Newton

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• Newtons Laws

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Mechanics - Study of Motion

• Mechanics - the study of motion
• Kinematics - How things move (time line for
  foundation of kinematics- early 1600's)
• work done by Galileo,
• Why do all things accelerate at one rate?
• How does the earth know to pull on more massive
  objects with a proportionally larger force than
  it pulls on smaller masses?
• work done by Kepler
• What is the force that emanates from the sun that
  is responsible for holding planets in elliptical
  orbits?
• Dynamics - Why things move as they do
• work done by Isaac Newton,
• Work began in 1666
• we will see in a later lecture how Newton unified
  these two seemingly unrelated fields with one
  master stroke
• His work led to the belief that all one had to do
  was to understand the rules governing motion and
  the world behaved as a machine producing the
  same result for the same given input
• There are only THREE types of motion that we need
  to describe
• a. objects at rest
• b. objects moving with constant velocity
• c. objects that are accelerating

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Inertia

• Aristotelian View of Forces
• a. The natural state of an object is to be at
  rest.
• b. In order to get an object to move, one must
  apply a force. (Push a book, etc.)
• c. However, once the force is taken away, the
  object once again comes to rest.
• Galileo's ramp experiments

Regardless of the angle of ramp C the ball always
seemed to rise to the same height that it had on
ramp B. What would happen if he were to remove
ramp C?
Clearly the implication would be that it would
continue on with uniform motion
forever. Galileos Definition of Inertia the
tendency of an object to resist a change in
motion. (the more massive an object, the greater
its inertia) Newton summarizes Aristotelian and
Galilean physics by stating in his book Principia
his 1st Law of Motion (what we have come to refer
to as the Law of Inertia)
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Law Of Inertia

• Newton's 1st Law - An object at rest, or in
  uniform straight line motion, will remain at
  rest, or in uniform straight line motion, unless
  acted upon by a net external force.
• Another way to state this law might be If there
  are no net external forces acting on a body, then
  it will continue in it's state of constant
  velocity (which may be zero).
• This is easier to write mathematically.

which translates to if we add up all of the
forces acting on a body from 1 to the nth force
and get zero as the resultant, then the body is
moving with constant velocity.
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Newtons 2nd Law

• Newton also explains what happens when the forces
  do not add up to be zero.
• Newton's 2nd Law - A net force acting on a body
  produces on that body, an acceleration that is
  directly related to the force impressed upon the
  body and inversely related to the mass of the
  body.
• An easier way to state it is

The units of force are directly derived from
this formula units of force kg m/s2. This is
sufficiently lengthy enough to warrant a short
hand version. Thus a unit of force is called a
Newton (N) and was made in his honor. Thus, when
keeping track of units N kg m/s2 Since
acceleration is a vector quantity, force is a
vector quantity as well. Caution - a common
mistake in solving problems is forgetting to add
up all of the forces before applying the second
part of Newton's 2nd Law.
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Field versus Contact Forces
For our purposes we will define a force as a push
or a pull on an object.
We will categorize forces into two
categories Contact forces forces that result
from the physical contact between two
objects Field Forces forces that arise from
the interaction of an object located within a
field of influence of another object. E.g., an
object in the gravitational field of the earth,
or the earth within the gravitational field of
the sun, or an electron within the electric field
of a proton, or a piece of iron near a magnet, et
cetera.
There are really only four quantified forces in
all of nature Strong interaction Weak
interaction Electromagnetic Gravitation
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3rd Law, Weight, and Normal Force

• Newton's 3rd Law - For every action there is an
  equal but opposite reaction
• or mathematically stated

It is an observation of Newton that forces
naturally occur in pairs
Example Weight - the force with which a
gravitational body (such as the earth) pulls on a
body Mathematically it is defined as Any body
that has mass, has weight when it is near to a
gravitational body. When a person (mass 70 kg)
is standing on a floor, the force that he exerts
on the floor is his weight
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3rd Law, Weight, and Normal Force

• The floor, by Newton's 3rd Law, exerts an equal
  but opposite force of 686N to prevent the person
  from falling through the floor.
• This force that acts perpendicular to the floor
  is referred to as the Normal Force and is another
  example of a Contact Force that we will encounter
  frequently.

It is referred to as the normal force, not
because it is always there, but because the term
normal is a mathematical term that means
perpendicular.
Not all surfaces are capable of exerting a force
equal in magnitude to the weight of object placed
upon them. Thin ice is a good example, but
almost any surface can be destroyed, or broken,
by placing a sufficiently large mass upon it.
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How does this Normal Force Arise?

• What then, is the nature of this normal force
  that surfaces seem to exert? How does a wall
  know to push back harder when I push with
  increasing force?
• At the most basic level the object placed upon a
  surface is repelled by electromagnetism.
• The outer most electrons that comprise the object
  are electrically repelled by the electrons that
  comprise the surface.
• The electrons offer a stronger and stronger
  repulsive force the closer and closer the object
  is moved to the surface - just as two similar
  ends of magnets repel any effort to touch them
  together.
• We can break the electric bonds between the atoms
  that make up the surface if we exert a large
  enough force.
• Hence the more massive an object, the greater
  gravity tends to pull them onto a surface, and
  the greater the surface tends to repel the
  object.
• The object will be at rest on the surface
  (according to Newt's 1st Law) only if the surface
  is capable of exerting an equal and opposite
  force to sustain it, otherwise the object crashes
  through the surface.

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Example
What force does the 5kg block exert on the 10 kg
block?
Look at the two block system as a single object
(N2L)
(N3L)
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Free Body Diagrams
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Free Body Diagrams
y
x
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Free Body Diagrams
?2
?1
?2
?1
y
x
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Train
Three railroad cars are being pulled with a force
of 12,000 N. Car 1 has a mass of 2000kg, car 2
has a mass of 3000 kg, and car 3 has a mass of
5000kg. Neglecting friction, what is the
acceleration of the train and what is the force
between car 2 and 3?
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Solution
A free body diagram would indicate only one force
if we neglect frictional forces
Car 3 we already know is accelerating at 1.2 m/s2
so it must have a net force acting on it
(provided by Car 2) of F23 5000(1.2) 6000N
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Tug of War

• Two teams are comprised of equal strength
  players, each capable of pulling with a force of
  400 Newtons. Each team has 4 players each. Each
  person has a mass of 80 kgs.

In this case, the two forces exerted horizontally
add up vectorally to be zero. Does that mean the
rope is not moving?
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Examples cont.
An additional force is exerted by one of the
players who becomes psyched. This person now
pulls with a force of 420N

• Now there is a net force of 20 Newtons to the
  right. This net force is acting upon a total mass
  of 640 kg (excluding the rope) which produces an
  acceleration of