular forces, the negatively-charged end
of a water molecule attracts the positively-charged end
of another water molecule, stuff like that.
When you bring two molecules close to each other,
sometimes the electrons in them will actually shuffle around
a bit to make the molecules have negative and positive ends
if they didn't already, and that causes the molecules to stick.
This molecular stickiness is actually
what's happening to surfaces when they touch each other.
It's forces between tons of tiny molecules
that make friction happen.
So saying that friction comes and resurfaces isn't wrong,
but it's not the whole story.
Fun fact, scientists have actually measured the friction
from a single molecule sliding across a surface,
and you can't exactly call a single molecule
a rough surface.
So there will be friction when two surfaces touch each other.
How much friction will there be?
That depends on two main factors.
Can you figure out what they are?
First, let's think about the surfaces.
Have you were tried to go ballroom dancing in socks?
It doesn't really work--
not a lot of friction there.
But if I put on rubbery climbing shoes
and hit the climbing gym wall,
there's a lot more friction
between my rubbery feet and the wall.
No slipping and sliding there.
So that's our first factor, the friction
between the two surfaces is going to
depend on what the surfaces are made of.
This is like a lot smoother, and this is a lot more rough.
OK, what else?
Try this--rub your hands together.
Now, rather than harder.
Now harder.
You can feel it.
The more force between your hands, the more friction.
So that's factor number two, the size
of the friction force between the two surfaces
depends on the size of the force between the surfaces.
Physicists call this force the normal force.
Normal means perpendicular in physics speak,
and that's the force that we want,
the force perpendicular to the surface--
this way.
When you push harder, the normal force gets bigger,
and the friction force resisting your motion
gets bigger as well.
So we've got it.
The amount of friction depends on these two factors--
what are the two services made of,
and what is the normal force at the interface
between the surfaces?
We will represent this with a straightforward equation.
All right, friction.
Friction force equals normal force times mu.
The mu is the coefficient of friction.
It represents factor 1--
what your surfaces are made of.
So the coefficient for ice skates on ice
will be a lot smaller than the coefficient for rubbing
your combat boots off on a mat.
And yeah, check it out, there's no units,
because we've got a force on the left and a force on the right,
so mu cannot have units.
It's just a number.
You can actually look up mu for a lot of combinations
of surfaces, like steel on ice or rubber on concrete,
and these coefficients can also depend
on things like temperature and whether the materials
are wet or dry, so it can be pretty messy.
So usually you just have to measure it.
OK, let's jump into an example.
Think about a car using its brakes.
You slam on the brakes so the tires lock,
and you screech across the concrete road.
We're going to find friction.
We'll use our tool, the free body diagram.
So here's our car.
It's a beetle.
It's moving in this direction, so there's
a velocity vector this way.
And when you hit the brakes, the friction force
is going to be the opposite direction of the motion
in this direction.
We don't know the size of the friction force yet,
but we're going to figure it out.
What do we know?
We know that there is a force of gravity pulling down
on the car.
That's going to be the mass of the car times g.
The mass of our car is, we'll say it's about 1,000 kilograms.
And then g is minus, because we're going to say
down is negative.
Minus 10 meters per second squared.
And that means that our downward force
is about minus 10,000 Newtons.
Or another way of putting that is minus 10
to the fourth Newtons-- scientific notation.
Or you could also write it as negative 10 kilonewtons.
So that's my force downward.
But the car is sitting on a surface on a road.
So Newton's third law tells us that there's
a normal force pointing upward that's exactly opposite
of the gravitational force.
So then our normal force is exactly opposite this.
So it's also 10 kilonewtons.
Or I'm going to write 10 to the fourth.
So we just found the normal force.
That's one part of finding our friction force.
Now, we have to find mu, so we just
look up the coefficient of friction
for rubber on concrete.
And it turns out that it's about 0.7.
So the force of friction here as our car screeches to a stop--
F equals the force of friction equals
mu times the normal force.
My mu is 0.7.
My normal force is 10 to the fourth Newtons.
So I get 7 times 10 to the third Newtons.
That's the force of friction, or that's also
7,000 Newtons or 7 kilonewtons.
Ta-da!
That's a big force.
But cars are pretty massive, so it takes a lot of force
to stop them.
Let's use F equals m a right now to find
the acceleration real quick.
So I've got my net force, F equals mass times acceleration.
I know my mass was 10 to the third kilograms times a.
That equals my net force, which is--
In this direction,
My force is 7 kilonewtons.
So that's 7 times 10 to the 3 newtons.
Bring this down, 10 to the 3.
And I get--kilograms--
my acceleration is 7 meters per second squared.
That seems pretty reasonable.
That's a decent amount of acceleration,
but it's not going to knock you out.
If this was all happening on a rainy day, so the road was wet,
we would need to use the coefficient of friction
for rubber on wet concrete, which is smaller.
It's the smaller mu.
So that gives us a smaller friction force.
And that's why cars slide more and take longer
to stop on wet roads.
So here's a quick and easy example of friction.
Take a book. Hold a book up against the wall.
And if you push up on it, it makes total sense
that you can hold it up against gravity
and keep it from falling, right?
But then you can also push straight into the book.
I don't know if can tell, but I'm pushing
a little sideways now, but basically
straight on into the book-- no up or downwards force.
And I can keep the book from falling.
I can even push down and into the wall,
and the book won't slide.
What is going on?
It is friction providing the force that's
necessary to resist gravity.
But wait, there's no sliding here, no motion.
So how can we talk about friction?
There are actually two kinds of friction.
The first kind of the friction of things
sliding against each other, like the locked car tires skidding
across concrete when you brake.
That's kinetic friction.
And the other kind of friction is called static friction.
This is the friction of objects that
aren't moving, like the book that isn't sliding on the wall.
Static friction resists starting your motion.
Static friction has the same basic physics
as kinetic friction.
The force of static friction is still
a coefficient of friction.
So we've got a coefficient of friction times normal force.
Static friction.
Let's try it out.
Get out a massive physics textbook and push on it gently.
You can feel resistance even if the book doesn't budge.
But if you push hard enough, the book
will start moving with a bit of a jerk.
That jerk happens because the situation
is switching from static to kinetic friction.
And for any given combination of surfaces,
the coefficient for static friction
is bigger than the coefficient for kinetic friction.
So when the force resisting the book's motion changes
from the bigger static force to the smaller kinetic force,
the book accelerates a bit, giving you that jerk.
Remember how we talked about friction
coming from the intermolecular forces between surfaces?
Well, the book goes from feeling static to kinetic friction,
and all those intermolecular bonds are breaking,
and the book can now slide across the surface.
The molecules in the book still form little bonds
with the table as the book moves, but not as many of them,
because there's other physics going on.
Isn't that wild?
I just learned that about the bonds
breaking from static to kinetic friction
myself while working on this lesson.
OK, so there's our introduction to friction.
Now, we can solve some problems.
Have you ever slid down a small hill
on a piece of cardboard or something like that, or maybe
a sled if you fancy?
If so, probably noticed that the steepness of the slope
affects how well you can slide down it.
Let's look at--I've got my cow sliding down the slope.
Not going anywhere until it gets steep enough, and then boom.
Also, here's an interesting place to look at materials.
The force of friction is different
for different materials.
So here's my pen, and it already starts to slide at this angle,
whereas the cow got up to that angle.
And then my phone case could get up to here.
What else have we got?
This is going to go flying.
Oh, this is dangerous.
OK.
Oh, actually, no.
Yeah, that didn't make it very far.
But also, this is heavy-- big normal force.
So the steepness of the slope affects
how well you can slide down it.
If the hill, or the slope, or the ramp, or whatever
is not steep enough, then it actually could
be kind of hard to start sliding, which is what we saw.
We're going to answer why steeper means easier.
So here we are trying to slide.
Let's think about the forces involved here.
We have a downward gravitational force, m g.
And to think about the friction forces,
we need to figure out what the normal force is.
We're looking for the force perpendicular to the surface.
In the car example before, the surface was flat.
So the normal force was just straight up and down,
opposite gravity, pointing upward.
But now, gravity is pulling at an angle
relative to our surface.
And it's not a 90 degree angle.
So now the gravitational force is doing two things.
So let's break it up into its two components.
So I've got my F g.
So gravity is pulling the cow into the surface of the ramp,
and it's pulling on the cow along the slope of the ramp,
trying to get it to slide down.
So now we'll use our usual SOH CAH TOA tool
to find the components of gravity.
One component will be F g times the sine of theta,
and the other is going to be F g times the cosine of theta.
Now, which is which?
One easy way to figure this out is
to think about an extreme case.
So if the ramp were totally flat, then the angle theta
would be 0.
And so there would be no sideways component
of the gravitational force.
It would just be up and down.
So sine of 0 is 0.
So the sideways component is going
to be F times sine of theta,
which makes the other F cosine theta.
This is going to be negative m g sine theta,
and this is going to be minus m g cosine of theta.
So if there was no friction, the force
of gravity along the slope, this m g sine theta part,
would just make the cow slide down the ramp.
But let's say there's just enough friction
opposing this component of the gravitational force
to keep the cow from sliding down the slope.
So we've got now a friction force.
So that's my F f, my force of friction.
We know what that friction force is.
It's the normal force times the coefficient of friction mu.
And we know the normal force, because we
know that it's equal and opposite
to the component of gravity pulling the cow
into the ramp surface.
That's m h cosine theta.
So this is going to be equal and opposite this direction.
And we know that it has to be equal and opposite,
because it's not accelerating this way.
It's not going through the ramp.
So that's my normal force, F n, equals m g cos theta.
So the friction force that keeps the cow
from sliding down the ramp here is mu times m g
cosine of theta.
So the net force that the cow feels along this slope
is the sum of the gravitational force that
wants to pull it down the slope and the friction force
that opposes it.
We said down was negative.
And we specified before that the cow is not moving,
because we see the friction force is just enough to keep it
from sliding down the slope.
So the acceleration is 0.
This is useful.
If acceleration is 0, then the net force is 0.
And I can rewrite my equation to say that mu m g cosine
theta equals m g sine theta.
By the way, the negative went away,
because if I say my net force is 0,
then I say this plus this equals 0.
So then I can just move this over to the other side.
Check it out, the m g's cancel.
Which means the mass does not matter here.
That is something interesting to think about.
Here, we're left with mu cosine theta equals sine theta.
I can rearrange a bit and get that mu equals sine theta
over cosine theta, which equals, if you
remember your trigonometry, the tangent of theta.
So, yo, I got something really interesting.
Tangent of theta equals my coefficient of friction.
So my coefficient of friction is just the tangent of theta.
That's a simple expression for the coefficient
of static friction between two surfaces.
And we just came up with a super quick easy way
to find it by using the two things we said were true.
We said that there's just enough friction force on the cow
to keep it from sliding down a slope.
In other words, the magnitude of the gravitational force
that wants to pull the cow down the slope
and the friction force that's resisting that motion
are equal and opposite.
And if this slope with steeper, gravity would win,
and the cow would slide down.
And if the slope was shallower, then there's
actually more friction force available
then we need to keep the cow from sliding.
So the angle of the slope we've picked
is just the right steepness where the competing gravity
and friction forces are equal.
So if you want to measure the coefficient of friction
between two surfaces, you can slowly
lift your ramp to a steeper and steeper angle
and stop it at just the moment that the object starts
sliding down the ramp.
That'll be pretty close to your just right,
Goldilocks angle where gravity has just barely enough strength
to overcome friction.
Then, take the tangent of that angle,
and, bam, you've measured the coefficient of friction.
You can do this at home.
You just need a protractor for measuring angles, something
to use as a ramp, like a wooden block,
a book, a piece of cardboard, anything,
and a smaller object to put on your ramp, like a square cow.
Everyone has those lying around.
So that is lesson 6, Frictions and Inclined Planes.
When they ask what you learned on YouTube today,
here are your two key takeaways--
there are two kinds of friction, static and kinetic.
Static is bigger.
And F f equals mu F n, the force of friction
is the coefficient of friction times the normal force.
And because you can only really learn physics
by doing the problems, here, again,
are all the problems we did in the lesson.
And you should definitely go work them again at home.
[MUSIC PLAYING]
I want to tell you something interesting and weird
about materials real quick.
In some labs, physicists use lasers to cool down atoms
to super close to absolute 0.
Do you know what absolute 0?
It's like the hypothetical coldest
the universe could ever get.
Like, you can't get colder than that.
So only millions or billions of a degree above absolute 0,
and that's how cold physicists get
matter when they use lasers to cool them down.
And this creates a weird new state
of matter called a Bose-Einstein condensate,
where all of the atoms clump together and they
behave in the same way, almost as if
they're all one giant atom.
And you might learn more about this if you continue on
and you take a physics class in quantum mechanics,
or atomic physics, or something like that.
I hope you do continue on physics.
And now, a message for you from a special guest.
Hi, everyone.
My name is Naomi Rowe-Gurney, and I am a student
at the University of Leicester.
I study the ice giants-- Uranus and Neptune.
I look at their atmospheres
using the Spitzer Space Telescope,
and that's all in preparation
for a brand-new space telescope called the James Webb
Space Telescope that's being launched next year.
So keep an eye out for that.
I was never very good at maths in school,
but now I'm a planetary scientist.
So always persevere, and I'm really excited that you've
decided to learn physics.
Keep going, and good luck with your studies.
[MUSIC PLAYING]