Great Idea

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Great Idea 2 Newtons universal laws of motion
and gravity predict the behavior of objects on
Earth and in space.

• Professor Hazen
• UNIV 301 September 6, 2006

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How Do Objects Move?

• Key Idea One set of laws describes motions on
  Earth and in space
• The universal law of gravity
• Universal laws of motion
• Key Terms
• Force
• Uniform Motion
• Acceleration
• Weight vs. Mass

3
What evidence do you have that the universe is
predictable?
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Newgrange, Ireland5,000-year old passage tomb
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Stonehenge

• On the Salisbury Plain of southern England
• 4500 years old
• Exact history is uncertain
• Stonehenge Decoded by Richard Hawking

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Measurements and Observations

• How would you measure a stars position?
• Compass direction to an object (degrees from
  North)
• Protractor w/ straw (degrees from horizon)
• Plot changes from night to night
• Planets (Mars) display
• retrograde motion
• Patterns emerge

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Ptolomys Model of the Solar System

• Model of the universe
• with Earth at the center
• Epicycle (wheels within wheels)
• Why is it important?
• Navigation
• Astrology
• Lasted 1500 years

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Dead White Males

• Nicolas Copernicus (1473-1543)
• Sun-centered solar system
• Tycho Brahe (1546-1601)
• Meticulous measurements of planet positions
• Johannes Kepler (1571-1630)
• Mathematical analysis of planetary orbits
• Galileo Galiei (1564-1642)
• Founder of experimental physics

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Copernican vs. Ptolomeic models

• Earth- vs. Sun-centered
• Perfect circles (still need epicycles)

Ptolomy Copernicus
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Tycho Brahe (1546-1601)

• Observed a new star
• Showed heavens can change over time
• Designed and used new astronomical instruments
• Collected data on planetary movement

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Tycho Brahe (1546-1601)
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Johannes Kepler (1571-1630)

• Mathematician
• Assistant to Tycho Brahe
• Inherited his notebooks
• Traditional ideas of the solar system are wrong
  (Keplers Laws)

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• Keplers Laws of
• Planetary Motions
• First Law Planets have elliptical orbits

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Elliptical orbits
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• Keplers Laws
• Second Law Orbits sweep out equal areas in equal
  times

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• Keplers Laws
• Third Law Distant orbits take longer
• (Average orbital radius)3 k (orbital period)2
• R3/P2 constant

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Galileo Galilei (1564-1642)

• Mathematician
• Improved the telescope
• Observational astronomy
• Founder of experimental science
• Musical training
• Arrogant, contemptuous, etc.
• Published in Italian (vernacular) promoting
  Copernican view
• Heretic (threatened with torture) so he recanted

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Speed, Velocity, and Acceleration

• Speed distance traveled over time
• Velocity speed with direction
• Equation for speed
• Acceleration rate of change of velocity
• Equation for velocity

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Galileo The Founder ofExperimental Science

• Galileo studied the relationship among distance,
  time, velocity and acceleration
• He observed that objects accelerate while falling

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Galileos Discoveries

• Constant acceleration
• Balls on a plane v at
• Freefall
• Constant acceleration at g
• g 9.8 m/s2 32 feet/s2
• Distance traveled (d) ½at2

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Galileos Laws of Motion

• Trajectories are parabolas
• All objects fall at the same velocity
• Distance of fall k(Time)2
• Remember Kepler (1571-1630)
• Orbits are ellipses
• Equal areas in equal times
• (Radius)3 k(Time)2

Now on to Sir Issac Newton (1642-1727)
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Sir Issac Newton (1642-1727)

• Born prematurely
• Abandoned by his mother
• Forced to run family farm
• Sent to Cambridge University
• Made fundamental advances in several scientific
  fields

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Issac Newtons Plague Years (1665-1666)

• Calculus
• 2. Laws of optics
• Broke white light into colored light
• 3. Universal laws of motion
• 4. Universal law of gravitation

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Two Types of Motions

• Uniform motion No change in velocity or
  direction
• Acceleration Change in velocity and/or direction

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Issac Newton Laws of Motion

• 1st Law Nothing happens without a force
• A moving object will continue moving in a
  straight line at a constant speed, and a
  stationary object will remain at rest, unless
  acted on by an unbalanced force.
• This law defines force

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Issac Newton Laws of Motion

• 1st Law Nothing happens without a force
• 2nd Law Force mass X acceleration (Fma)
• The acceleration produced on a body by a
  force is proportional to the magnitude of the
  force and inversely proportional to the mass of
  the object.
• This law defines mass

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Issac Newton Laws of Motion

• 1st Law Nothing happens without a force
• 2nd Law Force mass X acceleration (Fma)
• 3rd Law Forces always act in pairs
• For every action
• there is an equal
• and opposite
• reaction.

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Momentum

• Momentum depends on mass and speed
• Linear momentum p mv
• Law of conservation of linear momentum
• Angular momentum

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Gravity (a universal force)
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The Universal Force of Gravity

• Between any two masses there exists a force
  that is proportional to the masses and inversely
  proportional to the square of the distance
  between them
• FGm1m2/d2

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The Force of GravityF Gm1m2/d2

• Why mass x mass?
• Think of rays of mass radiating in all
  directions
• gravitational force of rays intersecting

m1
m2
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The Force of GravityF Gm1m2/d2

• Why inverse square of distance?
• Think about light
• light intensity increases
• at shorter distances
• (1/4 the area
• 4X the light)

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The Force of GravityF Gm1m2/d2

• What is G?

• G universal constant of direct proportionality
• Henry Cavendish
• G 6.67 x 10-11m3/s2-kg or
• 6.67 x 10-11N-m2/kg2

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Weight and Gravity

• Weight
• Gravity acting on an objects mass
• Weight depends on gravity
• Different on Earth vs. Moon
• Mass is constant

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Natural Laws Raise DeepPhilosophical Questions

• What about free will?
• Natural laws in other domains
• Economies (Adam Smith)
• Law (cause and effect)
• Politics (George Mason)