Unit 4: Newton

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Unit 4 Newtons Laws of Motion
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Causes of Motion Aristotle (384-322 BC) believed
that all objects had a natural place and that
the tendency of an object was to reside in its
natural place. All objects were classified
into categories of earth, water, air, or
fire. Natural motion occurred when an object
sought to return to its natural place after
being moved from it by some type of violent
motion. The natural state of an object was to
be at rest in its natural place. To keep an
object moving would require a force.
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These views remained widely supported until the
1500s when Galileo Galilei (1564-1642) popularized
experimentation.
Isaac Newton (16421727) proposed that the
tendency of an object was to maintain its current
state of motion.
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Forces

• A force is a push or a pull
• A force (F) can cause
• a stationary object to move
• a moving object to stop
• an object to accelerate (change speed or
  direction)
• Net force (Fnet)
• the combination of all the forces acting on an
  object.
• changes an objects state of motion.
• Balanced Force
• Fnet 0
• object at rest
• Or constant velocity
• Unbalanced Force
• Fnet gt 0
• Object moves
• Or accelerates

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Newtons Laws of Motion

• 1st Law (Law of Inertia) An object at rest will
  stay at rest, and an object in motion will stay
  in motion at constant velocity, unless acted upon
  by an unbalanced force.
• 2nd Law (Fma)Force equals mass times
  acceleration.
• 3rd Law (action-reaction)For every action there
  is an equal and opposite reaction.

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INERTIA
the tendency of an object to resist any change in
its motion
Inertia is a property of matter and does
not depend on the position or location of the
object. But it does depend on
MASS
a quantitative measure of inertia
FORCE
a push or pull
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Free Body Diagrams

• Gravity (Fg) always pulls straight down
• Normal force (FN) is perpendicular to surface and
  equal and opposite to component of gravitational
  force (Fg)
• Applied force (Fapp) is in the direction of the
  motion of the object. It is always parallel to
  the surface
• Frictional force (Ff) always opposes the motion.
  It is always parallel to the surface opposite the
  Fapp.

FN
FN
Ff
Fapp
Ff
Fapp
Fg
Fg
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What direction is normal force (FN).Example 1
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The net force acting on an object is the vector
sum of all the forces acting on it. Fnet F1
F2 F3 Examples
6 lb
9 lb
8 lb
4 lb
8 lb
7 lb
5 lb
4 lb
12 lb
Fnet
Fnet
Fnet
If an object is remaining at rest, it is
incorrect to assume that there are no forces
acting on the object. We can only conclude that
the net force on the object is zero.
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Example 2
Fnet magnitude _______ direction
_________ Balanced or Unbalanced?
Fnet magnitude _______ direction
_________ Balanced or Unbalanced?
Fnet magnitude _______ direction
_________ Balanced or Unbalanced?
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2nd Law

• The net force of an object is equal to the
  product of its mass and acceleration
• Fma.

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2nd Law

• Relates an objects mass and acceleration to the
  net force (force causes acceleration)
• Fma
• Mass is inversely related to acceleration
• Acceleration is directly related to net force

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Newtons 2nd Law proves that different masses
accelerate to the earth at the same rate, but
with different forces.

• We know that objects with different masses
  accelerate to the ground at the same rate.
• However, because of the 2nd Law we know that they
  dont hit the ground with the same force.

F ma 98 N 10 kg x 9.8 m/s2
F ma 9.8 N 1 kg x 9.8 m/s2
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Mass vs. Weight

• WEIGHT
• Force of gravity acting on a mass (On earth a
  9.8 m/s2)
• Symbol Fg
• Unit Newtons (N)
• Fgma
• 1N 1kg m/s2
• Changes depending on location due to pull from
  the center of earth
• -1 lb 4.5 N

• MASS
• How much and what material an object is made of
• Symbol m
• Unit kilograms (kg)
• Is constant for an object independent of location

To go from mass to weight, multiply by 9.8!
Mass conversion 2.2 lb 1 kg
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Calculating force and acceleration

• Remember Force mass x acceleration
• Fma
• If not given acceleration, find acceleration
  using one of the acceleration equations

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Example 3

• If a person pulls on the rope with a constant
  force what is the acceleration of the system? How
  far will it move in 3.02s?

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Example 4

• How much force must a 30,000kg jet develop to
  achieve an acceleration of 1.5m/s2? (neglecting
  air friction)
• Fma
• F(30,000 kg) (1.5 m/s2) 45,000 N

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Example 5

• If a 900 kg car goes from 0 to 60 mph (27 m/s) in
  5 seconds, how much force is applied to achieve
  this?

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Example 6

• If I throw a 0.145 kg baseball at 20 m/s baseball
  and my windup distance is 600 cm, how much
  force am I applying?

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Example 7

• A 2.2 kg book is slid across a table. If Fnet
  2.6 N what is the books acceleration?
• Fma
• 2.6 N (2.2kg) a
• a 1.18 m/s2

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Example 8

• If you drop a 20 kg object what is its
  acceleration? What is its weight?
• acceleration 9.8 m/s2
• Weight force
• Fgma
• Fg (20 kg) (9.8 m/s2)

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• Q If a jet cruises with a constant velocity and
  the thrust from its engines is constant 80,000
  N. What is the acceleration of the jet?
• A Zero acceleration because the velocity does
  not change.
• Q What is the force of air resistance acting on
  the jet?
• A 80,000 N in the opposite direction of the
  jets motion

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• Example 9
• After a birthday party, Bozo the clown went to
  dinner in his 250 kg car. To save room in the
  car, he let the left over balloons hang out the
  window. The engine of the car is exerting a force
  of 360 N. The balloons are creating drag in the
  air with a force of 35 N in the opposite
  direction of the cars motion.
• Draw the vector arrows on the free body diagram
• What is the net force (Fnet) acting on the car?
• What is the direction that force is acting?
•  Use Newtons 2nd Law to calculate the net
  acceleration of the car.

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3rd Law

• For every action, there is an equal and opposite
  reaction.

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3rd Law

• There are two forces resulting from this
  interaction
• a force on the chair (action)
• a force on your body (reaction)

action
reaction
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• If all forces have equal and opposing forces, how
  does anything move?
• Action-Reaction pairs are forces of objects on
  different objects
• F Net is sum of external forces acting on ONE
  object

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3rd Law
Flying gracefully through the air, birds depend
on Newtons third law of motion. As the birds
push down on the air with their wings, the air
pushes their wings up and gives them lift.
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Other examples of Newtons Third Law

• Action baseball forces the bat to the left
• Reaction bat forces the ball to the right

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Friction Tension

• Friction (Ff) - the force that opposes motion
• Tension (FT) - the pulling force exerted by a
  string, cable, chain on another object.

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Example 11

• Draw free body diagram for table
• Applied force from pusher, normal force,
  gravitational force, friction force
• If applied force is greater than friction, table
  moves

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Drawing Free Body DiagramsExample 12
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Drawing Free Body DiagramsExample 13
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Friction

• The force of friction (Ff)
• Is always opposite to the direction of motion or
  impending motion
• Usually has a smaller value if the object is
  moving than if it is stationary
• - (static friction gt kinetic friction)
• Depends on the nature of the pair of surfaces
  involved (the value of µ)

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Friction

• The force of friction (contd)
• Is proportional to the force pressing the
  surfaces together (the normal force)
• - static friction Ff µs FN
• - kinetic friction Ff µk FN
• Is usually independent of the contact area and
  speed.

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Example 14

• If a 1 kg mass sits on a flat surface with a
  coefficient of static friction of 0.5, what is
  the force of friction (Ff) if
• A horizontal force of 1 N is applied?
• A horizontal force of 10 N is applied?
• A horizontal force of 100 N is applied?

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Finding Force With Angles
FN

• Horizontal
• FN Fg
• Incline
• Fnet Fgsin?
• FN Fgcos ?

Fapp
Ff
Fg
FN
Ff
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FN
Fg
Fnet
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Example 15
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Example 16
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Example 17
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Example 18
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Statics

• The study of forces in equilibrium
• Balanced forces
• No acceleration

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Statics
FN

• If hanging from a wire
• Weight is shared equally between each wire
• Weight is NOT equal to Tension
• Find Tension and divide by number of
  strings/wires/etc.

FT1
FT2
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cos T FN FT
Fg
FT FN cos T
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Example 19

• At an art auction, you acquired a painting that
  now hangs from a nail on the wall. If the
  painting has a mass of 12.6 kg, what is the
  tension in each side of the wire supporting the
  painting?

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Example 20
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Example 21
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Example 22
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Example 23
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Physics 1 Assessment 4E

• 1. Two forces are applied to a 2.0 kg block on a
  frictionless, horizontal surface, as shown in the
  diagram. The acceleration of the block is
• 5.0 m/s2 to the right
• 3.0 m/s2 to the right
• 5.0 m/s2 to the left
• 3.0 m/s2 to the left

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Physics 1 Assessment 4E

• The vector diagram below represents two forces,
  F1 and F2, simultaneously acting on an object.
  Which vector best represents the resultant of the
  two forces? 
• A. B.
• C. D.

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Physics 1 Assessment 4E

• 3. A horizontal force is used to pull a 5.0 kg
  cart at a constant speed of 5.0 m/s across the
  floor, as shown in the diagram. If the force of
  friction between the cart and the floor is 10 N,
  the magnitude of the horizontal force along the
  handle of the cart is
• A.5.0 N
• B.10 N
• C.25 N
• D.50 N

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Physics 1 Assessment 4E

• The diagram below shows a sled and rider sliding
  down a snow-covered hill that makes an angle of
  30 with the horizontal. Which vector best
  represents the direction of the normal force, FN,
  exerted by the hill on the sled? 
• B. C. D.

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Physics 1 Assessment 4E

• 5. An electric model of a Boeing 757, has a mass
  of about 12 kg. If the owner adjusts the wing
  flaps to create 123 N of lift upwards, what is
  the net vertical force on the plane?
• A.0 N
• B.5.4 N
• C.10.3 N
• D.111 N
• E.241 N

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Example

• An object is being pulled by a 3 kiloNewtons
  force towards the north and a 4 kiloNewtons force
  eastward on a frictionless surface. What is the
  net force that will accelerate this object?

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Example

• What is the applied force acting against a
  frictional force of 10 N, if an object is pulled
  with a force of 200 N at angle of 60o from the
  ground? What is the net force?
• Solve for the Fa applied force along the x axis
  Fa(x)
• Fa(x) 200cos60
• Fa(x) 100 N
• The force applied opposite frictional force is
  100 N and not 200 N.
• We can solve for the net force Fnet then.
• Fnet Fa(x) Ff 100 N 10 N 90N

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Example

• What is the normal force Fn acting on a 180 N
  object on the ramp that made an angle of 60o from
  the ground?
• We will solve this problem using similar
  triangles.
• Take note Fn Fg , but opposite in direction.
• We will solve Fg using cosine.
• Our hypotenuse is the weight Fg 180 N.
• Fg is the adjacent side with respect to the
  angle 60o.
• cos O adjacent side / hyp.
• cos 60o Fg / Fg
• Fg 180cos60
• Fg 90 N
• Since Fg Fn
• Fn 90 N

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Example

• A crate is being pulled by cables along a
  frictionless surface with a force of 500 kN
  eastward and by another force of 400 KN _at_ 120o.
  What is the net force acting on the crate? Hint
  must find magnitude and direction!

Sin 30 Fx / 400 kN Fx 400sin30 Fx 200 kN
Cos 30 Fy / 400kN Fy 400cos30 Fy 346.41 kN
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• Magnitude
• Add all the vector forces along the x-axis.
• Fxtotal 500 kN - 200 kN
• Fxtotal 300 kN
• Add all the vector forces along the y-axis.
• Fytotal 346.41 kN
• Use Pythagorean Theorem to solve for Fnet
• Fnet v(Fx2 Fy2 )
• v(3002 346.412)
• 458.23 kN

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• Direction
• Tangent O opposite side/adjancent side
• O tan-1(Fytotal/Fx total )
• tan-1346.41 kN/300 kN
• O 49.11o
• Fnet 458.23 kN _at_ 49.11o