Dynamics

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• Dynamics
• Mechanics is the branch of physics that is
  concerned with the analysis of the action of
  forces on matter or material systems.
• Dynamics is the branch of mechanics that is
  concerned with the effects of forces on the
  motion of a body or system of bodies, especially
  of forces that do not originate within the system
  itself.

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Why are Forces Important?

• Forces help to describe much of what occurs in
  our Universe. For example, we know that if we
  push a box with a certain amount of force, it
  will move.
• In chemistry, intermolecular and intramolecular
  forces help describe why different elements react
  with each other and what happens at the subatomic
  level.

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• A force is defined by a push or a pull one object
  exerts on another and is measured in units of
  Newtons (N)
• 1 Newton is defined as the magnitude of force
  required to accelerate a 1.0 kg mass at a rate of
  1.0 m/s2.
• Forces are vector quantities (magnitude and
  direction). They are denoted as Fx (for example
  the force of gravity is denoted Fg)

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Examples of Forces

• Force of Gravity (Fg)
• Direction always toward centre of attracting mass
• Earth attracts us we attract earth

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Applied Force (Fa) -Contact action force applied
by one object to the other not
really in contact, repulsion of nuclei
Fa
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Normal Force (FN) -Perpendicular to and provided
by a supporting surface Once again due
to repulsion of nuclei, normal forces can be very
small or very large
FN
FN
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Frictional Force (Ff) - Direction of frictional
force generally opposes motion and is caused by
particles of both objects being attracted to each
other (intermolecular forces)
V
Ff (Frictional Force)
Other forces include the force of tension, FT,
and the force of compression, Fc.
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The Four Fundamental Forces
Each of the examples of forces mentioned can be
divided into the four fundamental forces of our
Universe.

• 1. Strong Interaction The strong interaction or
  strong force is the attractive force that holds
  protons and neutrons together in a nucleus.

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• 2. Electromagnetic force The force that exists
  between charged particles (repulsion or
  attraction). This force is transmitted by
  electric fields. Magnetic fields are linked to
  electric fields (as are electricity and
  magnetism) so it is called the electromagnetic
  force.

3. Gravitation or gravity is the attractive force
that exists between all matter.
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• 4. The weak interaction (often called the weak
  force or sometimes the weak nuclear force) is an
  interaction between elementary particles
  involving neutrinos or antineutrinos that is
  responsible for certain kinds of radioactive
  decay.

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All About Newtons Laws
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Newtons First Law of Motion

• Every object continues in its state of rest, or
  uniform motion in a straight line unless acted
  upon by an unbalanced force.

Constant velocity of the car
The car will continue to travel at the same speed
at which it is going unless an external force is
applied to it. For example, the force on wheels
caused by brakes!
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Newtons first law discusses a property of matter
known as inertia.

• Inertia is the property of matter that causes a
  body to resist changes in its state of motion.
  The amount of inertia an object possesses depends
  directly on its mass.

Think about a hockey puck on ice (which is
basically frictionless). It will continue to
glide at practically the same speed until it is
hit by a stick or hits the boards.
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• Forces Thinking Exercise
• In groups of two or three
• Think of as many examples of uses or dangers of
  Newtons first law. If there is a danger then
  state what counteractive measures are taken.

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Newtons Second Law of Motion

• When an unbalanced force acts on an object, the
  object will accelerate in the direction of the
  unbalanced force. The acceleration of the object
  is directly proportional to the size of the force
  and inversely proportional to the mass of the
  object.
• Demonstrate this with spring loaded cars, with
  roller bladed students, (can be done as part of
  third law as well)

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From Newtons Second Law, we can arrive at the
conclusion that the acceleration of an object is
equivalent to its net force divided by mass.
or
Mass is the quantity of matter in a body.
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Free Body Diagrams Newtons Second Law utilizes a
quantity called the net force on an object.
Forces are vector quantities and if more than one
force acts on an object then the forces can be
added (summed). The sum of these forces is called
the net force or resultant force. This force is
symbolized as shown below.
Free Body Diagrams A free body diagram (FBD)
shows all of the forces acting on a object. All
forces are shown as a pull on the object. Draw
free body diagrams of the following
situations pushing against a stationary chair
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Newtons Third Law of Motion

• If object A exerts a force on object B, then
  object B exerts a force equal in magnitude but
  opposite in direction on object A.
• These two forces are called action reaction
  pairs.
• For every action force there is an equal and
  opposite reaction force.

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Lets take someone pushing a wall for example.
When you (object A) push on a wall (object B)
Newtons Third Law dictates that the wall (object
B) should push back on you (object A).
A
B
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• Think about this concept. If there was no force
  pushing back on you, then essentially you would
  feel nothing and would be able to go through the
  wall (as there would no force pushing back on
  you).

Now what would be the reaction force to that of
the force of gravity on a man standing on Earth?
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The reaction force to the force of gravity (Earth
pulling down on the man) is the force of the man
pulling up on Earth!
Fg
FM
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Name the reaction pair to the forces below. a)
Bill pushes S on Mike. b) Jenny pulls westward
on the rope. c) Mack pushes a spring down. d) Sue
hits a tennis ball up. e) The Sun attracts Earth
towards it. f) John experiences friction while
sliding NW on the hardwood floor. g) Proton A
repels proton B left. h) Ana falls and hits the
ground.
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Fanyan and Atif each pull on a rope so that they
slide towards each other, on ice, with a constant
velocity (Assume rope is massless)
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Fanyan
Atif
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The ground pushes up on Fanyan and Fanyan pushes
down on the ground. Earth pulls down on Fanyan
and Fanyan pulls upwards on Earth. Fanyan pulls
the rope left and the rope pulls Fanyan right.
The ground attracts Fanyan to the right and
Fanyan attracts the ground to the left.
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• Draw a sketch of the following systems
  (underlined items) then draw individual free body
  diagrams. State action reaction force pairs (some
  reaction forces may not be present in your
  system)
• A box sits on the ground, is pushed by Sohaib
  and remains stationary.
• A ball falls with a constant velocity.
• Greg holds on to Ian who holds on to a rope.
• Alison sits and remains on a rough box that is
  being pushed west by a spring.

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Newton's Third Law at a Traffic
Intersection Ernie McFarland University of
Guelph   Many physics students seem to have the
impression that physics is something found only
in textbooks therefore it is particularly nice
to show them physics phenomena in the "real"
world. I recently noticed an interesting example
of Newton's third law at a traffic intersection
on campus, and students are quite intrigued by it.
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What happened to the lines? There are traffic
lights at this intersection, and each day
hundreds of cars stop just to the left of the
fines. When the light turns green, the cars
accelerate to the right (Fig. 2). To achieve this
acceleration, the car tires exert a backward
force on the road (to the left in the
photograph), and by Newton's third law, the road
exerts a forward force on the tires, i.e., on the
car. At this particular intersection, the top
layer of pavement is poorly bonded to the
underlying layers, and the backward force on the
road under the tires has actually caused the top
layer to slide to the left, as seen from the
photo, leading to the unusual bends in the
painted fines.
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Figure 1 shows part of a road at the
intersection, from the curb and gutter in the
foreground (bottom of photograph) to the center
of the road (top). The white lines painted on the
road show a rather unusual pattern -indeed, it
looks as if the road-painters went berserk!
However, the lines were straight when originally
painted, eventually assuming the shape in the
photograph.
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The Force of Gravity Earth is surrounded by a
gravitational force field. This means that every
mass, no matter how large or small feels a force
pulling it directly towards the center of Earth.
The force field is measured in N/kg. All objects
on Earth have the same ratio of force to mass
(demonstrate with spring scale). At Earths
surface this ratio is 9.81 N/kg down The
magnitude of this ratio decreases as one moves
farther from Earth.
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The gravitational field strength at Earths
surface can be denoted by g. 6400 km above
Earths surface the field strength has decreased
to 2.45 N/kg down (12800 km above 1.09
N/kg). Mass is defined as the quantity of matter
in an object (kg). The standard kilogram of
comparison is a Pt-Ir bar in France. The mass of
an object is constant everywhere. Mass is
measured with a balance. Weight is defined as the
force of gravity acting on an object (N). The
weight of an object is variable and depends on
the size of the other mass. For example a
persons weight on the moon is less than his/her
weight on earth. Weight is measured with a scale.
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Gravitational field strength (N/kg)
Acceleration due to gravity (m/s2)
g is a variable quantity! Text problems
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LAW OF UNIVERSAL GRAVITATION
FG gravitational force (in two directions) G
universal gravitation constant
6.67x10-11 Nm2/kg2 r distance between the
objects m1 mass of the larger object m2 mass
of smaller object
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at the Earths surface . . .
All objects at the same distance from a large
object experience the same acceleration due to
gravity. Text problems
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Calculate the gravitational field strength of all
of the planets and the Sun if you were on the
surface of each. G 6.67 x 10-11 Nm2/kg2
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• Force of Gravity Problems
• David (62 kg) stands on a scale in an elevator.
  Determine the reading on the scale in each of the
  following situations.
• The elevator is at rest.
• The elevator is moving with a constant velocity
  upwards.
• The elevator is moving with a constant velocity
  downwards.
• The elevator is accelerating at 2 m/s2 up.
• The elevator is accelerating at 7 m/s2 down.
• worksheet

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is up
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When dealing with forces we will treat
acceleration due to gravity as a scalar quantity.
g is used in many forces which do not have a
downward direction. The direction of the force
will be determined by the student by calculation
or analysis.
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a, b, c) The acceleration is 0 in each of these
situations.
Since the scale is pushing up on the rider with a
force of 608.2 N the scale will read a weight of
608.2 N
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d) The acceleration is 2 m/s2.
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d) The acceleration is -7 m/s2.
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Normal Forces When an object rests on a flat
surface (parallel to the ground) the normal force
of the surface is equal and opposite to the force
of gravity on the object. This balance also
applies to situations when the object is
accelerating parallel to the ground (height
remains the same). These situations are
encountered often and as a result people often
think the force of gravity and the normal force
are equal and opposite. Surfaces are, in fact,
capable of a wide range of forces. Surfaces are
capable of changing an objects velocity very
quickly and thus exert forces much larger than
force of gravity on the same object. The
following example will illustrate this point.
worksheet
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• Alison (55 kg) jumps off a 30 m building and
  lands in
• mud! She compresses the mud 20 cm while coming to
• rest.
• What velocity did she hit the mud with?
• What was Alisons acceleration in the mud?
• What was the muds normal force on Alison?

is up
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a)
Therefore Alison hits the mud with a velocity of
24.26 m/s down.
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a)
Alisons acceleration must first be calculated.
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Superhero Matt (60 kg) jumps upward with an
initial velocity of 40 m/s to catch a basketball.
He mis-calculates and finds himself embedded in
ceiling 50 cm. The ceiling is 15 m high. What
normal force did the ceiling exert on Superhero
Matt.
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FRICTION Textbook 96-108 Questions p. 97 13,
p. 98 4, p. 100 16, p. 103 16, p. 105 79,
p. 106 10, p. 107 18 The force of friction
(Ff) is the resistance to motion because of the
interaction of the object with its surroundings
(gas, liquid, solid). Forces of friction are very
important because they allow things to move or
stop. On a molecular level friction involves the
electrostatic forces between atoms or molecules
where the surfaces are in contact. There are two
types of friction. Static friction (Fs) occurs
when an object is stationary while kinetic
friction (Fk) occurs when an object is moving.
There are different types of friction such as
sliding, rolling and fluid friction. For each of
these types there are also static and
kinetic forms.
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Friction follows these two empirical laws. 1. It
is proportional to the normal force. 2. It is
approximately independent of the area of contact
over wide limits. When a stationary object is
acted upon by an unbalanced force that increases
so too does static friction (and the object does
not move). When the static frictional
force reaches a maximum it grows no longer and
the object begins to move. The frictional force
often decreases at this moment since the
coefficient of kinetic friction is generally
lower than the coefficient of static friction.
Kinetic frictional forces do change with
increasing velocity but not that dramatically. We
will treat kinetic friction as being independent
of an objects velocity. Both coefficients of
friction (kinetic and static) are dimensionless
constants that are generally less than one in
value.
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