Now that we've introduced three of these five important forces,
that we're going to discuss, gravity, the normal force and tension
and seeing how they work in some problems.
We're going to move to friction.
So the friction force arises from small interactions between two surfaces,
if we really zoomed in, what we would see is that the surface of this blue box
as I've drawn it and the surface that it's resting on are not entirely smooth in fact
that they have all sorts of ridges in them.
What happens is if one object tries to move over the object,
these ridges will catch with each other and push each other
either to the left or to the right depending on the motion of the object.
The force of friction if we wrote it down would be exactly what you would expect
if you were trying to derive this on your own.
Friction basically depends on two things, it depends on what I'm calling mu here,
it's a Greek letter mu that looks like a funny u.
This is telling me how rough a surface is
so it certainly depends on how rough the surface is.
So our force of friction which I'm calling F-sub-F force of friction
depends on the roughness of the surface which is given by this Greek letter mu
but it also depends on F-sub-n, the normal force.
In other words, how hard are these things pushing against each other?
The normal force is exactly the normal force that we've introduced already in this lecture
so you can solve for this normal force from a problem
and then find the frictional force based on that normal force.
The mu that I just mentioned which describes how rough or smooth the surface is,
is bigger for very rough surfaces like the one on the left here
and is smoother for small, or sorry it's a smaller for smooth surfaces
like ice or something where those ridges don't really have catches on each other.
Finally, you can see that this force air that I've drawn is pointing upwards
because anytime we're talking about forces,
we're considering forces on a particular object
and the object in question when considering the normal force is the box, not the ground.
And so the force of the ground on the box,
will be in the upwards direction and that's our normal force
but this does not mean that the force of friction is pointing upwards
because the normal force is just use as a magnitude in this equation for friction.
Finally, the direction of friction since it's certainly not upwards out of the surface,
is given by the velocity of your object. If your object is moving to the right, as I have shown here,
the force of friction will act always to oppose that motion.
If the velocity is to the left then the force will be acting to the right to oppose that motion.
So to find the direction of friction always remember that friction opposes motion all the time.
There's one caveat to the equation that I gave you
which is that the equation for friction that I gave you,
force of friction is equal to mu-sub-k the kinetic friction times the force,
the normal force is only exactly correct in the case of kinetic friction,
what we mean by kinetic friction is that an object is actually moving along the surface.
So if the object is moving, and you know that the object has a non-zero velocity,
it's actually moving in your problem,
then you can always use this equation that the force of friction
is equal to the coefficient of friction mu times the normal force.
I put a little k under the mu to say that this is the coefficient of kinetic friction
because it turns out that coefficient of friction, how rough surfaces are
and how much the frictional force depends on the roughness of the surface
actually depends on whether the object is moving or not.
So an object will have a different coefficient of friction
if it's moving then it will have if it's sitting still and so that brings us to the static case.
Suppose an object is sitting still, like anything you have in your table,
that's just not moving and suppose you tried to move it,
the frictional force will not necessarily be equal to the coefficient of friction times the normal force
but it will be less than or equal to the coefficient of friction times the normal force.
This coefficient of friction we now call the coefficient of static friction
or mu-sub-s and the reason it's less than or equal to is this.
Take an object that you have on your table and give it a tiny push that it doesn't move.
Since the object isn't moving, even though you're pushing on it very slightly,
you know that there must be some opposing force,
because otherwise it would be moving in the direction you're pushing it.
That opposing force is friction because the object doesn't wanna move even though you're pushing it.
The thing is, if you slightly increase the force, so that the object still isn't moving,
the frictional force will react again and it's still not moving.
So you can see that the frictional force is changing and adapting to how much you push it.
If you keep pushing, the frictional force gets stronger and stronger eventually you'll reach a point,
a threshold at which the frictional force can no longer combat
the amount that you're pushing that object like your book or something
and eventually, the object will move.
It will move when your force that you're applying is greater than mu-sub-s
the coefficient of static friction times the normal force of your object
and that's what we mean when we say that the force of friction for an object that is not moving
is less than or equal to mu-sub-s times f-sub-n
because it could be much smaller than that threshold
if you're not pushing very hard because it doesn't really need to have the full value.
It is just going to act to try to get the object to stay still.
One last very important thing is that the coefficient of kinetic friction
is less than the coefficient of static friction.
In other words, kinetic friction is weaker than static friction.
This is borne out by experience. You know that if you're pushing something
and it's hard to get it moving, once you've got them moving and beating friction, it easier to keep it moving.
And that's because once it's moving, the frictional force is less
because the roughness of the surface will matter less if the object is already moving.