- Good morning.
The equation for the Force of Friction is...
The Force of Friction equals the Coefficient of Friction
times the Force Normal, and today
we are going to make sure that you understand
what the Coefficient of Friction is.
- [Song] Flipping Physics!
- The symbol for the Coefficient of Friction
is the lowercase Greek letter mu.
The word "mu" is spelled m-u and
the symbol looks like a "u" with a tail at the front.
Let's solve for the units for the Coefficient of Friction.
When we divide both sides by the Force Normal,
we end up with the equation "The Coefficient of Friction
equals the Force of Friction divided by the Force Normal."
Bo, what then are the dimensions
for the Coefficient of Friction?
- Well, Newtons are the dimensions for both
the Force of Friction and the Force Normal.
Therefore, the units for the Coefficient of Friction
are Newtons divided by Newtons.
- But then the Newtons cancel out,
which leaves us with no dimensions.
Is the Coefficient of Friction dimensionless?
- Yes, mu, the Coefficient of Friction,
is our first dimensionless variable.
It has no units.
It represents the ratio of the Force of Friction
divided by the Force Normal for any two
given surfaces and therefore has no dimensions.
Now, the Coefficient of Friction depends on the materials
of the two surfaces which are interacting
to cause the Force of Friction.
There are many published values for
Coefficients of Friction.
Here is one table from Engineershandbook.com.
Now, there are too many numbers here
to discuss in this lecture, so let's
reduce this table down to a few values
and look more closely at those.
You can see, if aluminum is in contact
with mild steel, the Coefficient of Static Friction
is 0.61, and the Coefficient of Kinetic Friction is 0.47.
If glass is in contact with nickel, the Coefficient
of Static Friction is 0.78 and the Coefficient
of Kinetic Friction is 0.56.
You can find all sorts of tables
for coefficients of friction between different materials.
However, it is very important to understand
the statement made at the top of the table
I found at engineershandbook.com.
"Extreme care is needed in using friction
coefficients and additional independent
references should be used.
For any specific application the ideal method of determining
the coefficient of friction is by trials."
In other words, coefficients of friction
depend on the two specific surfaces
which are contacting one another,
and you should perform experiments
to determine the coefficients of friction
instead of relying on published values.
There's no theoretical way to determine
coefficients of friction, you must perform experiments.
Billy, could you please take a look
at the reduced table of coefficients
of friction and tell me what you see
about the relationship between the static
and kinetic coefficients of friction
for any set of two interacting materials.
- Well, for aluminum on mild steel,
the Static Coefficient of Friction
is greater than the Kinetic, and for
glass on glass, the Coefficient of Static Friction
is greater than the Coefficient of Kinetic Friction.
It looks like that's true for all of the materials
on this data table.
For any two contacting surfaces, the Static Coefficient
of Friction is greater than the Kinetic
Coefficient of Friction, right?
- Billy, you are correct.
Have you ever noticed it is harder
to start something moving than it is
to keep it in motion?
- Sure.
- Yeah.
- That is because for any two interacting
surfaces, the Coefficient of Static Friction
is greater than the Coefficient of Kinetic Friction.
Therefore, the maximum Force of Static Friction
is greater than the force of Kinetic Friction,
therefore it is harder to start something
moving than it is to keep it moving.
Bobby, what would the Coefficient of Friction
be if something were frictionless?
- If there were no friction, wouldn't
the Coefficient of Friction be zero?
- Yes, a frictionless interaction
would have a Coefficient of Friction of zero.
That would give us zero as a lowest
possible number for the Coefficient of Friction.
In other words, the Coefficient of Friction
could never be less than zero.
As far as an upper range, the highest
published value I have seen is a value
of four, and that was for drag racing tires
on dry concrete.
Admittedly, drag racing is a bit
of an extreme situation, therefore
under normal circumstances, I would say
a maximum is perhaps two.
So, if you're solving a problem
and it's under normal circumstances,
if you get something outside of that range
from zero to two, then I would say
you need to re-examine your solution.
Thank you very much for learning with me today.
I enjoyed learning with you.