- Good morning. The equation for the force of friction is...
The force of friction equals the
coefficient of friction times the force normal.
However, because the force of friction
can either be static or kinetic,
this equation actually works out
to be three different equations.
♫ Flipping Physics ♫
For kinetic friction, where the two surfaces slide
relative to one another, the equation is...
The force of kinetic friction equals
the coefficient of kinetic friction times the force normal.
All I did was add a k subscript for kinetic to
both the force of friction and the coefficient of friction.
Now, when it comes to static friction,
where the two surfaces do not slide
relative to one another, it is a bit more complicated.
The force of static friction is less than or equal to
the coefficient of static friction times the force normal.
Therefore, the force of static friction maximum
is equal to the coefficient of
static friction times the force normal.
- [Billy] Mr. P!
- Yes, Billy?
- Isn't that second equation for
static friction a bit redundant?
The equation force of static friction
is less than or equal to the coefficient
of static friction times force normal
already shows us the maximum force of
static friction is equal to the coefficient
of static friction times force normal.
I mean, that's a part of what
"less than or equal to" means, right?
- Yes, Billy, you are correct.
However, we end up using the equation
for the force of static friction maximum very often,
and therefore I find it helps students understand it better
that we have a separate equation for
the force of static friction maximum.
- Okay!
- Now we need an example.
Please watch carefully as I apply a force on this book.
Bobby, could you please tell me
all the forces and their directions
which are acting on the book while
I'm applying this force on it?
- There is the force applied to the right,
the force of gravity straight down,
the force normal up, and the force of friction to the left.
- [Mr. P] Is that static or kinetic friction?
- Static, because the book isn't
sliding relative to the table.
- Let's talk briefly about the direction of
the force of static friction in this free-body diagram.
Billy, could you please tell me the three things
Bobby told us to remember from his video
about the direction of the force of friction?
- The force of friction is always parallel to the surfaces,
is independent of the direction of the force applied, and...
- Opposes sliding or motion.
- That's right, it opposes sliding.
Now clearly, the force of static friction
is parallel to the table.
Now, as far as being independent of
the direction of the force applied,
we're gonna talk about that in later lessons, not today.
Now, as far as opposing the sliding motion,
I want to make sure we understand that,
so Bobby, what does this mean, that the book is
opposing sliding, I mean, the book doesn't move, does it?
- No, the book isn't moving...
If there were no friction, the book would
slide to our right, so the force of static friction is
preventing the book from sliding to the right, therefore,
the force of static friction needs to be to the left.
- [Mr. P] That is correct!
Now, let's talk about the magnitude
of the force of static friction.
That will help us to understand
this less than or equal to sign in the equation.
Bo, could you please sum the forces in the x direction?
- The net force in the x direction equals the force applied
minus the force of static friction,
which then equals mass times acceleration in
the x direction; because the book is at rest,
the acceleration of the book in the x direction is zero,
so the right hand side of the equation equals zero.
We can add the force of static friction to both sides,
therefore the force applied equals
the force of static friction.
Those two forces are equal in magnitude
and opposite in direction.
- Great! The magnitude of the force applied is
equal to the magnitude of the force of static friction.
Now, let's assume that the maximum force of static friction
between the book and the table is 1.8 newtons.
Now, if I apply a force of 1 newton to the book,
class, what is the magnitude of
the force of static friction?
- [All] One newton!
- Correct! We just showed that the force applied and
the force of static friction are equal in magnitude,
therefore if I applied a force of one newton,
the force of static friction will also
have a magnitude of one newton.
Now, what if I increase the force
I'm applying to the book to 1.5 newtons?
Class, what then is the force of static friction?
- [All] 1.5 newtons!
- [Mr. P] Correct again! If I apply a force of 1.7 newtons,
what is the magnitude of the force of static friction?
- [All] 1.7 newtons!
- Still correct! If I apply a force of 1.9 newtons,
what is the magnitude of the force of static friction?
- [Billy] 1.9... - [Bo] 1.8, uh...
- [Mr. P] (laughs) All right, let's try that one again.
If I apply a force of 1.9 newtons,
what is the magnitude of the force of static friction?
- Oh, it's larger than the maximum force of
static friction, so the book moves, and the
friction switches from static to kinetic.
- Then there is no force of static friction!
- Only kinetic friction, the force of static friction
is zero, because the book is moving.
- [Mr. P] Correct! The force of static friction
increases and decreases in an attempt to
prevent the object from moving.
In this particular case, once the force applied
exceeded the maximum force of static friction,
the book began to move, and the friction
switched from static to kinetic friction.
And again, that's what this less than or equal to
sign means in the force of static friction equation,
that force of static friction increases and decreases in
an attempt to prevent the object from moving.
Now, let's pretend for a moment that the
force of static friction always equaled its maximum value.
In this particular case, we're going to pretend that the
force of static friction always equals 1.8 newtons,
it doesn't adjust, it always equals 1.8 newtons.
What would happen, then, when I
apply a force of 1 newton to the book?
- The force of static friction would be greater
than the force applied, and the book was trying to
slide to the left, opposite the direction you pushed it.
- [Bo] Yeah, that doesn't make any sense.
- Right, that doesn't make any sense.
So, rather than being a constant number,
the force of static friction adjusts
in an attempt to prevent the object from moving.
Thank you very much for learning with me today,
I enjoyed learning with you.