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Gravity

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Why is the sky blue ? The atmosphere scatters the blue light more than red light Light and Matter Light is electromagnetic energy, due to interaction of electrical ... – PowerPoint PPT presentation

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Title: Gravity


1
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

2
Newton Three Laws of Motion
  1. Inertia
  2. F ma
  3. Action Reaction

3
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

4
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

5
Ball Swung around on a String
Same Speed, (in uniform circular motion) Changing
Direction (swinging around the circle)
6
Ball Swung around on a String
Same Speed, (in uniform circular motion) Changing
Direction (swinging around the circle)
7
Donut Swung around on a String
8
Donut Swung around on a String
9
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!

10
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!

11
Action Reaction
Equal and Opposite Force from the Table
Net Force is Zero, No Net Motion
12
Action Reaction
Equal and Opposite Force from the Table
Net Force is Zero, No Net Motion
13
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)

14
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

15
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
16
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

17
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

18
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

19
Object in orbit ? Continuous fall !
Object falls towards the earth at the same rate
as the earth curves away from it
20
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21
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22
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
23
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

24
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

25
Relativistic1 Jet From Black Hole
1. Relativistic velocities are close to the
speed of light
26
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27
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

28
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29
Stars and Galaxies Galileo to HST
  • http//thenextdigit.com/16961/nasa-telescopes-new-
    panoramic-view-andromeda-resolves-stars/

30
Why is the sky blue ?
The atmosphere scatters the blue light more than
red light
31
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

32
Radiation and Spectroscopy
  • Light is electromagnetic energy
  • Propagates as both particles and waves
  • Photons particles of light
  • Wavelength Velocity / Frequency

33
Light is electromagnetic waveDoes not require a
medium to propagate, unlike water or sound
Wavelength is the distance between successive
crests or troughs
34

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
35
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

36
Prisms disperse light into its component colors
Red-Violet
Prism
37
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?

38
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.
39
Decreasing Wavelength OR Increasing Frequency
40
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)
41
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

42
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43
The Hydrogen Atom
Electron orbits Discrete energies
44
Absorption of light (energy) photon by H-atom
45
Emission of light photon by H-atomphoton energy
?color
46
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48
Series of spectral lines of Hydrogen
49
Wavelengths of series of lines from Hydrogen
50
SPECTRAL SIGNATURE OF ELEMENTS
51
Continuous, Absorption, and Emission Spectra
52
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

53
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)
54
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
55
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

56
Doppler Effect in Sound
Low Pitch (long waves)
High Pitch (short waves)
57
Brightness decreases inversely as the square of
the distance
B1
B1/4
B1/9
58
The Doppler Effect
Velocity c frequency (f) x wavelength (l)
59
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)
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