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# PH 121 S15 6.4-6.6

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## Richard Datwyler

on 17 May 2018

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#### Transcript of PH 121 S15 6.4-6.6

Friction and Drag
Friction is not the most precise and
unambiguous of forces.

We can give a solid answer to the force
from a spring, or gravity, But friction
depends...
The model we will use has been around for
a long while. It states that friction is proportional
to the normal force.

And that each surface has a coefficient of friction.
These coefficients are not as precise as we would like to believe, but they are what we have.
We will discuss 3 types of Friction
Static
Kinetic
Rolling
Static friction is probably the
most complicated.
It is the force of friction if the object
is not moving. This is the same idea
as static equilibrium.
The stickiness to it is, that it can
range from zero, up to a maximum
value. Depending on the force and the
material of the surfaces.
This range however is 1-to-1 linear
from zero up to that max value.
Meaning that If I push on the object
with 5 N, static friction also pushes 5 N
10N to 10N and so on until the maximum
value is reached.
It takes the form of:
Where n is the normal force
and mu is the coefficient of
Static friction.
Things to note with this form of friction
It is not equal to that maximum value unless
it is just starting to slip.
Thus when these problems are written they look
like:

"what minimum force is require to start a book sliding"
or
"What is the maximum angle that a car can park if it is
not to slide..."
Kinetic friction

This is probably the most
common and most understood
of the different types of friction.
Kinetic friction exists when something
is moving against something else.
Kinetic friction is also nearly constant
and in our model of friction it will be
so:
Also to be noted is that this coefficient
is always less than the coefficient for
static friction. YET the kinetic friction force
is not always less than static. Again this is
because the static ranges from zero to max.
One often sees graphs for this like the following
Force push
Friction
static
at rest
kinetic
accelerating
max
F
fs
slope = 1
The last we will talk on is rolling friction
Rolling friction is not kinetic. It does not slide.

It is closer to static friction, especially when you talk about the causes of friction.
When a tire, circular object 'rolls'
It makes contact with the surface.
This contact is small, but not negligible
This contact makes a connection between
the surfaces, which has to be broken as
the wheel moves on. This is where the force
of rolling friction comes in.
But it is closer to kinetic friction in how it is
used. It is constant
Here is a little table to compare these coefficients for you.
Static

1.00

0.80

0.10

0.5

0.12

0.10
Kinetic

0.80

0.60

0.05

0.2

0.06

0.03
rolling

0.02

0.002
Material

Rubber on concrete
Steel on Steel (dry)
Steel 0n Steel (lubricated)
Wood on wood

Wood on Snow

Ice on Ice
Our model of friction
Which is the smallest of the three forces of friction:
A. Static
B. Kinetic
C. Rolling
D. Depends
Which has the Lowest coefficient
of the three types
A. Static
B. Kinetic
C. Rolling
D. Depends
This is just a model, it is not a perfect model
but it does pretty good.

What things are we missing, or ignoring in this
model?
no surface area.

Kinetic is independent of speed.

others...
Causes of Friction

What cause it?

In static friction the two surfaces
are in close contact and the atoms
actually form bonds between each surface.
Kinetic friction, this doesn't happen to as
much an extent.
Some bonds are formed, but not as many

This is why kinetic is less that maximum
static friction
In thinking on the causes of kinetic friction, at times a particular eruption of atoms sticks or
collides with another on the opposite surface. When this happens a bond is formed, and then the weaker bond inside the substance will break, leaving pieces of the object behind.

This is why shoes, and tires wear out. It is called abrasion.
With this idea comes lubricants.

Liquids often help make the atoms not
touch each other, but filling the space between
the substances, causing them to move by without
forming bonds.
Drag
Terminal speed.
The force of drag is always opposite the direction
of motion, think opposite velocity.
Also it increases in magnitude as the speed of the
object increases.
Drag is a very complex force.
It can take on different terms depending on
the speed, size and viscosity of the substance
that you move through.
In this text they use a simplified model that accounts for
Size (cross sectional, needs to be .001 - 10 m)
Speed must be relatively small
Just moving through atmosphere close to earth
With those three the force of Drag takes the form of:
As it rises, Drag 'works'
with gravity
Causing it to have a larger
acceleration
As it falls, Drag is opposite
the acceleration due to gravity
this causes it to accelerate slower on the way down.
Notice that although Drag doesn't depend on mass, the acceleration does
Because drag depends on speed, the force will
continue to grow until it becomes equal to the
force of gravity.
When this happens then the net force becomes
zero

This speed is defined as terminal speed,
it is the top speed possible for an object of
a specific shape and size.

We solve for this by setting the two forces equal.
Fg = D
Solving for velocity gives:
44.) A baggage handler drops your 10 kg suitcase onto a conveyor belt running at 2.0 m/s. The materials are such that the coefficients of static and kinetic friction are: 0.50 and 0.30 respectively. How far is your suitcase dragged before it is riding smoothly on the belt?
46.) It's moving day and you need to push a 100 kg box up a 20 degree ramp into the truck. The coefficients of friction for the box on the ram are 0.90 and 0.60, static and kinetic respectively. Your largest pushing force is 1000 N. Can you get the box into the truck without assistance if you get a running start at the ramp? If you stop on the ramp, will you be able to get the box moving again?
.68 m
yes a = 1.12
no

"Can we work some problems for drag?"
"so if friction is caused by electromagnetism, then do all things have a magnetic field?"
" Why are the equations for friction all so similar?"
"Talking about drag what happen when the object get past the speed of sound?"
"why is friction caused by electromagnetic forces and not gravitational?"
C is a constant that describes how Aerodynamic the object is (ranges form 0-1.5)
rho is the the density of the material (aire)
A is cross sectional area
v is velocity
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