Chapter 3: Energy Part 2

1
Chapter 3 Energy Part 2

• Alyssa Jean-Mary

2
Heat

• Heat is a form of energy
• Two centuries ago heat was actually not regarded
  as a form of energy it was thought of as an
  actual substance called caloric
• The scientists thought that if you absorb
  caloric, you get warmer, and that if caloric is
  lost, you get colder
• Caloric is considered to be weightless since your
  weight does not change whether you are warmer or
  colder
• It is also considered to be invisible, odorless,
  and tasteless, which is why it was not observable
• Benjamin Thompson, an American who became Count
  Rumford when he moved to Europe, was one of the
  first to view heat as a form of energy
• Rumford supervised the making of cannon for a
  German prince. During the making of cannon, he
  noticed that there was a large amount of heat
  given off by friction in the boring process. He
  showed that this heat could be used to boil
  water. Also, he showed that the heat could be
  produced again and again from one piece of metal.
  If heat was a substance (i.e. a liquid), it was
  reasonable that if you bore a hole in a piece of
  metal, the liquid will be allowed to escape. What
  Rumford found made him regard heat as a form of
  energy because even though this was reasonable,
  it did not seem reasonable that even a dull
  drill, which does not cut into the piece of
  metal, produced a great amount of heat, and also,
  it did not seem reasonable that a piece of metal
  has an infinite amount of a substance.
• James Prescott Joule performed an experiment that
  ended the argument as to whether heat was a
  substance or a form of energy. Joule put a small
  paddle wheel inside a container of water. Work
  was done against the resistance of the water to
  turn the paddle wheel. He measured how much heat
  was added to the water by the friction of turning
  the wheel. What he found that the same amount of
  work produced the same amount of heat, thus
  showing that heat is a form of energy, and not a
  substance.
• After performing chemical and electrical
  experiments in addition to his mechanical
  experiments much like this one, when he was 29,
  in 1847, he announced his results in the law of
  conservation of energy. Joule was a modest man,
  but received many honors for his work (for
  example, the SI unit of energy, the Joule, was
  named after him).

3
Momentum

• Linear momentum is a measure of the tendency of
  an object that is moving at a constant speed
  along a straight path to continue to do so
• Linear momentum is often referred to as just
  momentum
• The more linear momentum an object has, more is
  needed to slow it down or change its direction of
  motion
• Angular momentum is a measure of the tendency of
  an object that is spinning to continue to spin

4
Linear Momentum

• The equation for Linear momentum is
• p mv
• where p is the linear momentum (a vector
  quantity), m is the mass, and v is the velocity
  (a vector quantity)
• As the equation shows, linear momentum is
  directly proportional to both the mass and the
  velocity thus, if the mass is greater, the
  linear momentum is greater, AND if the velocity
  is greater, the linear momentum is also greater
• For example, a baseball that is hit by a bat is
  harder to stop than a baseball that is thrown
  because it is moving faster. Also, a bowling ball
  is harder to stop than a baseball because it has
  more mass.

5
Conservation of Momentum

• The Law of Conservation of Momentum In the
  absence of outside forces, the total momentum of
  a set of objects remains the same no matter how
  the objects interact with one another.
• In other words, if two objects are interacting
  only with each other, each object can have a
  change in momentum, only as long as the total
  momentum of the two objects does not change (i.e.
  if you add together the momentum of each object
  before the interaction and then add together the
  momentum of each object after the interaction,
  they should be equal)
• For example, if a girl is running towards a
  stationary sled and jumps on the sled, the girl
  and the sled move more slowly then the speed of
  the girl when she was running (of course,
  assuming that there was no friction between the
  sled and the snow), thus conserving the momentum.
  In other words, to conserve momentum, the
  original momentum of the girl and the sled, which
  is the original momentum of the girl, p m1v1,
  since the sled was not moving and thus had no
  momentum, has to be equal to the final momentum
  of the girl and the sled (p (m1 m2)v2). Since
  the final mass (m1 m2) is greater than the
  original mass (m1), v2 has to be less than v1 to
  obtain the same amount of momentum.

6
Rockets

• A rocket is operated based on the conservation of
  linear momentum
• On the launch pad, a rocked has zero momentum.
• When the rocket is fired, there are exhaust gases
  that rush downward. The momentum of these exhaust
  gases is balanced by the rocket moving in the
  opposite direction (i.e. upward).
• The total momentum of the system (i.e. the rocket
  plus the exhaust gases) remains zero, the
  momentum the rocket started with, because, since
  momentum is a vector quantity, the downward
  momentum of the gases cancels out the upward
  momentum of the rocket.
• Thus, rockets dont do work by pushing against
  the launch pad or the air they actually
  function best in space since there is no air to
  interfere with their motion
• The ultimate speed a rocket can reach is governed
  by two things
• the amount of fuel it can carry
• the speed of its exhaust gases

7
Multistage rockets

• Multistage rockets are used to explore space
  because both the amount of fuel a rocket can
  carry and the speed of a rockets exhaust gases
  are limited
• The first stage A large rocket, that has a
  smaller one mounted to the front of it, is fired.
  
• The second stage The second stage is fired after
  all the fuel in the first stage has been burnt up
  and the motor and the empty fuel tanks have been
  cast off.
• Since in the second stage the rocket is already
  moving rapidly and the motor and the empty fuel
  tanks have been cast off, the rocket can reach a
  much greater final speed than would have been
  possible if there was only one stage.
• Depending on the final speed needed for a
  mission, there can even be three or four stages
• There were three stages for the Saturn V launch
  vehicle, which contained the Apollo 11
  spacecraft, that was launched in July 1969. The
  entire thing was 111 m long and had a mass of
  almost 3 million kg

8
Angular Momentum

• The tendency of a rotating object is to continue
  to spin unless an outside source slows or stops
  the object
• For example, the earth has been turning for
  billions of years and will continue to do so for
  many more to come
• Also, the only reason a top stops spinning is
  because there is friction between its tip and the
  surface it is on if there was no friction, the
  top would continue to spin
• Angular momentum depends on
• the mass of the object the more mass an object
  has, the more angular momentum it has
• how fast the object is turning the faster an
  object rotates, the more angular momentum it has
• how the mass is arranged in the object the
  farther away from the axis of rotation the mass
  is distributed, the more angular momentum it has
• Just like linear momentum, angular momentum is
  conserved
• For example, a skater starts to spin by pushing
  against the ice with one skate. At first, both
  arms and one leg are extended, which means that
  the mass of the skater is spread as far as
  possible from the axis of rotation. When the
  skaters arms and leg are brought in tightly
  against the body, all the mass of the skater is
  as close as possible to the axis of rotation.
  Because of this change, the skater rotates
  faster, which conserves the angular momentum
  (i.e. since the way the mass was arranged
  changed, the speed has to change in order for the
  same amount of angular momentum to be present.

9
Spin Stabilization

• Just like linear momentum, angular momentum is a
  vector quantity (i.e. it has a magnitude and a
  direction)
• Because it is a vector quantity, the conservation
  of angular momentum means that in addition to
  maintaining the same amount of angular momentum,
  a spinning object also maintains the direction of
  its spin axis
• For example, a top that is not moving falls over
  right away, but when a top is spinning rapidly,
  it stays upright because its tendency to keep its
  axis in the same orientation, due to its angular
  momentum, is greater than its tendency to fall
  over

10
Special Relativity

• Albert Einstein published his theory of
  relativity at the age of 26 in 1905, in which he
  analyzed how measurements of time and space are
  affected by motion between an observer and what
  he or she is studying.
• In addition to linking time and space, this
  theory links energy and matter
• Many predictions made from the theory of
  relativity have been proven true by
  experimentation
• Eleven years from this publication, Einstein took
  his theory one step further by interpreting
  gravity as a distortion in the structure of space
  and time, which allowed even more predictions to
  be made
• This first relativity, published in 1905, is
  called special relativity because it is
  restricted to constant velocity. Later, when he
  included gravity and acceleration, it was
  referred to as general relativity.

11
Einsteins First Postulate

• If someone takes a measurement of the length of
  an airplane while onboard the airplane, Einstein
  said that the value obtained will be different
  from the value obtained if someone measured the
  length of the airplane from the ground while the
  airplane is in the air.
• The position of something compared to the
  position of something else is called the frame of
  reference when we say that something is moving,
  what we mean is that it is changing its position
  relative to something else, for example, us.
• For instance, a person walking on an airplane is
  moving relative to the airplane, the airplane is
  moving relative to the earth, the earth is moving
  relative to the sun, etc.
• In order to say that something is moving, a frame
  of reference is always needed. For example, if
  you are on a airplane without a window, you would
  not be able to tell if the airplane was moving
  with constant velocity or was at rest on the
  ground, because you have no external frame of
  reference.
• Einsteins First Postulate The laws of physics
  are the same in all frames of reference moving at
  constant velocity with respect to one another.
• If the laws of physics were different for
  different observers in relative motion, it would
  be possible for the observers to use these
  differences to find out which of them were
  stationary and which of them were moving, but
  since this is not the case, there is the
  Einsteins First Postulate

12
Einsteins Second Postulate

• Einsteins Second Postulate The speed of light
  in free space has the same value for all
  observers.
• From many experiments, Einstein found that the
  speed of light in free space is equal to 3 x 108
  m/s, which is about 186,000 mi/s

13
Relativity Length, Time, and Mass

• I am on an airplane, under the following
  criteria the airplane is moving at constant
  velocity, v, relative to you on the ground, the
  length of the airplane is L0, the mass of the
  airplane is m, and there is a certain amount of
  time, t0. According to Einstein, you on the
  ground would find the following
• The length, L, that you measure is less than the
  length, L0, that I measured, so the airplane
  appears shorter to you than to me
• The time, t, that you measure is more than the
  time, t0 that I measured, so my watch appears to
  tick more slowly than yours
• The kinetic energy that you determine is greater
  than the equation for kinetic energy, mv2/2, so
  to you the airplane appears to have more kinetic
  energy than to me
• The differences between the values measure (i.e.
  L and L0, t and t0, and KE and mv2/2) depends on
  the ratio v/c, which is the ration between the
  speed v of the frames of reference (in this
  example, the seed of the airplane relative to the
  ground) and the speed of light c
• Since the speed of light is so great, it is hard
  to detect these differences for the speed of an
  airplane, because these differences are too
  small. The differences can be calculated for the
  speed of a spacecraft, however.
• At speeds that are near the speed of light, such
  as the speeds of subatomic particles like
  electrons and protons, relativistic effects are
  quite obvious. At these high speeds, the kinetic
  energy equation, mv2/2, is not valid as it is at
  lower speeds, and instead, the kinetic energy is
  higher than this. As the graph shows, the closer
  the speed of the object is to the speed of light,
  the closer the KE gets to infinity. Since an
  infinite kinetic energy is not possible, this
  shows that nothing can travel as fast as light or
  even faster than light i.e. the speed of light
  is the absolute speed limit in the universe

14
Rest Energy

• One conclusion of special relativity is that mass
  and energy are so closely related to each other
  that matter can be converted into energy and
  energy can be converted into matter.
• The rest energy of an object is the energy
  equivalent to its mass.
• The equation for rest energy is
• E0 mc2
• where E0 is the rest energy, m is the mass, and
  c is the speed of light
• For example, a book that has a mass of 1.5 kg has
  a rest energy of 1.35 x 1017 J, which is enough
  energy to send a million tons to the moon. The
  potential energy of this book when the book is on
  the top of Mount Everest, which is 8850 m high,
  relative to sea level, is less than 104 J.
• All around us matter is being converted into
  energy (for instance, when lighting a match, or
  the nuclear fusion that powers the sun) even
  the smallest amount of matter can be converted
  into a large amount of energy
• This equation for the rest energy, E0 mc2, has
  led to a better understanding of nature as well
  as to the nuclear power plants and the nuclear
  weapons that are so important in todays world

15
Example Calculations using Rest Energy

• Example How much rest energy does an object have
  if it has a mass of 63.5kg?
• Answer
• 1. Given 63.5kg
• 2. Looking for rest energy
• 3. Equation E0 mc2
• 4. Solution E0 mc2 (63.5kg)(3 x 108m/s)2
  5.715 x 1018J

16
General Relativity

• Einsteins general theory of relativity was
  published in 1916.
• It relates gravitation to the structure of space
  and time.
• In other words, we can think of the force of
  gravity as arising from a warping of spacetime
  around a body of matter so that a nearby mass
  tends to move toward the body
• This new view of gravity led to many remarkable
  discoveries that would have been impossible under
  the old view of gravity
• The most spectacular of these discoveries is that
  light is subject to gravity. The effect of
  gravity on light is so small, that an object with
  a large mass, like the sun, is needed to detect
  it. Einstein predicted that when light rays pass
  near the sun, they should be bent toward the sun
  by 0.0005, which is the diameter of a dime seen
  from a mile away. His prediction was verified by
  taking a photograph of stars that appeared in the
  sky near the sun during an eclipse in 1919, when
  they could be seen because the moon obscured the
  suns disk, and comparing these with photographs
  of the same region of the sky that were taken
  when the sun was far away.

17
Energy and Civilization

• Without the discovery of resources of energy and
  the development of ways to transform these
  resources into useful energy, the rise of modern
  civilization would have been impossible
• Everything we do requires energy the more
  energy we have, the more we can satisfy our
  desires (i.e. food, clothing, shelter, etc.)
• Most of the energy we used today is from oil and
  gas. They are the most convenient fuels,
  especially because they are currently abundant
  and not too expensive. The problem is that they
  have limited reserves, so we need to look for
  another source for energy, but all other energy
  sources have at least one handicap and nuclear
  energy is a technology of the future.
• An energy strategy for the future is critical
  because, since the world population is
  increasing, we need more and more energy

18
The Sources of Energy

• Almost all the energy available to us today is
  from one source the sun
• Light and heat are obtained from the sun
• Food and wood obtain their energy from the sun
• Water power is obtained when the sun evaporates
  water and then the water falls as rain and snow
  on high ground
• Wind power is obtained from the unequal heating
  of the earths surface by the sun, which causes
  motion in the atmosphere
• Coal, oil, and natural gas (i.e. the fossil
  fuels) are obtained from plants and animals that
  lived and stored their energy from the sun
  millions of years ago
• Only nuclear energy and heat from sources inside
  the earth are not energy from the sun

19
Energy Consumption

• Advanced countries are not likely to need more
  energy since they have a high standard of living
  and a stable population. Their energy need might
  even decrease as the use of energy is made more
  efficient.
• In most of the world, each person consumes less
  than 1 kW, which is low, but in the United
  States, each person consumes about 11 kW
• Since there are more and more people, more and
  more energy is needed

20
Fossil Fuels

• As stated before, most of the energy we use comes
  from oil and gas, two of the fossil fuels, and
  these will be the first to be exhausted.
• If the current rate of consumption of oil remains
  the same, the known oil reserves will last only
  about another century. Even though new oil
  reserves will be found and better technology will
  increase the amount of oil that is obtained from
  existing reserves, eventually oil will run out.
• The benefits of oil and gas are that they burn
  efficiently and are easy to extract, process, and
  transport. These benefits will be lost once the
  reserves of oil and gas run out.
• Although coal, another fossil fuel, can be made
  into liquid fuel and used as raw material for
  synthetics, it is more expensive and has a
  greater risk to health and to the environment.
• If the current rate of consumption of coal
  remains the same, the known coal reserves will
  last several hundred more years (i.e. the coal
  reserves have 5 times as much energy content as
  the oil reserves).
• Before 1941, coal was where most of the energy we
  used came from, and once oil and gas run out, it
  will probably again be where most of the energy
  we use comes from.

21
The Problems with Coal

• Mining coal is dangerous and usually leaves large
  areas of land unfit for further use
• The air pollution from burning coal adversely
  affects the health of millions of people
• In the United States, over 10,000 deaths per year
  can be traced to the burning of coal
• In China, the situation is worse because coal
  supplies 73 of their energy. 7 of the 10 most
  air polluted cities are located in China, and
  thus they have more death and illness due to the
  burning of coal
• Coal-burning power plants actually expose people
  to more radioactivity that nuclear power plants
  do

22
Fossil Fuels and Carbon Dioxide

• The carbon that fossil fuels contain combine with
  oxygen from the air to form carbon dioxide
• Carbon dioxide is one of the gases that traps
  heat in the atmosphere, thus adding to the
  greenhouse effect and warming the atmosphere,
  which is thought to have serious future
  consequences

23
Nuclear Energy

• The benefits of nuclear energy
• They have more reserves than the fossil fuels
  have
• Properly built and properly operating nuclear
  plants are excellent energy sources
• In the United States, about one-fifth of the
  energy we use comes from nuclear energy
• Many other countries also use nuclear energy,
  some to even a greater extent for instance, in
  France, about three-fourths of the energy they
  use comes from nuclear energy
• The drawbacks of nuclear energy
• Nuclear power plants are expensive
• The safety of nuclear power plants is in question
  because of the two major reactor accidents (at
  Three Mile Island in Pennsylvania and at
  Chernobyl in Ukraine) that have occurred
• A small amount of radioactive materials have
  leaked into the environment from badly run
  nuclear power plants
• Although the public-health record of nuclear
  power plants is better than that of coal-burning
  power plants, there is still something to worry
  about
• A nuclear reactor produces many tons of
  radioactive wastes each year. The safe disposal
  of this waste (still not under agreement) is
  expensive

24
Energy The Future

• A practical way to utilize the energy of nuclear
  fusion, the ultimate source of energy, might
  eventually be developed
• A fusion reactor will get its fuel from the sea,
  will be safe and nonpolluting, and will not be
  able to be adapted for military purposes.
• So, assuming that we will eventually utilize the
  energy of nuclear fusion, what do we do until
  that time?
• We can use fossil fuels for awhile, but this will
  cost more human suffering and more damage to the
  environment, including enhancing global warming.
• We can use nuclear energy to bridge the gap,
  especially with more efficient and safer nuclear
  power plants.
• We can use the energy of sunlight, of winds and
  tides, of falling water, of trees and plants, and
  of the earths own internal heat, but even though
  the technology needed to use these renewable
  resources exists, these alternative energy
  sources are not easy to supply for all future
  needs because either it is expensive, or it is
  practical only in certain locations on the earth.
  Also, some of them cannot provide energy all the
  time, and they all need a lot of space. Even
  though they do have drawbacks, these energy
  resources do have value in places where
  conditions are suitable, but it is not likely
  that the entire energy of the world can be
  supplied by these energy resources alone.
• For example, for a city that needs 1000 MW of
  power, less than 150 acres are needed for a
  nuclear power plant, 5000 acres (including
  rooftops) are needed for solar power, 10,000
  acres are needed for wind power, and 200 square
  miles are needed to grow crops for conversion to
  fuel.
• Since there is no simple solution, we should
  practice conservation and try to get the most
  from the various available renewable resources,
  even though they have limitations, while
  continuing to pursue fusion energy as rapidly as
  possible. If the full potential of the various
  available renewable resources is realized and the
  population of the world stabilizes or even
  decreases, then social disaster (i.e. starvation,
  war, etc.) and environmental catastrophe may well
  be avoided even if fusion energy never becomes
  utilized.