Happy New Quarter day

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Happy New Quarter day

• I sent an arrow into the air and it landed I know
  not where.
• But, It was launched at 30 degrees with a
  velocity of 50m/s. So, how long was it airborne???

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(1)Dynamics

• Newtons Laws

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Dynamics

• Dynamics is the study of forces and the resulting
  motion.
• Here, we study acceleration and its causeforce

• Force
• the agency of change.
• changes the velocity.
• is a vector quantity.
• measured in Newtons.

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Newtons First Law The Law of Inertia

• Inertia is the tendency of a body in motion to
  stay in motion and a body at rest to stay at
  rest.

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What is Inertia?

• Inertia is the property of matter to resist
  change in motion
• Mass is the measure of inertia
• Mass is measured in kilograms (kg)
• How and when will mass change???

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Newtons First Law

• When an object is at rest or at constant
  velocity, its acceleration is zero.
• Under these conditions the object is said to be
  in a state of equilibrium.
• An object in the state of equilibrium has no net
  forces acting upon it.
• A net force (unbalanced force) is needed to
  change the state of motion of an object.

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Newtons Second Law
The Law of Acceleration

• A net force causes an acceleration.
• Force is directly proportional to acceleration.
• F ? a
• The resulting acceleration is inversely
  proportional to the mass of the object
• a ? 1/m
• F ma
• is the single most important equation in Physics.

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Newtons Second Law

• The Newton (N) is the unit of force.
• 1 N kgm/s2
• A 1.00 kg mass that undergoes a 1.00 m/s2
  acceleration is experiencing a force of 1.00
  Newton.

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Force of hand accelerates the brick
The same force accelerates 2 bricks 1/2 as much
Twice as much force produces twice as much
acceleration
Twice the force on twice the mass gives the same
acceleration
3 bricks, 1/3 as much acceleration
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Newtons Third Law The Law of Action
and Reaction Forces

• For every force on an object, there is always an
  equal and opposite force exerted by the object.
• Forces always come in pairs known as
  action-reaction pairs.

Action tire pushes on road Reaction road
pushes on tire
Action gas pushes on rocket Reaction rocket
pushes on gas
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Action-Reaction Pairs
Action man pulls on spring Reaction spring
pulls on man
Action Earth pulls on ball Reaction ball
pulls on Earth
In the interaction between the hammer and the
stake, each exerts the same amount of force on
the other.
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• Even objects at rest on a surface have pairs of
  forces acting on them.

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The force exerted against the recoiling rifle is
just as great as the force that drives the
bullet. Why, then, does the bullet accelerate
more than the rifle?
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(2)Dynamics

• Weight vs Mass

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Mass vs Weight

• Mass is
• the quantity of matter in an objectthe amount of
  stuffmeasured in kilograms.
• is the measure of the inertia of an object.
• Weight (FW) is
• the measure of the gravitational force on an
  object.
• a force Fw mg
• is measured in Newtons (N).

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Mass vs Weight

• An anvil in outer space, between the Earth and
  Moon, for example, may be weightless, but it is
  not massless.

• The astronaut in space finds it is just as
  difficult to shake the "weightless" anvil as it
  would be on Earth.

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Two Kinds of Mass

• Gravitational Mass the mass measured by a beam
  balance or spring scale measured from gravity.
• Inertial Mass the mass of an object is the
  ratio of the net force exerted on the object and
  its acceleration.

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The ratio of weight (Fw) to mass (m) is the same
for all objects in the same locality hence,
their accelerations are the same in the absence
of air resistance.
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(3)Dynamics

• Free Body Diagrams
• Net Forces
• Equilibrium

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Forces Come in Many Forms

• All forces can be calculated using F ma
• Be sure to identify your forces.
• Net Force FNet
• Normal Force FN
• Applied Force FA
• Opposing Force Fo
• Frictional Force Ff
• Tension FT
• Lift Force FL
• Drag Force FD

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Free Body Diagrams

• Display all of the forces on an object at a given
  time.
• Use an abstract form (rectangle, circle, etc.) to
  represent the object.
• Are indicated by arrow pointing in the direction
  of the force.
• The length of the arrow is relative to the
  magnitude of the force.

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FBD of an object moving across a flat surface
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Net Force

• The net force is the sum of all forces acting on
  an object.
• When two forces act on an object the forces are
  cumulative (they are added together).
• Net force is called a resultant and can be
  calculated using geometry.

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Net Force

• The net force is the sum of all the forces acting
  on an object in a given direction.

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Net Force

• The rate and the direction of movement of this
  ship are determined by a combination of direction
  and magnitude of force from each of the tugboats.
  Which direction are the two tugboats pushing?
  If the tugboat by the numbers is pushing with a
  greater force and the back tugboat is keeping the
  ship from moving, what will happen?

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Forces are Vectors so Directions are Important
Total Force 0
Forces Add
Forces Cancel!
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(A)When two parallel forces are acting on the
cart in the same direction, the net force is the
two forces added together.
10 N east
20 N east
10 N east
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(B) When two forces are opposite and of equal
magnitude, the net force is zero.
10 N east
0 N
10 N west
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(C) When two parallel forces are not of equal
magnitude, the net force is the difference in the
direction of the larger force.
10 N east
10 N west
20 N west
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Net Force
Its the sum of all the forces that determines
the acceleration
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Equilibrium

• If the net forces on an object equal zero, the
  object is in equilibrium.
• Net force of zero means no acceleration.
• It may be at rest
• Or, it may be moving at a constant velocity.

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Forces in a Single Plane

• Horizontal
• Force applied opposes the force of friction.
• FNET Fa Ff
• Vertical
• Force applied opposes the force of gravity, that
  is, the weight.
• FNET Fa Ff

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Normal Force

• The normal force (FN) on an object supported by a
  surface is the component of the supporting force
  that is perpendicular to the surface.
• When an object is sitting on a level surface then
  the normal force is always equal and opposite of
  the weight of the object

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Normal Force

• Anytime two surfaces are in contact there will be
  a normal force
• Normal force is always perpendicular to the
  surfaces so
• The word Normal is often synonymous with the word
  perpendicular!

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(4)Dynamics

• Friction

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Happy Hallows Eve

• A lighter than air balloon is accelerating
  upwards at 2m/s/s. Its total mass is 2000 kg.
  What must be the net force?
• Bonus What is the lift force?

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Friction

• Is the force that opposes the motion of two
  surfaces in contact.
• Static Friction
• friction that opposes the start of motion
• friction from rest.
• Sliding Friction
• friction of motion
• friction from constant velocity.
• Static frictional forces always greater than
  sliding ones

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The force of friction depends on two things

• The nature of the surfaces in contactthe
  coefficient of friction.
• The force pushing the surfaces togetherthe
  normal force.
• Ff ?FN

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Whats Happening With Friction

• Fa gt Ff ? acceleration
• Fa lt Ff ? deceleration
• Fa Ff ? equilibrium

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(4)Dynamics

• Forces on an Inclined Plane

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What is an Inclined Plane?

• An inclined plane is a simple machine designed to
• Reduce the amount of force required to do a given
  quantity of work
• By extending the distance over which the force is
  exerted.

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Components