Resistance

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Resistance
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Resistance Mechanical
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Review of Forces

• Force is the prime mover in the mechanical system
• Force is a vector that can be represented by an
  arrow
• Vectors have magnitude and direction
• Types of forces
• Contact Applied, Tension, Normal, Friction
• Long-range Gravitational, Electric, Magnetic

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Review Force Diagrams

• Draw the object as a point
• Draw all forces as arrows (length represents the
  relative magnitude)
• Choose a positive and a negative direction
• Treat horizontal and vertical forces separately
• Find the net force

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Review Newtons 1st Law

• Also called the Law of Inertia
• Objects at rest remain at rest, and objects in
  motion remain in motion with a constant velocity
  unless acted upon by a net force.
• When all the forces on an object are balanced,
  the object is in equilibrium
• No change in motion (no acceleration) or shape
• When the forces are unbalanced, the net force
  causes a change
• Acceleration or deformation
• Acceleration is always in the same direction as
  the net force

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Resistance

• Inertia The tendency of an object to RESIST a
  change in motion
• Mass is a measure of inertia
• More mass, the harder to move or stop
• Measured in kg in the Metric system
• Measured in slugs in the English system
• The greater the mass of an object, the harder it
  is to move with the same applied force.
• The less massive object will experience a greater
  change in motion.

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Newtons 2nd Law of Motion (Acceleration)

• The acceleration of an object is directly
  proportional to the net force (Fnet) acting on
  the object and inversely proportional to the mass
  (m) of the object.

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Newtons 2nd Law

• If Acceleration Force/Mass
• Then Force Mass x Acceleration
• Fnet m a
• UNITS
• 1 Newton (N) 1 kgm/s2
• In the metric system One Newton is the force
  required to accelerate a 1 kg mass by 1 m/sec2
• Then 1 pound 1 slug-ft/s2

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Example Problems

• A 1200 kg car accelerates at 4 m/s2. Calculate
  the net force that pushes the car forward.
• Fnet m a
• (1200 kg) (4 m/s2) 4,800 kgm/s2 4,800 N
• 3 forces of 4 N to the right, 2 N to the left,
  and 3 N upward act on a 2.5 kg object. Find the
  acceleration of the object.
• a Fnet / m
• a (5 N) / (2.5 kg) 2 m/s2

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Weight.. Here We Go Again

• Objects on Earth are affected by the
  Gravitational force, causing them to accelerate
  at 10 m/s2
• Another way to write Newtons 2nd Law for
  gravitational forces
• Fg m g
• Where g is the acceleration due to gravity, 10
  m/s2
• g can also be measured in N/kg
• Fg is also called the weight

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Acceleration due to Gravity

• The elephant weighs more, but has more inertia
• The mouse weighs less, but also has less inertia
• The ratios equal out They accelerate at the same
  rate

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Using Newtons 2nd Law to calculate Weight and
Mass

• Wile E. Coyote is standing next to a cliff
  waiting for the road runner. (Why does he always
  stand next to a cliff?)
• His weight (Fg) is balanced by the upward force
  exerted on him by the mountain. Therefore, he
  does not fall.

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Using Newtons 2nd Law to calculate Weight and
Mass

• Inevitably, the road runner sneaks up from
  behind, makes that weird sound and the coyote
  jumps off the cliff.
• Once he jumps the upward force of the mountain is
  removed, gravity takes over and he falls
  (accelerates) at 10 m/s2 toward the canyon floor.

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Using Newtons 2nd Law to calculate Weight and
Mass

• This gravitational acceleration (g) is the
  constant used to determine an objects weight.
• 1 kg 10 N, or 2.2 lbs (1 lb 4.45 N)
• Calculate your mass in kg and your weight in
  Newtons
• If the Wile E. has a mass of 40 kg, what is the
  gravitational force on him? (Find his weight)
• Fg m g
• (40 kg)(10 m/s2)
• 400 N

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Newtons 2nd Law and Force Diagrams

• A person with a mass of 50 kg is riding the
  Rocket at Lagoon and it is moving upward at a
  rate of 4 m/s2. With how much force does the
  chair push up on the person?
• Fnet FN Fg
• (ma) FN (mg)
• (ma) (mg) FN
• (50 kg)(4 m/s2) (50 kg)(10 m/s2) FN
• 200 N 500 N FN
• 700 N FN

FN ?
Fg 500 N
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Newtons 2nd Law and Force Diagrams

• If the person with a mass of 50 kg is riding the
  Rocket is moving downward at a rate of 6 m/s2,
  with how much force does the chair push up on the
  person?
• Fnet Fg FN
• (ma) (mg) FN
• (50 kg)(6 m/s2) 500 N FN
• 500 N - 300 N FN
• 200 N FN

FN ?
Fg 500 N
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Friction

• Friction in solids results from any one or a
  combination of two general causes.
• Surface finish
• (nature of the surfaces)
• Cohesion or adhesion of molecules.
• Cohesion is the attraction of like molecules (two
  pieces of glass).
• Glue and tape are good examples of Adhesion.

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Friction

• Sometimes it is not desirable
• Hard to move stuff
• Slows you down
• Rubbing creates heat
• Sometimes it is desirable
• Required for walking, and between tires and road
• Conveyor belt can move boxes thanks to friction
• Brakes in your car require friction

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Finding the Frictional Force

• Weight (downward force caused by gravity) is
  equal to the normal force on a flat surface.
• Remember, the normal force is always
  perpendicular to the two surfaces sliding past
  one another.
• When at rest or constant speed
• Pull force equals friction

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Types of Friction

• Static (Fs)
• When stationary
• Harder to start moving
• Kinetic (Fk)
• Once in motion
• Easier to keep moving

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Frictional Force

• FFriction µ FN
• µ (Greek letter miu) coefficient of friction
• FN Normal force
• The coefficient of friction is a description of
  the proportionality of the friction force and
  normal force depending on the materials used
• Surface µs µk
• Wood on wood 0.5 0.2
• Wood on concrete 0.6 0.4
• Rubber on dry concrete 0.8 0.7
• Rubber on wet concrete 0.65 0.57
• Steel on steel (dry) 0.78 0.58
• Steel on steel (oiled) 0.11 0.05
• Steel on Teflon 0.04 0.04

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Example Problem

• If a person needs to slide a 10 kg wooden chest
  across the wooden floor of a cabin (µs 0.5),
  how much force will it take to get the chest to
  start moving?
• Fs µs FN
• µs Fg
• µs m g
• (0.5)(10 kg)(10 m/s2)
• 50 N

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Example Problem 2

• How much force is required to keep the same crate
  (m 10 kg) moving at a constant speed if the
  coefficient of kinetic friction is µk 0.2?
• Fs µk FN
• µk Fg
• µk m g
• (0.2)(10 kg)(10 m/s2)
• 20 N

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Lubrication

• Fluids can be used to decrease the friction
  between solid objects
• Fluids like oil flow in layers sliding past each
  other
• Much less friction than two rough surfaces
  sliding past each other!

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Resistance Fluid
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Fluid Resistance

• What a Drag!
• Just like friction, whenever there is relative
  motion between two objects, there is a drag force
  opposing the motion
• Frictional drag
• When layers of fluid flow past an object or wall
  of a pipe
• When layers of fluid flow past each other
• Pressure drag
• When there is a pressure difference in the fluid
  in front of and behind an object

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Laminar vs. Turbulent Flow

• Laminar or Streamlined Flow
• When a fluid flows smoothly in layers
• Paths of individual fluid particles do not cross
• Drag Friction between layers
• Turbulent Flow
• Disordered flow with eddies or wakes
• High speeds, around irregular shapes or sharp
  bends
• Drag Pressure differences are created

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Drag vs. Speed

• At low speed there is negligible turbulence and
  drag and speed have a linear relationship.
• At higher speeds turbulence starts which causes
  drag to increase dramatically

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Turbulence and Streamlining

• As an airplane moves through the air it drags
  layers of air with it. The layer closest to the
  plane moves the most and successive layers move
  less and less. Drag is a result of friction
  between these layers.
• Shape affects turbulence produced. Turbulence
  consists of small whirlpools of fluid that move
  in different directions. Streamlining an object
  allows the layers of fluid to flow smoothly over
  the object decreasing turbulence.

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Factors affecting Fluid Resistance

• Area of the pipe
• Length of the pipe
• Viscosity of fluid
• Think density..
• In liquids, viscosity decreases with temperature
• In gases, it increases with temperature

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Factors affecting Fluid Resistance

• Inside surface of the pipe
• Restrictions or blockage
• Turbulent or Laminar flow, relative speed

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Terminal Velocity

• As drag force depends on relative speed, it
  changes as an object accelerates
• When it reaches its maximum (depending on surface
  area, viscosity, and velocity) it balances out
  the weight of the object
• When forces are balanced, the object no longer
  accelerates

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Terminal Velocity

• Lighter objects quickly reach terminal velocity
  as not much drag is required to balance out their
  weight.
• Heavier objects continue to accelerate until the
  drag is enough to balance their weight and reach
  a higher terminal velocity.

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Newtons 3rd Law

• For every force, there is an equal (in magnitude)
  and opposite (in direction) force
• Also called the law of action-reaction
• When you fire a gun, why do you feel a
  kickback?
• How does a rocket accelerate in space?
• How do you win a Tug-of-War?

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Which Pulls Harder?

• An inanimate object like a paper or a wall can
  exert forces
• When the man connects the rope to the wall, he
  pulls with a force of 500 N. With what force
  does the wall pull back?
• Change the wall for an elephant.. If he pulls
  with 500 N..
• So does the elephant!

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Action-Reaction Pairs

• When a bat hits a ball, the ball hits the bat
  right back with the same amount of force.
• When a book rests on a table, what are the
  action-reaction pairs of forces?
• Earth pulls on book, book pulls on Earth
  book pushes on the table, table pushes on
  bookNOT Fg and FN!
• Two feet kick the same ball. Identify all the
  action reaction forces.
• NOT A and C!
• A on B, B on A C on B, B on C

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Same Force, Different Effects

• When a bug hits your windshield, which exerts a
  greater force? Bug or windshield?
• Same force, but because the bug has a very small
  inertia, by Newtons 2nd Law
• Its easy to accelerate or crush
• Your car has a lot of inertia so by Newtons 2nd
  Law
• Its hard to accelerate or crush!

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Review Mechanical

• Newtons 1st Law
• Law of Inertia
• No net force, no change in motion
• Newtons 2nd Law
• Fnet ma
• Net force causes acceleration More force, more
  acceleration more mass, less acceleration
• Newtons 3rd Law
• Action-reaction
• Equal and opposite force but acting on 2
  different objects!

• Friction always opposes (resists) motion
• Frictional force depends on
• the surfaces in contact (µ)
• the Normal force
• whether it has started moving or not
• Two types of friction
• Static Stationary (more)
• Kinetic In motion (less)
• Lubrication can help reduce friction between
  surfaces

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Review Fluid

• Laminar Flow
• Streamlined
• Friction between layers
• Turbulent Flow
• Whirlpools and eddies
• Pressure drag
• Terminal Velocity
• Drag increases with speed until it balances out
  the weight
• Depends on area, viscosity, weight

• Factors affecting Fluid Resistance
• Area of pipe
• Length of pipe
• Viscosity of fluid
• Inside surface of pipe
• Restrictions or blockage
• Laminar or Turbulent flow (depending on velocity
  and shape of object in fluid)