Gravity

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Gravity

• Galileos observations on gravity led to Newtons
  Law of Gravitation and the three Laws of Motion
• Objects fall at the same rate regardless of mass
  because more massive objects have more inertia or
  resistance to motion
• Fgrav G (m1 x m2) / r2
• Force of gravity between two masses is
  proportional to the product of masses divided by
  distance squared ? inverse square law

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Newton Three Laws of Motion

1. Inertia
2. F ma
3. Action Reaction

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Newtons Laws of Motion

• Law of Inertia A body continues in state of
  rest or motion unless acted on by an external
  force Mass is a measure of inertia
• Law of Acceleration For a given mass m, the
  acceleration is proportional to the force applied
• F m a
• Law of Action equals Reaction For every action
  there is an equal and opposite reaction momemtum
  (mass x velocity) is conserved

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Velocity, Speed, Acceleration

• Velocity implies both speed and direction speed
  may be constant but direction could be changing,
  and hence accelerating
• Acceleration implies change in speed or
  direction or both
• For example, stone on a string being whirled
  around at constant speed direction is constantly
  changing therefore requires force

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Ball Swung around on a String
Same Speed, (in uniform circular motion) Changing
Direction (swinging around the circle)
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Ball Swung around on a String
Same Speed, (in uniform circular motion) Changing
Direction (swinging around the circle)
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Donut Swung around on a String
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Donut Swung around on a String
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Conservation of momemtumaction equal reaction

• The momemtum (mv) is conserved before and after
  an event
• Rocket and ignited gases
• M(rocket) x V(rocket) m(gases) x v(gases)
• Two billiard balls
• m1 v1 m2 v2 m1 v1 m2 v2
• v1,v2 velocities before collision
• v1,v2 velocities after collision
• Example you and your friend (twice as heavy)
  on ice!

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Conservation of momemtumaction equal reaction

• The momemtum (mv) is conserved before and after
  an event
• Rocket and ignited gases
• M(rocket) x V(rocket) m(gases) x v(gases)
• Two billiard balls
• m1 v1 m2 v2 m1 v1 m2 v2
• v1,v2 velocities before collision
• v1,v2 velocities after collision
• Example you and your friend (twice as heavy)
  on ice!

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Action Reaction
Equal and Opposite Force from the Table
Net Force is Zero, No Net Motion
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Action Reaction
Equal and Opposite Force from the Table
Net Force is Zero, No Net Motion
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Acceleration due to gravity

• Acceleration is rate of change of velocity,
  speed or direction of motion, with time ? a v/t
• Acceleration due to Earths gravity a ? g
• g 9.8 m per second per second, or 32 ft/sec2
• Speed in free-fall
• T (sec) v (m/sec) v
  (ft/sec)
• 0 0
  0
• 1 9.8
  32
• 2 19.6
  64
• 3 29.4
  96
• 60 mi/hr 88 ft/sec (between 2 and 3
  seconds)

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Galileos experiment revisited

• What is your weight and mass ?
• Weight W is the force of gravity acting on a
  mass m causing acceleration g
• Using F m a, and the Law of Gravitation
• W m g G (m MEarth) /R2
• (R Radius of the Earth)
• The mass m of the falling object cancels out
  and does not matter therefore all objects fall
  at the same rate or acceleration
• g GM / R2
• i.e. constant acceleration due to gravity
  9.8 m/sec2

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Galileos experiment on gravity

• Galileo surmised that time differences between
  freely falling objects may be too small for human
  eye to discern
• Therefore he used inclined planes to slow down
  the acceleration due to gravity and monitor the
  time more accurately

v
Changing the angle of the incline changes the
velocity v
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g on the Moon

• g(Moon) G M(Moon) / R(Moon)2
• G 6.67 x 10-11 newton-meter2/kg2
• M(Moon) 7.349 x 1022 Kg
• R(Moon) 1738 Km
• g (Moon) 1.62 m/sec/sec
• About 1/6 of g(Earth) objects on the Moon
  fall at a rate six times slower than on the Earth

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Escape Velocity and Energy

• To escape earths gravity an object must have
  (kinetic) energy equal to the gravitational
  (potential) energy of the earth
• Kinetic energy due to motion
• K.E. ½ m v2
• Potential energy due to position and force
• P.E. G m M(Earth) / R
• (note the similarity with the Law of
  Gravitation)
• Minimum energy needed for escape K.E. P.E.
• ½ m v2 G m M / R
• Note that the mass m cancels out, and
• v (esc) 11 km/sec 7 mi/sec 25000 mi/hr
• The escape velocity is the same for all
  objects of mass m

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Escape Velocity and Energy

• To escape earths gravity an object must have
  (kinetic) energy equal to the gravitational
  (potential) energy of the earth
• Kinetic energy due to motion
• K.E. ½ m v2
• Potential energy due to position and force
• P.E. G m M(Earth) / R
• (note the similarity with the Law of
  Gravitation)
• Minimum energy needed for escape K.E. P.E.
• ½ m v2 G m M / R
• Note that the mass m cancels out, and
• v (esc) 11 km/sec 7 mi/sec 25000 mi/hr
• The escape velocity is the same for all
  objects of mass m

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Object in orbit ? Continuous fall !
Object falls towards the earth at the same rate
as the earth curves away from it
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Angular Momentum
Conservation of angular momentum says that
product of radius r and momentum mv must be
constant ? radius times rotation rate (number of
rotations per second) is constant
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Angular Momentum

• All rotating objects have angular momentum
• L mvr acts perpendicular to the plane of
  rotation
• Examples helicopter rotor, ice skater, spinning
  top or wheel (experiment)
• Gyroscope (to stabilize spacecrafts) is basically
  a spinning wheel whose axis maintains its
  direction slow precession like the Earths axis
  along the Circle of Precession

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Conservation of Angular Momentum

• Very important in physical phenomena observed in
  daily life as well as throughout the Universe.
  For example,
• Varying speeds of planets in elliptical orbits
  around a star
• Jets of extremely high velocity particles, as
  matter spirals into an accretion disc and falls
  into a black hole

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Relativistic1 Jet From Black Hole
1. Relativistic velocities are close to the
speed of light
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Quiz 1

• Each quiz sheet has a different 5-digit
  symmetric number which must be filled in (as
  shown on the transparency, but NOT the same
  one!!!!!)
• Please hand in both the exam and the answer
  sheets with your name on both
• Question/answer sheets will be handed back on
  Wednesday after class
• Please remain seated until we begin collecting
  (20-25 minutes after start)
• Class after quiz

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Stars and Galaxies Galileo to HST

• http//thenextdigit.com/16961/nasa-telescopes-new-
  panoramic-view-andromeda-resolves-stars/

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Why is the sky blue ?
The atmosphere scatters the blue light more than
red light
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Light and Matter

• Light is electromagnetic energy, due to
  interaction of electrical charges
• Matter is made of atoms equal number of
  positive and negative particles
• An atom is the smallest particle of an element
  natural element H to U
• Atom ? Nucleus (protons neutrons), with
  orbiting electrons
• No. of protons in nucleus Atomic Number
• Science of light ? Spectroscopy

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Radiation and Spectroscopy

• Light is electromagnetic energy
• Propagates as both particles and waves
• Photons particles of light
• Wavelength Velocity / Frequency

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Light is electromagnetic waveDoes not require a
medium to propagate, unlike water or sound
Wavelength is the distance between successive
crests or troughs
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WAVES Frequency, Wavelength, Speed
Frequency (f) ( waves/second)
Frequency f is the number of waves passing a
point per second
Speed wavelength x frequency ? c
l f
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Units of wavelength and frequency

• Frequency is the number of cycles per second
• Since speed of light is constant, higher the
  frequency the shorter the wavelength and
  vice-versa
• Wavelengths are measured in Angstroms 1A
  1/100,000,000 cm 1/10 nanometer (nm)
• The higher the frequency the more energetic the
  wave
• Wavelength (or frequency) defines radiation or
  color

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Prisms disperse light into its component colors
Red-Violet
Prism
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Visible Light

• Forms a narrow band within the electromagnetic
  spectrum ranging from gamma rays to radio waves
• Human eye is most sensitive to which color?
• Yellow. Why?

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Light Electromagnetic SpectrumFrom Gamma Rays
to Radio Waves
Gamma X-Ray UV Visible
Gamma rays are the most energetic (highest
frequency, shortest wavelength), Radio waves are
the least energetic.
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Decreasing Wavelength OR Increasing Frequency
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Visible light spectrum Each color is defined by
its wavelength, frequency or energy
Red - Blue ? 7000 - 4000 Angstroms ( 1 nm
10 A, 1 A 10-8 cm) Blue light is more
energetic than red light Light also behaves like
particles called photons Photon energy,
frequency, wavelength E h f hc/l Plancks
Law (h is a number known as Plancks constant)
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Matter and Particles of Light Quantum Theory

• Light (energy) and matter in motion behave both
  as waves and particles
• Wave-Particle Duality - Quantum Theory
• Particles of light are called photons E hf
  hc/l
• Photons of a specific wavelength l may be
  absorbed or emitted by atoms in matter
• Matter is made of different natural elements
  lightest Hydrogen (1 proton), heaviest Uranium
  (92 protons)
• Smallest particle of an element is atom, made up
  of a nucleus (protons and neutrons), and orbiting
  electrons
• Electrons and protons attract as opposite
  electrical charges, NOT gravitationally like
  planets and Sun

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The Hydrogen Atom
Electron orbits Discrete energies
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Absorption of light (energy) photon by H-atom
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Emission of light photon by H-atomphoton energy
?color
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Series of spectral lines of Hydrogen
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Wavelengths of series of lines from Hydrogen
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SPECTRAL SIGNATURE OF ELEMENTS
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Continuous, Absorption, and Emission Spectra
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Brightness and Temperature

• Brightness is related to the total energy
  emitted, or the luminosity of an object
• The energy emitted is related to the temperature
  of the object
• B s T4 (s is a constant)
• Stefan-Boltzmann Law

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Color Indicates Temperature and Energy of the
Source
Blackbody Perfect absorber and emitter Of
radiation at a given Temperature T
Surface T (Sun) 5600 K (Mercury)
800 K
Objects generally emit radiation at all
wavelengths, but mostly at one peak Wavelength
depending on their temperature (e.g. blue hot,
red cool)
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TEMPERATURE SCALES
Astronomers usually use the Kelvin Scale
Room Temp 300 K 27 C 81 F
K C 273 C (F - 32) x 5/9 (F - 30)
/ 2 F (C x 9/5) 32 C x 2 30
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The Doppler Effect

• Why does the pitch of a police siren differ
  when, say, a police car is approaching you, or
  when you are running away from the police (not
  recommended) ?
• The frequency (the number of sound waves per
  second) is higher when approaching, and smaller
  when receding from the source

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Doppler Effect in Sound
Low Pitch (long waves)
High Pitch (short waves)
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Brightness decreases inversely as the square of
the distance
B1
B1/4
B1/9
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The Doppler Effect
Velocity c frequency (f) x wavelength (l)
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Doppler Shift of Wavelengths

• What about the wavelength?
• What about light?
• Shorter wavelength ? Blue-shift,
• Longer wavelength ? Red-shift
• We can determine the velocity of astronomical
  objects, moving away or towards the Earth, by
  measuring the wavelength of light from the object
• Observed red-shift of galaxies all over the sky
  shows that galaxies are moving away from one
  another ? the Universe is expanding (Hubbles
  Law)