Title: Gravity
1Gravity
- 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 -
2Newton Three Laws of Motion
- Inertia
- F ma
- Action Reaction
3Newtons 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
4Velocity, 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
5Ball Swung around on a String
Same Speed, (in uniform circular motion) Changing
Direction (swinging around the circle)
6Ball Swung around on a String
Same Speed, (in uniform circular motion) Changing
Direction (swinging around the circle)
7Donut Swung around on a String
8Donut Swung around on a String
9Conservation 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!
10Conservation 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!
11Action Reaction
Equal and Opposite Force from the Table
Net Force is Zero, No Net Motion
12Action Reaction
Equal and Opposite Force from the Table
Net Force is Zero, No Net Motion
13Acceleration 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) -
14Galileos 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
15Galileos 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
16g 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 -
17Escape 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
18Escape 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
19Object in orbit ? Continuous fall !
Object falls towards the earth at the same rate
as the earth curves away from it
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22Angular 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
23Angular 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
24Conservation 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
25Relativistic1 Jet From Black Hole
1. Relativistic velocities are close to the
speed of light
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27Quiz 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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29 Stars and Galaxies Galileo to HST
- http//thenextdigit.com/16961/nasa-telescopes-new-
panoramic-view-andromeda-resolves-stars/
30Why is the sky blue ?
The atmosphere scatters the blue light more than
red light
31Light 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
32Radiation and Spectroscopy
- Light is electromagnetic energy
- Propagates as both particles and waves
- Photons particles of light
- Wavelength Velocity / Frequency
33Light 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
35Units 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 -
36Prisms disperse light into its component colors
Red-Violet
Prism
37Visible 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?
38Light 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.
39Decreasing Wavelength OR Increasing Frequency
40Visible 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)
41Matter 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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43The Hydrogen Atom
Electron orbits Discrete energies
44Absorption of light (energy) photon by H-atom
45Emission of light photon by H-atomphoton energy
?color
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48Series of spectral lines of Hydrogen
49Wavelengths of series of lines from Hydrogen
50SPECTRAL SIGNATURE OF ELEMENTS
51Continuous, Absorption, and Emission Spectra
52Brightness 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
53Color 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)
54TEMPERATURE 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
55The 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
56Doppler Effect in Sound
Low Pitch (long waves)
High Pitch (short waves)
57Brightness decreases inversely as the square of
the distance
B1
B1/4
B1/9
58The Doppler Effect
Velocity c frequency (f) x wavelength (l)
59Doppler 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)