Transcript Summary of most of Physics

Energy
• kinetic energy:
– bulk motion: a moving car, orbiting planet:
E = ½mv2
– thermal energy: E = 1.5 kT
• potential energy:
– lifting a rock up a hill increases its
potential energy: E = mgh
– Rolling it down the hill decreases its
potential energy
What is temperature?
• temperature is a measure of thermal kinetic energy of
matter.
• absolute zero: when matter has no thermal energy it is
as cold as it can be: zero Kelvin or T = 0 K.
• When water ice has enough thermal kinetic energy to go
from solid to liquid, T = 273 K. When liquid water gains
enough thermal energy to boil, T = 373 K.
• Large changes in temperature are often associated with
physical, chemical and nuclear reactions.
Atomic Theory
• The idea that matter is made
up of many many particles, the
so called atomic theory, is at
the heart of our understanding
of temperature.
• Temperature can be thought of
as the average thermal energy
of the molecules
solid
liquid
gas
Kinetic Theory
Every once in a while we get a collision
of the molecule on the wall. This
pushes on the wall - adding up all the
pushes gives pressure
What will happen to the number of collisions if
the temperature increases?
It will go up - in other words the pressure
increases as the Temperature increases.
What if the box is made smaller (so that
the density increases) What happens to
the number of collisions then?
It will go up - in other words the pressure
increases as the density increases
Temperature
Temperature is the amount
of energy in the molecules
of the substance
Heat
Heat is the flow of energy
between two (or more)
substances.
Temperature is an intrinsic
property of the material and
can be measured in Kelvin.
We can’t measure heat,
only the temperature
change heat flow causes
Temperature does not depend
on how many molecules you
have, only the energy per
particle.
More molecules will
transfer heat more
efficiently
Heat Transport
• Conduction
– a hot metal rod transfers energy to your hand via
conduction.
– energy transferred without moving the molecules
– important for metals (where electrons within the metal
transfer the energy)
• Convection
– a boiling pot of water transfers heat from the bottom of
the pot to the air above via convection
– moves molecules (either individually or in large groups)
• Radiation
– the hot filament of a light bulb provides light and heat
via radiation.
– doesn’t require matter at all.
Review of Energy
• Energy is conserved
– Kinetic Energy: Energy of Motion
– Potential Energy: Energy of Position
• Kinetic Theory: Atoms are tiny & elastic
– Temperature is the average kinetic energy of the atoms
– Pressure is the number of collisions
• a cold, dense gas can exert the same pressure as a warm,
less dense gas
• In stars, the inward pull of gravity balances the outward
push of thermal pressure.
• Heat energy can be transported by Conduction, Convection,
and Radiation
Energy Concept Test
As a satellite’s orbit decays, it plunges toward the earth.
Describe what happens to the total energy, the kinetic
energy, and the potential energy of the satellite.
The potential energy decreases steadily as the satellite
gets closer to the earth, while the kinetic energy increases
steadily as the satellite moves faster and faster. If we
neglect friction and other losses of energy, all the
potential is converted to kinetic and so the total energy
remains constant.
What is matter?
• matter is the amount of stuff: protons, neutrons,
electrons.
– How do you measure the stuff?
• By the gravitational attraction it exerts on
other matter (gravitational mass)
• By its resistance to changes in motion
(inertial mass)
– In general, the inertial mass is the same as the
gravitational mass, both are measured in kg
Conservation of Mass?
• Physical and chemical reactions appear to conserve mass: the
amount of inertial mass before the reaction is the same as after
the reaction.
• However, nuclear reactions show that what is conserved is
matter + energy. You can convert mass to energy:
E = mc2
Atomic matter
In a neutral atom, the
number of electrons equals
the number of protons.
Every proton has a +1
charge, and every electron a
-1 charge. Ions are formed
by adding or removing
electrons, never protons
Atomic number: number
of protons. All atoms of
an element have the
same atomic number
Atomic Weight: the
number of protons and
neutrons (electrons
weigh almost nothing).
Atomic matter and the periodic table
Isotopes of an element
have the same atomic
number but different
atomic weights. They
differ only in the number
of neutrons.
States of matter
When thermal motions are very
large (hot), the electrons fly
away from the nucleus. This
state is a plasma.
When thermal motions are
moderate (warm), the electrons
are bound to the nucleus, but
atoms cannot bind to form
molecules. This is atomic gas.
When thermal motions are low
(cold), the electrons are bound to
the nucleus and most atoms are
bound together in molecules. This
is molecular gas.
At high pressure, warm and cold
atoms and molecules condense to
form liquids and solids.
Johannes Kepler (1571-1630): first law

1. The orbit of a
planet about the
Sun is an ellipse
with the Sun at
one focus
Kepler’s 2nd and 3rd laws

2. A line joining a
planet and the
Sun sweeps out
equal areas in
equal times.

3. The square of a planet’s sidereal
period is directly proportional to
the cube of its orbit’s semi-major
axis.
2
3
P (in earth years) = a (in au)
It takes as
much time to go
from C to D as
from A to B:
These two areas
are the same
planets move faster
closer to the sun
Newton’s First Law
• An object will continue in a state of rest or a
state of straight motion in the absence of any
force.
– An object will not start moving by itself
– An object will not stop moving by itself
• Why did Aristotle and friends think every object
would naturally become stationary?
– Because they didn’t know about friction, the
force that acts to slow things down
• This implies that the planets are being acted on
by a force, since they are not moving in a
straight line or remaining at rest.
This is where the
planet would move,
if it were moving
in a straight line
Force
This is where the
planet does move, some
force must be pushing
it sideways
Newton’s Second Law
• Objects accelerate more if they are pushed with
bigger forces; less massive objects accelerate
more for the same force than more massive
objects.
• In other words, F = ma
– F is force
– m is mass, we can measure that in kg
– a is acceleration, the rate of change of speed.
• For example, if you are going 60 mph, and you slam on the
brakes, and you stop in 5 seconds, your acceleration was -12
miles per hour per second.
• We usually measure acceleration in m s-2 (both time units the
same)
• acceleration is not just speeding up and slowing down,
changing direction requires acceleration as well
Newton’s Third Law
• For every action, there is an equal and opposite
reaction.
• For example, if you step off a skateboard, you
move forward and the skateboard moves backward
• This also allows rocket propulsion to work
Rocket is pushed this way
Fuel is pushed this way
Gravity
Recall that this change in
acceleration meant some
force pointing inward
This force is gravity
We can show that this
force is greatest for the
interior planets and
weaker for the exterior
planets
In fact, it turns out this force obeys an inverse-square law; i.e. the
force decreases as the square of the distance.
Thus if you double the distance, the force decreases to 1/4.
If you triple the distance, the force decreases to 1/9
Acceleration and Gravity
Orbits and Gravity
When Newton used his
newly discovered calculus
to solve the his newly
discovered law of gravity,
he found three kinds of
solutions: elliptical,
parabolic, hyperbolic.
He found that for the
elliptical orbits, gravity
explained Kepler’s 2nd
and 3rd laws.
But how does gravity act
on objects over such
great distances?
Newton’s Law of Gravitation
F = GM1M2 / d2
The gravitational force (F) on an object is proportional to the
mass of the first object (M1) times the mass of the second object
(M2) divided by the distance between them (d) squared.
Gravity
• Because of Newton’s third law, we know that gravity
acts two ways. The earth exerts a force on you, you
exert a force on the earth.
• Even though the forces are the same, the effects
are different. The acceleration, remember is bigger
for lighter objects. Since the earth is much more
massive than us, we feel a big acceleration and the
earth feels a smaller acceleration.
Correcting Kepler
• If both the sun and planets exert a
force on one another, then they are
orbiting each other.
• Thus the focus of the ellipse is not the
Sun, instead it is their center of mass.
If there are two orbiting suns?
Then they both orbit a common center of mass,
somewhere between them.
Spring tides are
the highest
tides because
the Sun and the
Moon’s gravity
are working
together.
Neap tides are
lower than
spring tides
because the
Sun’s gravity
opposes the
Moon’s gravity.
Gravity causes tidal forces. The
gravitational force is greatest on the
surface of the Earth facing the
Moon and weakest on the opposite
side. The result is two tidal bulges.
The Earth’s rotation produces bulges
slightly ahead of the Moon. Thus we
experience about two high and two
low tides every day.
Inverse Square Law
As you move away
from a light source,
the intensity
decreases as the
square of the
distance.
If you double the distance, the intensity goes down by four times
If you triple the distance, the intensity goes down by nine times
If you quadruple the distance, the intensity goes down by sixteen times
If you half the distance, the intensity goes up by 4 times.
Waves
Short Wavelength
Long wavelength
•
•
•
•
wavelength
All light waves travel at the same speed, c = 300,000 km/s
Wavelength is the distance between two crests of the wave
Frequency is the number of crests that pass by you in a second
The longer the wavelength, the lower the frequency, the lower the
energy of the photon
10-14
Gamma rays
nucleus
X rays
atom
10-12
10-10
10-8
Ultraviolet
virus
Visible
10-6
10-4
• E = hf
• E = hc/
Infrared
Pin head
FM
Human
• c = f
10-2
102
104
Wavelength
Lower energy
Lower frequency
1
Radio
AM
Mountain
the electromagnetic spectrum
Two Laws of Radiation
• The hotter the material the more radiation the matter emits.
– This tell us that the sun, at about 6000 K, emits more
radiation than the earth, at 300 K
– Something twice times as hot (its absolute temperature is
twice as high) emits 16 times as much radiation
• The hotter the material, the higher the energy of the average
photon and the higher the frequency of the radiation
– this tells us the sun emits mostly visible light and the earth
emits infrared light
The area under
the curve is
proportional to
the luminosity
The sun appears
yellow because it
Spectra
emits more
yellow
light than any other
kind.
As the temperature increases,
the peak wavelength decreases
As the temp increases, the
luminosity increases
Emission
The electron jumps down to lower state
emitting photons with an energy exactly
equal to the energy difference between
the two states of matter
The outgoing photon can only have certain
energies, corresponding to the energy
difference between different states.
In other words, only very exact
wavelengths are emitted.
What is it made of
Hydrogen Spectra
The spectra of radiation
emitted by Hydrogen only
shows a few wavelengths,
corresponding to the
energy difference
between the electrons
allowed states
What is it made of
Emission Spectra
H2
H
Since different elements have different spectra, we can use the
spectrum of a star to determine its composition.
Absorption
Incoming radiation is absorbed and the
electron jumps to a higher energy state
The incoming radiation is only absorbed if the
energy is the same as the difference in energy
between two states. In other words, only very
exact wavelengths are absorbed
The electron jumps down to its basic state,
emitting a photon
Sometimes the electron goes down in steps,
emitting lower energy photons than it absorbed.
Emission and Absorption of Hydrogen
Emission and Absorption lines
Looking at the
hot light source
through cooler
gas produces
absorption lines.
incident light is a
continuous blackbody
spectrum
If the cooler gas is hot
enough and thin
enough, it produces its
own emission spectrum.
The Solar Spectrum
The darkest lines were observed in the solar spectrum by
William Wollaston in 1802, but Fraunhofer catalogued them 10
years later; they are now known as Fraunhofer Lines
Just as the pitch of the train
whistle tells us whether the
train is moving away or toward
us, the wavelength of light from
a star or galaxy tells us whether
it is moving away or toward us.
Summary
• Temperature can be determined from the wavelength peak of
the emitted radiation
• Composition can be determined from the spectral absorption or
emission lines of the object
• The speed of the object toward or away from you can be
determined by the Doppler shift of the spectral lines.