# Review friction

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```					Newton’s Laws

Applications
Friction
   Friction is the force that opposes a sliding
motion.
   Friction is due to microscopic irregularities
in even the smoothest of surfaces.
Microscopic View
Big view:
N      Surfaces look
perfectly smooth.
(friction)
Fpush
f
W
Small view:
Microscopic
irregularities
resist movement.

Friction may or may not exist between two surfaces. The direction of
friction, if it exists, is opposite to the direction object will slide when
subjected to a horizontal force. It is always parallel to the surface.
Friction
   Friction is the force that opposes a sliding
motion.
   Friction is due to microscopic irregularities
in even the smoothest of surfaces.
   Friction is highly useful. It enables us to
walk and drive a car, among other things.
   Friction is also dissipative. That means it
causes mechanical energy to be converted
Friction depends on the
normal force.
   The friction that exists between two surfaces is
directly proportional to the normal force.
   Increasing the normal force increases friction;
decreasing the normal force decreases friction.
   This has several implications, such as…
   Friction on a sloping surface is less than friction on a flat
surface (since the normal force is less on a slope).
   Increasing weight of an object increases the friction
between the object and the surface it is resting on.
   Weighing down a car over the drive wheels increases the
friction between the drive wheels and the road (which
increases the car’s ability to accelerate).
Static Friction
   This type of friction occurs between
two surfaces that are not slipping
relative to each other.
   f s  s N
   fs : static frictional force (N)
   s: coefficient of static friction
   N: normal force (N)
fs < sN is an inequality!
   The fact that the static friction equation is an inequality
has important implications.
   Static friction between two surfaces is zero unless there
is a force trying to make the surfaces slide on one
another.
   Static friction can increase as the force trying to push an
object increases until it reaches its maximum allowed
value as defined by s.
   Once the maximum value of static friction has been
exceeded by an applied force, the surfaces begin to slide
and the friction is no longer static friction.
Static friction and applied
horizontal force

Force Diagram

N

Physics
surface
W

fs = 0
There is no static friction since there is no applied
horizontal force trying to slide the book on the surface.
Static friction and applied
horizontal force

Force Diagram

N

fs         Physics       F
surface
W

0 < fs < sN   and   fs = F
Static friction is equal to the applied horizontal force, and
there is no movement of the book since SF = 0.
Static friction and applied
horizontal force

Force Diagram

N

fs                    Physics             F
surface
W

fs = sN   and   fs = F
Static friction is at its maximum value! It is still equal to F,
but if F increases any more, the book will slide.
Static friction and applied
horizontal force

Force Diagram

N

fk                  Physics                           F
surface
W

fs = sN      and   fs < F
Static friction cannot increase any more! The book accelerates to the
right. Friction becomes kinetic friction, which is usually a smaller force.
Kinetic Friction
   This type of friction occurs between
surfaces that are slipping past each other.
   fk = kN
   fk : kinetic frictional force (N)
   k: coefficient of kinetic friction
   N: normal force (N)
   Kinetic friction (sliding friction) is
generally less than static friction
(motionless friction) for most surfaces.
Sample Problem
A boulder of mass 45 kg is pushed on a surface with a coefficient
of kinetic friction of 0.85. What force has to be applied to
produce an acceleration of 0.20 m/s2?
Problem
The coefficient of kinetic friction for wood on wood is 0.55.
What is the force of friction of a wood block of mass 3.5 kg
being pulled on a wood floor?
Sample Problem
A brick has a mass of 1.2 kg. A force of 5.4 N is needed to move
the brick along the floor with a constant velocity. What is the
coefficient of friction?
Static friction on a ramp

Without friction, the
book will slide down the
ramp. If it stays in
place, there is
sufficient static
q                    friction holding it there.

Wx = mgsinq and N = mgcosq
At maximum angle before the book slides, we can
prove that s = tanq.
Static friction on a ramp

Assume q is
maximum angle                SF = 0
for which book               Wx = fs
stays in place.              mgsinq = smgcosq
s = sinq/cosq = tanq
q
q
fs = mgsinq and N = mgcosq
At maximum angle before the book slides, we can
prove that s = tanq.
Tension and Strings and Springs
Tension
   Tension is a pulling force that arises when
a rope, string, or other long thin material
resists being pulled apart without
stretching significantly.
   Tension always pulls away from a body
attached to a rope or string and toward
the center of the rope or string.
A physical picture of tension

Imagine tension to be the internal force preventing a rope
or string from being pulled apart. Tension as such arises
from the center of the rope or string. It creates an equal
and opposite force on objects attached to opposite ends
of the rope or string.
Tension examples

Note that the
pulleys shown are
magic! They
affect the
tension in any
way, and serve
only to bend the
line of action of
the force.
Springs (Hooke’s Law)
   The magnitude of the force exerted by a
spring is proportional to the amount it is
stretched.
   F = kx
   F: force exerted by the spring (N)
   k: force constant of the spring (N/m or N/cm)
   x: displacement from equilibrium (unstretched
and uncompressed) position (m or cm)
   The direction of the force is back toward
the equilibrium (or unstretched) position.
Sample problem
A 1.50 kg object hangs motionless from a spring with a
force constant of k = 250 N/m. How far is the spring
stretched from its equilibrium length?
Sample problem
A 1.80 kg object is connected to a spring of force constant 120
N/m. How far is the spring stretched if it is used to drag the
object across a floor at constant velocity? Assume the
coefficient of kinetic friction is 0.60.
Uniform Circular Motion
   An object that moves at uniform speed in a
circle of constant radius is said to be in
uniform circular motion.
   Question: Why is uniform circular motion
accelerated motion?
   Answer: Although the speed is constant,
the velocity is not constant since an object
in uniform circular motion is continually
changing direction.
Centrifugal Force
   Question: What is centrifugal force?
   Answer: That’s easy. Centrifugal force is
the force that flings an object in circular
motion outward. Right?
   Wrong! Centrifugal force is a myth!
   There is no outward directed force in
circular motion. To explain why this is the
case, let’s review Newton’s 1st Law.
Newton’s         1st   Law and cars
•When a car accelerates forward suddenly,
you as a passenger feel as if you are flung
backward.
• You are in fact NOT flung backward. Your body’s
inertia resists acceleration and wants to remain
at rest as the car accelerates forward.
•When a car brakes suddenly, you as a
passenger feel as if you are flung forward.
• You are NOT flung forward. Your body’s inertia
resists acceleration and wants to remain at
constant velocity as the car decelerates.
When a car turns

   You feel as if you are flung to the outside. You call this apparent, but
nonexistent, force “centrifugal force”.
   You are NOT flung to the outside. Your inertia resists the inward
acceleration and your body simply wants to keep moving in straight line
motion!
   As with all other types of acceleration, your body feels as if it is being
flung in the opposite direction of the actual acceleration. The force on
your body, and the resulting acceleration, actually point inward.
Centripetal Acceleration
   Centripetal (or center-seeking)
acceleration points toward the center
of the circle and keeps an object
moving in circular motion.
   This type of acceleration is at right
angles to the velocity.
   This type of acceleration doesn’t
speed up an object, or slow it down, it
just turns the object.
Centripetal Acceleration
   ac = v2/r
   ac: centripetal
acceleration in m/s2
   v: tangential speed in m/s   v ac

Centripetal acceleration always points
toward center of circle!
Centripetal Force
   A force responsible for
centripetal acceleration is
referred to as a centripetal
force.                             Fc
   Centripetal force is simply mass
times centripetal acceleration.
   Fc = m ac
Always toward
   Fc = m v2 / r

   Fc: centripetal force in N
center of circle!
   v: tangential speed in m/s
Any force can be centripetal
   The name “centripetal” can be applied to
any force in situations when that force is
causing an object to move in a circle.
   You can identify the real force or
combination of forces which are causing
the centripetal acceleration.
   Any kind of force can act as a centripetal
force.
Static friction
As a car makes a
what is the real
identity of the
centripetal force?
Tension

As a weight is tied
to a string and spun
in a circle, what is
the real identity of
the centripetal
force?
Gravity
As the moon orbits the
Earth, what is the real
identity of the
centripetal force?
Normal force with help from
static friction
As a racecar turns on a
banked curve on a
racing track, what is
the real identity of the
centripetal force?
Gravity, with some help from
the normal force
When you are
riding the
CAROLINA
COBRA at
Carowinds, what
is the real
identity of the
centripetal force
when you are on a
vertical loop?
Sample problem
   A 1200-kg car rounds a corner of radius r = 45 m.
If the coefficient of static friction between tires
and the road is 0.93 and the coefficient of kinetic
friction between tires and the road is 0.75, what
is the maximum velocity the car can have without
skidding?

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