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					Unit 4: Newton’s Laws of
         Motion
         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.
These views remained widely
supported until the 1500s
when Galileo Galilei (1564-1642)
popularized experimentation.



           Isaac Newton (1642–1727)
           proposed that the tendency of
           an object was to maintain its
           current state of motion.
                            Forces
• A force is a push or a pull
• A force can cause
   – a stationary object to move
   – a moving object to stop
   – an object to accelerate (change speed or direction)
• Net force
   – the combination of all the forces acting on an object.
   – changes an object’s state of motion.
• Balanced Force
   – Net force = 0
   – object at rest
   – Or constant velocity
• Unbalanced
   – Net force is greater than zero
   – Object moves
   – Or accelerates
      Newton’s 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 – (F=ma)Force equals mass times
 acceleration.
• 3rd Law – (action-reaction)For every action
 there is an equal and opposite reaction.
                        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”
                Mass vs. Weight
• MASS                          • WEIGHT
  – How much and what             – Force of gravity acting on
    material an object is           a mass
    made of (what types of        – Measured in Newtons
    atoms and how many of
    them)                               Fg=mag
  – Measured in grams or
    kilograms (kg)                – 1N = 1kg· m/s2
  – Is constant for an object
    independent of location
      Normal Force and Gravity
• Gravity always pulls straight down
• Normal force (FN) is perpendicular to surface
  and equal and opposite to component of
  gravitational force (Fg)           FN
            FN

                   Fg                Fg
• This may lead to an unbalanced ‘sliding’ force
  that is the component of the gravitational
  force
    The net force acting on an object is the
    vector sum of all the forces acting on it.

    Examples:
                                            9 lb   6 lb
         8 lb
                                4 lb
                     8 lb

                                7 lb
                                           5 lb
        12 lb                                      4 lb



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.
What direction is normal force (FN).
            Example 1
          Example 9
Fnet
       magnitude _______
       direction _________

Balanced or Unbalanced?

                             Fnet
                                    magnitude _______
                                    direction _________

Fnet                         Balanced or Unbalanced?
       magnitude _______
       direction _________

Balanced or Unbalanced?
Example 12
          2nd   Law
   The net force of an object is
equal to the product of its mass
       and acceleration
           F=ma.
                    2nd Law
• Relates an object’s mass and acceleration to
  the net force (force causes acceleration)

• Mass is inversely related to acceleration

• Acceleration is directly related to net force
 Newton’s 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 don’t
  hit the ground with the same
  force.




                                       F = ma                    F = ma
                               98 N = 10 kg x 9.8 m/s2   9.8 N = 1 kg x 9.8 m/s2
 Calculating force and acceleration
• Remember Force = mass x acceleration
           F=ma
• And acceleration is change in velocity over
  time
                v f  vi
           a
                   t
                Example 2
• How much force must a 30,000kg jet plane
  develop to achieve an acceleration of
  1.5m/s2? (neglecting air friction)
• F=ma
• F=(30,000 kg) (1.5 m/s2)= 45,000 N
                 Example 3
• 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?
                 Example 4
• If I throw a 0.145 kg baseball at 20 m/s
  baseball and my ‘windup distance’ is 0.6
  meters, how much force am I applying?
                   Example 5
• A 2.2 kg book is slid across a table. If Fnet = 2.6
  N what is the book’s acceleration?
• F=ma
• 2.6 N = (2.2kg) a
• a = 1.18 m/s2
                  Example 6
• If you drop a 20 kg object what is its
  acceleration? What is its weight?
• acceleration = 9.8 m/s2
• Weight = force
• Fg=ma
• Fg= (20 kg) (9.8 m/s2)
• 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 jet’s
    motion
Example 7:
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 Newtons in the opposite direction of the car’s 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 Newton’s 2nd Law to calculate the net acceleration of the car.
             3rd Law
• For every action, there is an
  equal and opposite reaction.
                            3rd Law
• There are two forces resulting from this interaction
   • a force on the chair (action)
   • a force on your body (reaction)




                   action




                 reaction
• 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
                 3rd Law
Flying gracefully through the air, birds depend
on Newton’s 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.
Other examples of Newton’s Third Law

• Action: baseball forces
  the bat to the left
• Reaction: bat forces the
  ball to the right
            Friction & Tension
• Friction (Ff) - the force that opposes motion

• Tension (FT) - the pulling force exerted by a
  string, cable, chain on another object.
Drawing Free Body Diagrams
        Example 10
Drawing Free Body Diagrams
        Example 11
                     Example 7
• 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
                          Friction
• The force of friction (Ff):
   1. Is always opposite to the direction of motion or
      impending motion
   2. Usually has a smaller value if the object is
      moving than if it is stationary
     - (static friction > kinetic friction);
   3. Depends on the nature of the pair of surfaces
      involved (the value of μ);
                          Friction
• The force of friction (cont’d):
  4. Is proportional to the force pressing the surfaces
     together (the normal force);
     - static friction: Ff ≤ μs FN
     - kinetic friction: Ff =μk FN
  5. Is usually independent of the contact area and
     speed.
                   Example 13
• 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?
      Finding Force With Angles
                                          FN

• Horizontal        Ff                                Fapp
  – FN = Fg
                                     Fg
                                               FN
• Incline                Ff


  – Fnet = Fgsinθ                                   20°
  – FN = Fgcos θ              FN
                                          Fg
                                   Fnet         20°
                      Statics
• The study of forces in equilibrium
  – Balanced forces
  – No acceleration
                     Statics
                               FT1        FT2
• If hanging from a wire
  – Weight is shared equally
    between each wire
  – Weight is NOT equal to
    Tension




                                     Fg
                Example 14
• 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?
         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
A. 5.0 m/s2 to the right
B. 3.0 m/s2 to the right
C. 5.0 m/s2 to the left
D. 3.0 m/s2 to the left
         Physics 1 Assessment 4E
2. 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.
         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
         Physics 1 Assessment 4E
4. 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?




A.            B.             C.             D.
         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
  Applying 2D Forces & Free-Body
             Diagrams
• Forces are not always acting in one direction (same
  or opposite).
• The forces along the x-axis and y-axis may not be in
  equilibrium.
• We use Pythagorean theorem to resolve the net
  force acting on an object.
                     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?
                        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
                                      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 Ɵ = adjacent side / hyp.
•   cos 60o = Fg’ / Fg
•   Fg’ = 180cos60
•   Fg’ = 90 N
•   Since Fg’ = Fn
•   Fn = 90 N
                      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 @ 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
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 = √(Fx2 + Fy2 )
      = √(3002 + 346.412)
      = 458.23 kN
Direction
• Tangent Ɵ = opposite side/adjancent side
  Ɵ = tan-1(Fytotal/Fx total )
    = tan-1346.41 kN/300 kN
  Ɵ = 49.11o
Fnet = 458.23 kN @ 49.11o

				
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