Introducing Newton

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Introducing Newton

• Dr Bryce
• 2950

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Class Notices

• An exciting week for lab students
• Homework Quiz 3 is now available
• Some students will see a sensible score for
  Homework Quiz 2, expect the scores to be correct
  by the end of this week!

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Aims

• We need to formally define motion.
• Newtons laws of motion
• What is gravity?
• We need to understand the difference between
  weight and mass
• Conservation of energy and momentum
• These subjects are the core of classical
  mechanics in physics.
• The most Fundamental Principles we will meet
• We are also going to discuss Energy

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Motion?

• Speed the rate at which an object moves, units
  are meters per second or ms-1 or m/s
• Velocity speed and direction
• Acceleration the change in velocity, units are
  meters per second per second or ms-2 or m/s2
• In our day to day life we will often speak of
  miles per hour or the numbers of seconds it takes
  a car to go from 0 to 60 (again mph)
• 1 meter per second is about 2.2 mph

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Acceleration

• We tend to think of acceleration as objects
  increasing in speed
• In fact acceleration occurs whenever there is a
  change in speed positive or negative
• AND when there is a change in direction

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Momentum

• Momentum mass velocity
• A net force changes momentum, usually a change in
  velocity (an acceleration)
• Angular momentum is the momentum of a spinning or
  orbiting object (Remember that an orbiting object
  is constantly changing direction, even if the
  velocity is constant there is always an
  acceleration)

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Isaac Newton 1642-1727

• Formulated laws of motion and gravity.
• The same laws on Earth are also applicable to
  planets and stars.
• Also famous for optics, calculus

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Newtons first law of motion

• An object moves at constant velocity, unless a
  net force acts to change its speed or direction.

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Balanced forces versus a net force
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Thought QuestionIs there a net force? Y/N

• A car coming to a stop.
• A bus speeding up.
• An elevator moving up at constant speed.
• A bicycle going around a curve.
• A moon orbiting Jupiter.

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Newtons second law of motion

• Force mass acceleration

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Newtons third law of motion

• For every action there is an equal and opposite
  reaction

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Gravity

• Produces acceleration, eg towards the centre of
  the Earth
• All falling objects accelerate at the same rate
  (if we ignore the effects of air resistance)
• On Earth the acceleration (g) is 10 m/s2, so with
  each second of falling the speed increases by 10
  m/s

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Acceleration of Gravity

• Galileo and David Scott demonstrated that g is
  the same for all falling objects regardless of
  their mass
• Although g on the Moon is much lower than on the
  Earth!

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Mass and Weight

• Mass The amount of matter in an object
• Weight The force that acts upon an object
• An object in freefall is weightless not massless

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Thought QuestionOn the Moon

• My weight is the same, my mass is less.
• My weight is less, my mass is the same.
• My weight is more, my mass is the same.
• My weight is more, my mass is less.

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The Universal Law of Gravitation

• Every mass attracts every other mass.
• Attraction is directly proportional to the
  product of their masses.
• Attraction is inversely proportional to the
  square of the distance between their centers.

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Universal Law of Gravitation

• F is the Gravitational force
• M the larger mass and m is the smaller
• G is the Gravitational constant 6.672610-11m3/kg
  s2

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Centre of Mass

• Because of momentum conservation, orbiting
  objects orbit around their center of mass

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Newton and Keplers Laws

• His laws of gravity and motion showed that the
  relationship between the orbital period and
  average orbital distance of a system tells us the
  total mass of the system.
• Examples
• Earths orbital period (1 year) and average
  distance (1 AU) tell us the Suns mass.
• Orbital period and distance of a satellite from
  Earth tell us Earths mass.
• Orbital period and distance of a moon of Jupiter
  tell us Jupiters mass.

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Newtons version

• p orbital period
• aaverage orbital distance (between centers)
• (M1 M2) sum of object masses

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Escape Velocity

• If an object gains enough orbital energy, it may
  escape (change from a bound to unbound orbit)

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Changing an Orbit

• So what can make an object gain or lose orbital
  energy?
• Friction or atmospheric drag
• A gravitational encounter.

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Gravity causes Tides

• Moons gravity pulls harder on near side of Earth
  than on far side
• Difference in Moons gravitational pull stretches
  Earth

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Tides Phases

• Size of tide depends on the phase of the Moon
• Spring and Neap tides

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Tidal Friction

• Tidal friction gradually slows Earth rotation
  (and makes Moon get farther from Earth).
• Tidal friction caused the Moon to lock in
  synchronous rotation.

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Why do objects fall at the same rate?
The gravitational acceleration of an object like
a rock does not depend on its mass because Mrock
in the equation for acceleration cancels Mrock in
the equation for gravitational force This
coincidence was not understood until Einsteins
general theory of relativity.
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Newtonian Gravity

• Tells us virtually all we need to know about
  Gravity
• Einstein improved on Newtons Universal law of
  Gravitation with his theory of General Relativity
  in 1915

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Gravity, Newton, and Einstein

• Newton viewed gravity as a mysterious action at
  a distance
• Einstein removed the mystery by showing that what
  we perceive as gravity arises from curvature of
  spacetime

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Rubber Sheet Analogy

• Mass of Sun curves spacetime
• Free-falling objects near Sun follow curved paths
• Circles near Sun have circumference lt 2pr

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Conservation of momentum

• The total momentum of interacting objects cannot
  change unless an external force is acting on them
  
• Interacting objects exchange momentum through
  equal and opposite forces

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Types of Energy

• Kinetic
• Radiative
• Stored or potential
• Energy can change types, but it cannot be created
  or destroyed.

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Thermal energy (Kinetic)
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Thermal Energy the collective kinetic energy of
many particles(for example, in a rock, in air,
in water)
Thermal energy is related to temperature but it
is NOT the same. Temperature is the average
kinetic energy of the many particles in a
substance.
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Thermal energy

• Is the measure of the total kinetic energy of all
  particles in a substance.
• It therefore depends on temperature and density.
• Heat is not the same as hot!
• Compare boiling water to an oven at the same
  temperature.

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Gravitational Potential Energy

• On Earth, depends on
• objects mass (m)
• strength of gravity (g)
• distance object could potentially fall

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Gravitational Potential Energy

• In space, an object or gas cloud has more
  gravitational energy when it is spread out than
  when it contracts.
• A contracting cloud converts gravitational
  potential energy to thermal energy.

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Mass Energy

• Mass itself is a form of potential energy
• A small amount of mass can release a great deal
  of energy
• Concentrated energy can spontaneously turn into
  particles (for example, in particle accelerators)

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Conservation of Energy

• Energy can be neither created nor destroyed.
• It can change form or be exchanged between
  objects.
• The total energy content of the Universe was
  determined in the Big Bang and remains the same
  today.

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Fundamental Properties of Matter

• The objects we are surrounded by the air we
  breathe in and our bodies are all comprised of
  atoms
• Atoms are made up out of electrons, protons and
  neutrons
• Electrons are very small and have a negative
  charge
• Protons and Neutrons are relatively larger,
  protons have a positive charge, neutrons have no
  charge

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Atomic Terminology

• Atomic Number number of protons in nucleus
• Atomic Mass Number number of protons neutrons

• Molecules consist of two or more atoms (H2O,
  CO2)

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Atomic Terminology

• Isotope same number of protons but different
  number of neutrons. (4He, 3He)

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What are the phases of matter?

• Familiar phases
• Solid (ice)
• Liquid (water)
• Gas (water vapor)
• Phases of same material behave differently
  because of differences in chemical bonds
• Plasma is the fourth phase of matter, the Sun,
  fluorescent light bulbs

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How is energy stored in atoms?
Excited States
Ground State

• Electrons in atoms are restricted to particular
  energy levels