Friction Friction Problem Situations

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FrictionFriction Problem Situations

• Physics
• Montwood High School
• R. Casao

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Friction

• Friction Ff is a force that resists motion
• Friction involves objects in contact with each
  other.
• Friction must be overcome before motion occurs.
• Friction is caused by the uneven surfaces of the
  touching objects. As surfaces are pressed
  together, they tend to interlock and offer
  resistance to being moved over each other.

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Microscopic Friction
Surface Roughness
Adhesion
Magnified section of a polished steel surface
showing surface bumps about 5 x 10-7 m (500 nm)
high, which corresponds to several thousand
atomic diameters.
Computer graphic from a simulation showing
gold atoms (below) adhering to the point of a
sharp nickel probe (above) that has been in
contact with the gold surface.
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Friction

• Frictional forces are always in the direction
  that is opposite to the direction of motion or to
  the net force that produces the motion.
• Friction acts parallel to the surfaces in
  contact.

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Types of Friction

• Static friction maximum frictional force
  between stationary objects.
• Until some maximum value is reached and motion
  occurs, the frictional force is whatever force is
  necessary to prevent motion.
• Static friction will oppose a force until such
  time as the object breaks away from the surface
  with which it is in contact.
• The force that is opposed is that component of an
  applied force that is parallel to the surface of
  contact.

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Types of Friction

• The magnitude of the static friction force Ffs
  has a maximum value which is given by
• where µs is the coefficient of static friction
  and FN is the magnitude of the normal force on
  the body from the surface.

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Types of Friction

• Sliding or kinetic friction frictional force
  between objects that are sliding with respect to
  one another.
• Once enough force has been applied to the object
  to overcome static friction and get the object to
  move, the friction changes to sliding (or
  kinetic) friction.
• Sliding (kinetic) friction is less than static
  friction.
• If the component of the applied force on the
  object (parallel to the surface) exceeds Ffs then
  the magnitude of the opposing force decreases
  rapidly to a value Fk given bywhere µk is the
  coefficient of kinetic friction.

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Static Friction
The static frictional force keeps an object
from starting to move when a force is applied.
The static frictional force has a maximum value,
but may take on any value from zero to the
maximum, depending on
what is needed to keep the sum of forces zero.
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Types of Friction

• From 0 to the maximum value of the static
  frictional force Fs in the figure, the applied
  force is resisted by the static frictional force
  until breakaway.
• Then the sliding (kinetic) frictional force Fk is
  approximately constant.

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Types of Friction

• Static and sliding friction are dependent on
• The nature of the surfaces in contact. Rough
  surfaces tend to produce more friction.
• The normal force (Fn) pressing the surfaces
  together the greater Fn is, the more friction
  there is.

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Friction vs. Area
Question Why doesnt friction depend on
contact area? The microscopic area of
contact between a box and the floor is only a
small fraction of the macroscopic area of the
boxs bottom surface. If the box is turned
on its side, the macroscopic area is increased,
but the microscopic area of contact remains the
same (because the contact is more distributed).
Therefore the frictional force f is independent
of contact area.
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Types of Friction

• Rolling friction involves one object rolling
  over a surface or another object.
• Fluid friction involves the movement of a fluid
  over an object (air resistance or drag in water)
  or the addition of a lubricant (oil, grease,
  etc.) to change sliding or rolling friction to
  fluid friction.

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Coefficient of Friction

• Coefficient of friction (?) ratio of the
  frictional force to the normal force pressing the
  surfaces together. ? has no units.
• Static
• Sliding (kinetic)

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The maximum frictional force is 50 N. As the
applied force increases from 0 N to 50 N, the
frictional force also increases from 0 N to 50 N
and will be equal to the applied force as it
increases.
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Once the static frictional force of 50 N has been
overcome, only a 40 N force is needed to overcome
the 40 N kinetic frictional force and produce
constant velocity (a 0 m/s2).
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As the applied force increases beyond 40 N, the
kinetic frictional force remains at 40 N and the
100 N block will accelerate.
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A Model of Friction
Friction
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Static Friction
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Kinetic Friction
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Kinetic Friction and Speed
The kinetic frictional force is also
independent of the relative speed of the
surfaces, and of their area of contact.
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Rolling Friction
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Horizontal Surface Constant Speed

• Constant speed a O m/s2.
• The normal force pressing the surfaces together
  is the weight Fn Fw

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Horizontal Surface a gt O m/s2
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Horizontal Surface a gt O m/s2

• If solving for
• Fx
• Ff
• a

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Horizontal Surface Skidding to a Stop or
Slowing Down (a lt O m/s2)

• The frictional force is responsible for the
  negative acceleration.
• Generally, there is no Fx.

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Horizontal Surface Skidding to a Stop or
Slowing Down (a lt O m/s2)

• Most common use involves finding acceleration
  with a velocity equation and finding mk
• Acceleration will be negative because the speed
  is decreasing.

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Horizontal Surface Skidding to a Stop or
Slowing Down (a lt O m/s2)

• The negative sign for acceleration a is dropped
  because mk is a ratio of forces that does not
  depend on direction.
• Maximum stopping distance occurs when the tire is
  rotating. When this happens, a -msg.
• Otherwise, use a -mkg to find the
  acceleration, then use a velocity equation to
  find distance, time, or speed.

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Friction, Cars, Antilock Brakes
The diagram shows forces acting on a car
with front-wheel drive. Typically, Fn gt Fn
because the engine is over the front wheels. The
largest frictional force fs the tire can exert on
the road is µsFn. Attempts to make the tire
exert a force larger than this causes the tire to
burn rubber and actually reduces the force,
since µkltµs. Note that while all points on
the rolling tire have the same speed v in the
reference frame of the car, in the reference
frame of the road the bottom of the tire is at
rest, while top is moving forward with a speed of
2v. Antilock brakes sense the wheel
rotation and ease off if it close to stopping,
maintaining static friction with the road and
allowing better control of steering than if the
wheels were locked.
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Antilock Brakes
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ExampleThe Effect of Antilock Brakes
A car is traveling at 30 m/s along a
horizontal road. The coefficients of friction
are ms0.50 and mk0.40. (a) What is the braking
distance ?xa with antilock brakes? (b) What is
the braking distance ?xb if the brakes lock?
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Example A Game of Shuffleboard
A cruise-ship passenger uses a shuffleboard
cue to push a shuffleboard disk of mass 0.40 kg
horizontally along the deck, so that the disk
leaves the cue at a speed of 8.5 m/s. The disk
then slides a distance of 8.0 m. What is the
coefficient of kinetic friction between the disk
and deck?
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Down an Inclined Plane
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Down an Inclined Plane

• Resolve Fw into Fx and Fy.
• The angle of the incline is always equal to the
  angle between Fw and Fy.
• Fw is always the hypotenuse of the right triangle
  formed by Fw, Fx, and Fy.

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Down an Inclined Plane

• The force pressing the surfaces together is NOT
  Fw, but Fy Fn Fy.
• or

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Down an Inclined Plane

• If we place an object on an inclined plane and
  increase the tilt angle ? to the point at which
  the object just begins to slide.
• What is the relation between ? and the static
  coefficient of friction µs?

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Down an Inclined Plane

• If the object slides down the incline at constant
  speed (a 0 m/s2), the relation between ? and
  the kinetic coefficient of friction µk

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Down an Inclined Plane

• To determine the angle of the incline
• If moving
• If at rest

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Example A Sliding Coin
A hardcover book is resting on a tabletop
with its front cover facing upward. You place a
coin on the cover and very slowly open the book
until the coin starts to slide. The angle ? is
the angle of the cover just before the coin
begins to slide. Find the coefficient of
static friction µs between the coin and book.
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ExampleDumping a file cabinet
Steel on dry steel Þ
Free-body diagram
A 50.0 kg steel file cabinet is in the back of a
dump truck. The trucks bed, also made of steel,
is slowly tilted. What is the size of the static
friction force when the trucks bed is tilted by
20? At what angle will the file cabinet begin
to slide?
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ExampleDumping a file cabinet
File cabinet will begin to slide when
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Non-Parallel Applied Force on Ramp
If an applied force acts on the box at an angle ?
above the horizontal, resolve FA into parallel
and perpendicular components using the angle ?
? FA cos (? ?) and FA sin (? ?) FA
serves to increase acceleration directly and
indirectly directly by FA cos (? ?) pulling
the box down the ramp, and indirectly by FA sin
(? ?) lightening the normal support force with
the ramp (thereby reducing friction).
FA sin(? ? )
FA
N
fk
?

?
FA cos(? ? )
mg sin?
?
mg
mg cos?
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Non-Parallel Applied Force on Ramp
FA sin (? ?)
If FA sin(? ? ) is not big enough to lift the
box off the ramp, there is no acceleration in the
perpendicular direction. So, FA sin(? ? )
FN mgcos?. Remember, FN is what a scale
would read if placed under the box, and a scale
reads less if a force lifts up on the box. So,
FN mg cos? - FA sin(? ? ), which means
fk ?k FN ?k mg cos? - FA sin(? ? ).
FA
N
fk
?

?
FA cos(? ? )
mg sin?
?
mg cos?
mg
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Non-Parallel Applied Force on Ramp

FA sin(? ? )
FA
N
fk
?

?
FA cos(? ? )
mg sin?
?
If the combined force of FA cos(? ? ) mg
sin? is is enough to move the box FA cos(?
? ) mgsin? - ?k mgcos? - FA sin(?
? ) ma
mg cos?
mg
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Up an Inclined Plane
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Up an Inclined Plane

• Resolve Fw into Fx and Fy.
• The angle of the incline is always equal to the
  angle between Fw and Fy.
• Fw is always the hypotenuse of the right triangle
  formed by Fw, Fx, and Fy.

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Up an Inclined Plane

• Fa is the force that must be applied in the
  direction of motion.
• Fa must overcome both friction and the
  x-component of the weight.
• The force pressing the surfaces together is Fy.

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Up an Inclined Plane

• For constant speed, a 0 m/s2.
• Fa Fx Ff
• For a gt 0 m/s2.
• Fa Fx Ff (ma)

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Pulling an Object on a Flat Surface
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Pulling an Object on a Flat Surface

• The pulling force F is resolved into Fx and Fy.

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Pulling an Object on a Flat Surface

• Fn is the force that the ground exerts upward on
  the mass. Fn equals the downward weight Fw minus
  the upward force Fy from the pulling force.
• For constant speed, a 0 m/s2.

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Example Pulling A Sled
Two children sitting on a sled at rest in
thesnow ask you to pull them. You pull on the
sleds rope, which makes an angle of 40
withthe horizontal. The children have a
combinedmass of 45 kg, and the sled has a mass
of 5.0 kg. The coefficients of static and
kineticfriction are µs0.20 and µk0.15, and the
sled is initially at rest. Find the acceleration
of the sled and children if
the rope tension is 100 N.
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Simultaneous Pulling and Pushing an Object on a
Flat Surface
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Simultaneous Pulling and Pushing an Object on a
Flat Surface
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Pushing an Object on a Flat Surface
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Pushing an Object on a Flat Surface

• The pushing force F is resolved into Fx and Fy.

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Pushing an Object on a Flat Surface

• Fn is the force that the ground exerts upward on
  the mass. Fn equals the downward weight Fw plus
  the upward force Fy from the pushing force.
• For constant speed, a 0 m/s2.

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Pulling and Tension

• The acceleration a of both masses is the same.

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Pulling and Tension

• For each mass
• Isolate each mass and examine the forces acting
  on that mass.

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Pulling and Tension

• m1 mass
• T1 may not be a tension, but could be an applied
  force (Fa) that causes motion.

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Pulling and Tension

• m2 mass

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Pulling and Tension

• This problem can often be solved as a system of
  equations
• See the Solving Simultaneous Equations notes for
  instructions on how to solve this problem using a
  TI or Casio calculator.

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Revisiting Tension and Friction
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Revisiting Tension and Friction

• For the mass on the table, m1

• For the hanging mass, m2
• The acceleration a of both masses is the same.

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Revisiting Tension and Friction
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Example A Sliding Block

• A block of mass m2 5.0 kg has been adjusted so
  that the block m1 7.0 kg is just on the verge
  of sliding.
• What is the coefficient of static friction ms
  between the table and the block?

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Example A Sliding Block

• (b) With a slight push, the blocks move with
  acceleration a. Find a if µk 0.54.

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Normal Force Not Associated with Weight.

• A normal force can exist that is totally
  unrelated to the weight of an object.

FN applied force
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Friction is Always Parallel to Surfaces.

• In this case, for the block to remain in position
  against the wall without moving
• the upward frictional force Ff has to be equal
  and opposite to the downward weight Fw.
• The rightward applied force F has to be equal ad
  opposite to the leftward normal force FN.

F
(0.20)