Download Course Objectives - Seattle Public Schools

Seattle Public Schools
9-12 Science
Course Objectives
Physical Science pp. 2-7; Biology pp. 8-13; Chemistry pp. 14-18; Physics pp. 19-26
6/27/2011
High School Physical Science Course Objectives
From the Washington State K-12 Science Learning Standards, June 2009
Physical Science Topic: Force and Motion
9-11 PS1A
Content Standards
Performance Expectations
Students know that:
Students are expected to:
Average velocity is defined as a change in
position with respect to time. Velocity
includes both speed and direction.
•
Calculate the average velocity of a moving object,
given the object’s change in position and time.
(v = x2-x1/ t2-t1)
•
Explain how two objects moving at the same speed
can have different velocities.
Average acceleration is defined as a change
in velocity with respect to time.
Acceleration indicates a change in speed
and/or a change in direction.
•
Calculate the average acceleration of an object,
given the object’s change in velocity with respect to
time. (a = v2-v1/ t2-t1)
Explain how an object moving at constant speed can
be accelerating.
9-11 PS1C
An object at rest will remain at rest unless
acted on by an unbalanced force. An object
in motion at constant velocity will continue
at the same velocity unless acted on by an
unbalanced force. (Newton’s First Law of
Motion, the Law of Inertia)
•
Given specific scenarios, compare the motion of an
object acted on by balanced forces with the motion
of an object acted on by unbalanced forces.
9-11 PS1D
A net force will cause an object to
accelerate or change direction. A less
massive object will speed up more quickly
than a more massive object subjected to
the same force. (Newton’s Second Law of
Motion, F=ma)
•
Predict how objects of different masses will
accelerate when subjected to the same force.
Calculate the acceleration of an object, given the
object’s mass and the net force on the object, using
Newton’s Second Law of Motion (F=ma).
9-11 PS1B
•
•
9-11 PS1E
Whenever one object exerts a force on
another object, a force of equal magnitude
is exerted on the first object in the opposite
direction. (Newton’s Third Law of Motion)
•
Illustrate with everyday examples that for every
action there is an equal and opposite reaction (e.g.,
a person exerts the same force on the Earth as the
Earth exerts on the person).
9-11 PS1F
Gravitation is a universal attractive force by
which objects with mass attract one
another. The gravitational force between
two objects is proportional to their masses
and inversely proportional to the square of
the distance between the objects.
(Newton’s Law of Universal Gravitation)
•
Predict how the gravitational force between two
bodies would differ for bodies of different masses or
different distances apart.
Explain how the weight of an object can change
while its mass remains constant.
•
2
Physical Science Topic: Matter
Content Standards
Performance Expectations
Students know that:
Students are expected to:
9-11 PS2A
Atoms are composed of protons, neutrons,
and electrons. The nucleus of an atom takes
up very little of the atom’s volume but makes
up almost all of the mass. The nucleus
contains protons and neutrons, which are
much more massive than the electrons
surrounding the nucleus. Protons have a
positive charge, electrons are negative in
charge, and neutrons have no net charge.
•
Describe the relative charges, masses, and
locations of the protons, neutrons, and electrons
in an atom of an element.
9-11 PS2B
Atoms of the same element have the same
number of protons. The number and
arrangement of electrons determines how
the atom interacts with other atoms to form
molecules and ionic crystals.
•
Given the number and arrangement of electrons
in the outermost shell of an atom, predict the
chemical properties of the element.
9-11 PS2C
When elements are listed in order according
to the number of protons, repeating patterns
of physical and chemical properties identify
families of elements with similar properties.
This Periodic Table is a consequence of the
repeating pattern of outermost electrons.
•
Given the number of protons, identify the element
using a Periodic Table.
Explain the arrangement of the elements on the
Periodic Table, including the significant
relationships among elements in a given column
or row.
9-11 PS2D
9-11 PS2E
•
Ions are produced when atoms or molecules
lose or gain electrons, thereby gaining a
positive or negative electrical charge. Ions of
opposite charge are attracted to each other,
forming ionic bonds. Chemical formulas for
ionic compounds represent the proportion of
ion of each element in the ionic crystal.
(Introduced, revisited in Chemistry)
•
Molecular compounds are composed of two
or more elements bonded together in a fixed
proportion by sharing electrons between
atoms, forming covalent bonds. Such
compounds consist of well-defined molecules.
Formulas of covalent compounds represent
the types and number of atoms of each
element in each molecule. (Introduced,
revisited in Chemistry)
•
•
•
3
Explain how ions and ionic bonds are formed (e.g.,
sodium atoms lose an electron and chlorine atoms
gain an electron, then the charged ions are
attracted to each other and form bonds).
Explain the meaning of a chemical formula for an
ionic crystal (e.g., NaCl).
Give examples to illustrate that molecules are
groups of two or more atoms bonded together
(e.g., a molecule of water is formed when one
oxygen atom shares electrons with two hydrogen
atoms).
Explain the meaning of a chemical formula for a
molecule (e.g., CH4 or H2O).*a
9-11 PS2G
Content Standards
Performance Expectations
Chemical reactions change the arrangement
of atoms in the molecules of substances.
Chemical reactions release or acquire energy
from their surroundings and result in the
formation of new substances. (Introduced,
revisited in Chemistry)
•
•
•
4
Describe at least three chemical reactions of
particular importance to humans (e.g., burning of
fossil fuels, photosynthesis, rusting of metals).
Use a chemical equation to illustrate how the
atoms in molecules are arranged before and after
a reaction.
Give examples of chemical reactions that either
release or acquire energy and result in the
formation of new substances (e.g., burning of
fossil fuels releases large amounts of energy in the
form of heat).
Physical Science Topic: Energy
Content Standards
Performance Expectations
Students know that:
Students are expected to:
Although energy can be transferred from
one object to another and can be
transformed from one form of energy to
another form, the total energy in a closed
system remains the same. The concept of
conservation of energy, applies to all
physical and chemical changes.
•
9-11 PS3B
Kinetic energy is the energy of motion. The
kinetic energy of an object is defined by the
2
equation: Ek = ½ mv
•
Calculate the kinetic energy of an object, given the
object’s mass and velocity.
9-11 PS3C
Gravitational potential energy is due to the
separation of mutually attracting masses.
Transformations can occur between
gravitational potential energy and kinetic
energy, but the total amount of energy
remains constant.
•
Give an example in which gravitational potential
energy and kinetic energy are changed from one to
the other (e.g., a child on a swing illustrates the
alternating transformation of kinetic and
gravitational potential energy).
9-11 PS3D
Waves (including sound, seismic, light, and
water waves) transfer energy when they
interact with matter. Waves can have
different wavelengths, frequencies, and
amplitudes, and travel at different speeds.
•
Demonstrate how energy can be transmitted by
sending waves along a spring or rope. Characterize
physical waves by frequency, wavelength,
amplitude, and speed.
Apply these properties to the pitch and volume of
sound waves and to the wavelength and magnitude
of water waves.
Electromagnetic waves differ from physical
waves because they do not require a
medium and they all travel at the same
speed in a vacuum. This is the maximum
speed that any object or wave can travel.
Forms of electromagnetic waves include Xrays, ultraviolet, visible light, infrared, and
radio.
•
9-11 PS3A
9-11 PS3E
Describe a situation in which energy is transferred
from one place to another and explain how energy is
conserved.
Describe a situation in which energy is transformed
from one form to another and explain how energy is
conserved.
•
•
Illustrate the electromagnetic spectrum with a
labeled diagram, showing how regions of the
spectrum differ regarding wavelength, frequency,
and energy, and how they are used (e.g., infrared in
heat lamps, microwaves for heating foods, X-rays for
medical imaging).
5
Physical Science Topic: Earth Systems
Content Standards
Performance Expectations
Students know that:
Students are expected to:
9-11 ES1A
Stars have “life cycles.” During most of their
“lives”, stars produce heavier elements from
lighter elements starting with the fusion of
hydrogen to form helium. The heaviest
elements are formed when massive stars
“die” in massive explosions.
•
Connect the life cycles of stars to the production
of elements through the process of nuclear fusion.
9-11 ES1B
The Big Bang theory of the origin of the
universe is based on evidence (e.g., red shift)
that all galaxies are rushing apart from one
another. As space expanded and matter
began to cool, gravitational attraction pulled
clumps of matter together, forming the stars
and galaxies, clouds of gas and dust, and
planetary systems that we see today. If we
were to run time backwards, the universe
gets constantly smaller, shrinking to almost
zero size 13.7 billion years ago.
•
Cite evidence that supports the “Big Bang theory”
(e.g., red shift of galaxies or 3K background
radiation).
9-11 ES2A
Global climate differences result from the
uneven heating of Earth’s surface by the
Sun. Seasonal climate variations are due to
the tilt of Earth’s axis with respect to the
plane of Earth’s nearly circular orbit around
the Sun.
•
Climate is determined by energy transfer
from the sun at and near Earth's surface.
This energy transfer is influenced by
dynamic processes such as cloud cover and
Earth's rotation, as well as static conditions
such as proximity to mountain ranges and
the ocean. Human activities, such as
burning of fossil fuels, also affect the global
climate.
•
9-11 ES2B
Explain that Earth is warmer near the equator and
cooler near the poles due to the uneven heating of
Earth by the Sun.
Explain that it’s warmer in summer and colder in
winter for people in Washington State because the
intensity of sunlight is greater and the days are
longer in summer than in winter. Connect these
seasonal changes in sunlight to the tilt of Earth’s
axis with respect to the plane of its orbit around the
Sun.
•
Explain the factors that affect climate in different
parts of Washington state.
6
9-11 ES3A
Content Standards
Performance Expectations
Students know that:
Students are expected to:
Interactions among the solid Earth, the
oceans, the atmosphere, and organisms
have resulted in the ongoing evolution of
the Earth system. We can observe changes
such as earthquakes and volcanic eruptions
on a human time scale, but many processes
such as mountain building and plate
movements take place over hundreds of
millions of years.
•
Interpret current rock formations of the Pacific
Northwest as evidence of past geologic events.
Consider which Earth processes that may have
caused these rock formations (e.g., erosion,
deposition, and scraping of terrain by glaciers,
floods, volcanic eruptions, and tsunami).
Construct a possible timeline showing the
development of these rock formations given the
cause of the formations.
•
7
High School Biology Course Objectives
From the Washington State K-12 Science Learning Standards, June 2009
Biology Topic: Evolution
9-11 LS3A
9-11 LS3C
Content Standards
Performance Expectations
Students know that:
Students are expected to:
Biological evolution is due to: (1) genetic
variability of offspring due to mutations
and genetic recombination, (2) the
potential for a species to increase its
numbers, (3) a finite supply of resources,
and (4) natural selection by the
environment for those offspring better
able to survive and produce offspring.
•
Explain biological evolution as the consequence of
the interactions of four factors: population growth,
inherited variability of offspring, a finite supply of
resources, and natural selection by the environment
of offspring better able to survive and reproduce.
Predict the effect on a species if one of these factors
should change.*a
•
The great diversity of organisms is the
result of more than 3.5 billion years of
evolution that has filled available
ecosystem niches on Earth with life forms.
•
9-11 LS3D
The fossil record and anatomical and
molecular similarities observed among
diverse species of living organisms provide
evidence of biological evolution.
•
Using the fossil record and anatomical and/or
molecular (DNA) similarities as evidence, formulate a
logical argument for biological evolution as an
explanation for the development of a representative
species (e.g., birds, horses, elephants, whales).
9-11 LS3E
Biological classifications are based on how
organisms are related, reflecting their
evolutionary history. Scientists infer
relationships from physiological traits,
genetic information, and the ability of two
organisms to produce fertile offspring.
•
Classify organisms, using similarities and differences
in physical and functional characteristics.
Explain similarities and differences among closely
related organisms in terms of biological evolution
(e.g., “Darwin’s finches” had different beaks due to
food sources on the islands where they evolved).
Explain how the millions of different species alive
today are related by descent from a common
ancestor.
Explain that genes in organisms that are very
different (e.g., yeast, flies, and mammals) can be very
similar because these organisms all share a common
ancestor.
•
•
8
Biology Topic: Homeostasis
9-11 LS1C
Cells contain specialized parts for
determining essential functions such as
regulation of cellular activities, energy
capture and release, formation of proteins,
waste disposal, the transfer of information,
and movement.
•
Draw, label, and describe the functions of
components of essential structures within cells
(e.g., cellular membrane, nucleus, chromosome,
chloroplast, mitochondrion, ribosome)
9-11 LS1D
The cell is surrounded by a membrane that
separates the interior of the cell from the
outside world and determines which
substances may enter and which may leave
the cell.
•
Describe the structure of the cell membrane and
how the membrane regulates the flow of
materials into and out of the cell.
9-11 LS1F
All of the functions of the cell are based on
chemical reactions. Food molecules are
broken down to provide the energy and the
chemical constituents needed to synthesize
other molecules. Breakdown and synthesis
are made possible by proteins called
enzymes.
•
Explain how cells break down food molecules and
use the constituents to synthesize proteins,
sugars, fats, DNA and many other molecules that
cells require.
Describe the role that enzymes play in the
breakdown of food molecules and synthesis of the
many different molecules needed for cell
structure and function.
Explain how cells extract and store energy from
food molecules.
Some of these enzymes enable the cell to
store energy in special chemicals, such as
ATP, that are needed to drive the many other
chemical reactions in a cell.
•
•
9
Biology Topic: Energy, Matter, and Organization
Content Standards
Performance Expectations
Students know that:
Students are expected to:
9-11PS2F
All forms of life are composed of large
molecules that contain carbon. Carbon atoms
bond to one another and other elements by
sharing electrons, forming covalent bonds.
Stable molecules of carbon have four covalent
bonds per carbon atom.
•
Demonstrate how carbon atoms form four
covalent bonds to make large molecules. Identify
the functions of these molecules (e.g., plant and
animal tissue, polymers, sources of food and
nutrition, fossil fuels).
9-11 LS1A
Carbon-containing compounds are the
building blocks of life. Photosynthesis is the
process that plant cells use to combine the
energy of sunlight with molecules of carbon
dioxide and water to produce energy-rich
compounds that contain carbon (food) and
release oxygen.
•
Explain how plant cells use photosynthesis to
produce their own food. Use the following
equation to illustrate how plants rearrange atoms
during photosynthesis:
•
Explain the importance of photosynthesis for both
plants and animals, including humans.
9-11 LS1B
The gradual combustion of carbon-containing
compounds within cells, called cellular
respiration, provides the primary energy
source of living organisms; the combustion of
carbon by burning of fossil fuels provides the
primary energy source for most of modern
society.
•
Explain how the process of cellular respiration is
similar to the burning of fossil fuels (e.g., both
processes involve combustion of carboncontaining compounds to transform chemical
energy to a different form of energy). *a
9-11 LS2A
Matter cycles and energy flows through living
and nonliving components in ecosystems. The
transfer of matter and energy is important for
maintaining the health and sustainability of
an ecosystem.
•
Explain how plants and animals cycle carbon and
nitrogen within an ecosystem.
Explain how matter cycles and energy flows in
ecosystems, resulting in the formation of differing
chemical compounds and heat.
6CO2+6H2O+light energy —> C6H12O6+6O2 *a
•
10
Biology Topic: Continuity
Content Standards
Performance Expectations
Students know that:
Students are expected to:
The genetic information responsible for
inherited characteristics is encoded in the
DNA molecules in chromosomes. DNA is
composed of four subunits (A,T,C,G). The
sequence of subunits in a gene specifies the
amino acids needed to make a protein.
Proteins express inherited traits (e.g., eye
color, hair texture) and carry out most cell
function.
•
9-11 LS1G
Cells use the DNA that forms their genes to
encode enzymes and other proteins that
allow a cell to grow and divide to produce
more cells, and to respond to the
environment.
•
Explain that regulation of cell functions can occur
by changing the activity of proteins within cells
and/or by changing whether and how often
particular genes are expressed.
9-11 LS1H
Genes are carried on chromosomes. Animal
cells contain two copies of each chromosome
with genetic information that regulate body
structure and functions. Most cells divide by a
process called mitosis, in which the genetic
information is copied so that each new cell
contains exact copies of the original
chromosomes.
•
Describe and model the process of mitosis, in
which one cell divides, producing two cells, each
with copies of both chromosomes from each pair
in the original cell.
9-11 LS1I
Egg and sperm cells are formed by a process
called meiosis in which each resulting cell
contains only one representative
chromosome from each pair found in the
original cell. Recombination of genetic
information during meiosis scrambles the
genetic information, allowing for new genetic
combinations and characteristics in the
offspring. Fertilization restores the original
number of chromosome pairs and reshuffles
the genetic information, allowing for
variation among offspring.
•
Describe and model the process of meiosis in
which egg and sperm cells are formed with only
one set of chromosomes from each parent.
Model and explain the process of genetic
recombination that may occur during meiosis and
how this then results in differing characteristics in
offspring.
Describe the process of fertilization that restores
the original chromosome number while
reshuffling the genetic information, allowing for
variation among offspring.
Predict the outcome of specific genetic crosses
involving two characteristics
9-11 LS1E
•
•
•
•
11
Describe how DNA molecules are long chains
linking four subunits (smaller molecules) whose
sequence encodes genetic information.
Illustrate the process by which gene sequences
are copied to produce proteins.
9-11 LS3B
Random changes in the genetic makeup of
cells and organisms (mutations) can cause
changes in their physical characteristics or
behaviors. If the genetic mutations occur
in eggs or sperm cells, the changes will be
inherited by offspring. While many of
these changes will be harmful, a small
minority may allow the offspring to better
survive and reproduce.
•
•
Describe the molecular process by which
organisms pass on physical and behavioral traits
to offspring, as well as the environmental and
genetic factors that cause minor differences
(variations) in offspring or occasional “mistakes”
in the copying of genetic material that can be
inherited by future generations (mutations).
Explain how a genetic mutation may or may not
allow a species to survive and reproduce in a given
environment.
Biology Topic: Development
9-11 LS1H
Content Standards
Performance Expectations
Students know that:
Students are expected to:
Genes are carried on chromosomes. Animal
cells contain two copies of each chromosome
with genetic information that regulate body
structure and functions. Most cells divide by a
process called mitosis, in which the genetic
information is copied so that each new cell
contains exact copies of the original
chromosomes.
•
12
Describe and model the process of mitosis, in
which one cell divides, producing two cells, each
with copies of both chromosomes from each pair
in the original cell.
Biology Topic: Ecology
9-11 LS2B
Content Standards
Performance Expectations
Students know that:
Students are expected to:
Living organisms have the capacity to produce
very large populations. Population density is the
number of individuals of a particular population
living in a given amount of space.
•
•
Evaluate the conditions necessary for rapid
population growth (e.g., given adequate living
and nonliving resources and no disease or
predators, populations of an organism
increase at rapid rates).
Given ecosystem data, calculate the population
density of an organism.
9-11 LS2C
Population growth is limited by the availability of
matter and energy found in resources, the size of
the environment, and the presence of competing
and/or predatory organisms.
•
Explain factors, including matter and energy, in
the environment that limit the growth of plant
and animal populations in natural ecosystems.
9-11 LS2D
Scientists represent ecosystems in the natural
world using mathematical models.
•
Draw a systems diagram to illustrate and
explain why introduced (nonnative) species
often do poorly and have a tendency to die
out, as well as why they sometimes do very
well and force out native species.
9-11 LS2E
Interrelationships of organisms may generate
ecosystems that are stable for hundreds or
thousands of years. Biodiversity refers to the
different kinds of organisms in specific
ecosystems or on the planet as a whole.
•
Compare the biodiversity of organisms in
different types of ecosystems (e.g., rain forest,
grassland, desert) noting the
interdependencies and interrelationships
among the organisms in these different
ecosystems.
9-11 LS2F
The concept of sustainable development
supports adoption of policies that enable people
to obtain the resources they need today without
limiting the ability of future generations to meet
their own needs. Sustainable processes include
substituting renewable for nonrenewable
resources, recycling, and using fewer resources.
•
Explain how scientific concepts and findings
relate to a resource issue currently under
discussion in the state of Washington (e.g.,
removal of dams to facilitate salmon spawning
in rivers; construction of wind farms).
Explain how the concept of sustainable
development may be applied to a current
resource issue in the state of Washington.
13
•
High School Chemistry Course Objectives
The purpose of the chemistry course objectives is to identify core concepts that students should understand by the end of a
chemistry course. This is a minimum list; teachers can teach above and beyond this list. The order of the standards does not imply
the order in which topics are taught. A number system was created for ease of use and communication.
These standards are taken from the following resources:
9-11 PS_ refers to Washington State Science Learning Standards, June 2009
Mass. refers to Massachusetts Science and Technology/Engineering Curriculum Framework, October 2006
CB-PE refers to Science College Board Standards for College Success, Performance Expectations, 2009
Chemistry Topic: Phases of Matter
PM1
Translate among macroscopic (e.g., a beaker of water), symbolic [e.g., H2O(s)], and atomic-molecular level
representations of states. Describe, using representations, the relative arrangement of particles in solids,
liquids, and gases. Or conversely, identify the state of matter depicted in atomic-molecular level pictures or
animations. (CB-PE.1.5.1)
PM2
Construct atomic-molecular level representations of changes that occur when thermal energy is added to a pure
substance. Explain, using these representations, why the continuous addition of thermal energy to a pure
substance will generally result in a change of state (not a chemical reaction). (CB-PE.1.5.5)
Chemistry Topic: Atoms
A1
Recognize discoveries from Dalton (atomic theory), Thomson (the electron), Rutherford (the nucleus), and Bohr
(planetary model of atom), and understand how each discovery leads to modern theory. (Mass. 2.1)
A2
Identify the major components (protons, neutrons, and electrons) of the nuclear atom and explain how they
interact. (Mass. 2.2)
A3
Electrical force is a force of nature independent of gravity that exists between charged objects. Opposite
charges attract while like charges repel. Predict whether two charged objects will attract or repel each other,
and explain why. (9-11 PS1G)
A4
The number of neutrons in the nucleus of an atom determines the isotope of the element. Radioactive isotopes
are unstable and emit particles and/or radiation. Though the timing of a single nuclear decay is unpredictable, a
large group of nuclei decay at a predictable rate, making it possible to estimate the age of materials that contain
radioactive isotopes. Given the atomic number and atomic mass number of an isotope, students draw and label
a model of the isotope’s atomic structure (number of protons, neutrons, and electrons). Given data from a
sample, use a decay curve for a radioactive isotope to find the age of the sample. Explain how the decay curve is
derived. (9-11 PS1J)
A5
Nuclear reactions convert matter into energy, releasing large amounts of energy compared with chemical
reactions. Fission is the splitting of a large nucleus into smaller pieces. Fusion is the joining of nuclei and is the
process that generates energy in the Sun and other stars. Distinguish between nuclear fusion and nuclear fission
by describing how each process transforms elements present before the reaction into elements present after
the reaction. (9-11 PS1K)
14
Chemistry Topic: Quantum
Q1
Explain, based on repeating patterns of core and valence electrons, the organization of the periodic table.
Represent, using the periodic table, the electron configurations of main group elements. (CB-PE.1.2.3)
Q2
Electrons in atoms have definite energy levels, with no values in between. When an electron moves from one
energy level to another, it emits or absorbs a photon that has energy equal to the energy difference between
the levels. The energy levels of electrons are different for each element. Consequently, each element has a
unique emission or absorption spectrum. Both the emission and absorption spectra can be used to identify
elements wherever they are located in the universe. (CB-Objective 1.2: Electrons, Essential Knowledge #3 &#4)
Q3
Each orbital can describe the probability for a maximum of two electrons. Different types of orbitals are
represented by lowercase letters (e.g., s, p, d, and f). Each type of orbital has a different shape (e.g., s has a
spherical shape and p has a dumbbell shape). Instruction should focus on s and p orbitals. (CD-Objective 1.2:
Electrons, Essential Knowledge Bullet #7)
Chemistry Topic: Periodic Trends
PT1
Explain the relationship of an element’s position on the periodic table to its atomic number. Identify families
(groups) and periods on the periodic table. (Mass. 3.1)
PT2
Use the periodic table to identify the three classes of elements: metals, nonmetals, and metalloids. (Mass. 3.2)
PT3
Relate the position of an element on the periodic table to its electron configuration and compare its reactivity to
the reactivity of other elements in the table. (Mass. 3.3)
PT4
Identify trends on the periodic table (ionization energy, electronegativity, and relative sizes of atoms and ions.
(Mass. 3.4)
15
Chemistry Topic: Ionic and Covalent Bonding
B1
Ions are produced when atoms or molecules lose or gain electrons, thereby gaining a positive or negative
electrical charge. Ions of opposite charge are attracted to each other, forming ionic bonds. Chemical formulas
for ionic compounds represent the proportion of ion of each element in the ionic crystal. Explain how ions and
ionic bonds are formed (e.g., sodium atoms lose an electron and chlorine atoms gain an electron, then the
charged ions are attracted to each other and form bonds). Explain the meaning of a chemical formula for an
ionic crystal (e.g., NaCl). (9-11 PS2D)
B2
Molecular compounds are composed of two or more elements bonded together in a fixed proportion by sharing
electrons between atoms, forming covalent bonds. Such compounds consist of well-defined molecules. Formulas
of covalent compounds represent the types and number of atoms of each element in each molecule. Give
examples to illustrate that molecules are groups of two or more atoms bonded together (e.g., a molecule of
water is formed when one oxygen atom shares electrons with two hydrogen atoms). Explain the meaning of a
chemical formula for a molecule (e.g., CH4 or H2O). (9-11 PS2E)
B3
Explain how atoms combine to form compounds through both ionic and covalent bonding. Predict chemical
formulas based on the number of valence electrons. (Mass. 4.1)
B4
Name and write the chemical formulas for simple ionic and molecular compounds, including those that contain
polyatomic ions. (Mass. 4.6)
B5
Identify how intermolecular forces affect a variety of physical, chemical and biological phenomena. (Mass. 4.5
modified)
B6
Use electronegativity to explain the difference between polar and non-polar covalent bonds. (Mass. 4.3)
B7
Draw Lewis dot structures for simple molecules. (Mass. 4.2)
B8
Use valence-shell electron-pair repulsion theory (VSEPR) to predict the molecular geometry (linear, trigonal
planar, and tetrahedral) of simple molecules. (Mass. 4.4)
Chemistry Topic: Reactions and Equations
R1
Chemical reactions change the arrangement of atoms in the molecules of substances. Chemical reactions release
or acquire energy from their surroundings and result in the formation of new substances. Describe at least three
chemical reactions of particular importance to humans (e.g., burning of fossil fuels, photosynthesis, rusting of
metals). Use a chemical equation to illustrate how the atoms in molecules are arranged before and after a
reaction. Give examples of chemical reactions that either release or acquire energy and result in the formation
of new substances (e.g., burning of fossil fuels releases large amounts of energy in the form of heat). (9-11
PS2G)
R2
The rate of a physical or chemical change may be affected by factors such as temperature, surface area, and
pressure. Predict the effect of a change in temperature, surface area, or pressure on the rate of a given physical
or chemical change. (9-11 PS2I)
R3
Make a claim about the evidence required to differentiate between a chemical change and a physical change
(i.e. chemical reactions are the result of electrons transferring or sharing). (CB-PE.2.2.9a)
R4
Classify chemical reactions as synthesis (combination), decomposition, single displacement (replacement),
double displacement, and combustion. (Mass. 5.2)
R5
Balance chemical equations by applying the laws of conservation of mass and constant composition (definite
proportions). (Mass. 5.1)
R6
Construct a balanced symbolic representation, based on given reactants and products, of a chemical reaction.
Construct a molecular-level representation of the chemical reaction, and explain, using the concept of atoms,
why matter is conserved during any change. (CB-PE.2.3.1)
16
Chemistry Topic: Mole
M1
Use the mole concept to determine number of particles and molar mass for elements and compounds. (Mass.
5.3)
Chemistry Topic: Stoichiometry
St1
Use the mole concept to interconvert between amounts of reactants and products in chemical reactions at the
macroscopic level for solids, liquids, gases and solutions. (CB-PE.2.3.3)
Chemistry Topic: Gases
G1
Explain why gases expand to fill a container of any size, while liquids flow and spread out to fill the bottom of a
container and solids hold their own shape. Justification includes a discussion of particle motion and the
attractions between the particles. (CB-PE.1.5.2)
G2
Investigate the behavior of gases. Investigation is performed in terms of volume (V), pressure (P), temperature
(T), and amount of gas (n) by using the ideal gas law both conceptually and mathematically. (CB-PE.1.5.3)
Chemistry Topic: Solutions
S1
Solutions are mixtures in which particles of one substance are evenly distributed through another substance.
Liquids are limited in the amount of dissolved solid or gas that they can contain. Aqueous solutions can be
described by relative quantities of the dissolved substances and acidity or alkalinity (pH). Give examples of
common solutions. Explain the differences among the processes of dissolving, melting, and reacting. Predict the
result of adding increased amounts of a substance to an aqueous solution, in concentration and pH. (9-11 PS2H)
S2
Construct atomic-molecular level representations of the solution process for both ionic and molecular species.
Describe, using these representations, the process of dissolving a solute in a solvent. Compare and contrast the
solution of an ionic compound in water and the solution of a polar molecular compound (e.g., sucrose) in water.
Predict, using molecular structure, the conductivities of the resulting solutions. (CB-PE.2.2.6)
S3
Calculate concentration in terms of molarity. Use molarity to perform solution dilution and solution
stoichiometry. (Mass. 7.2)
Chemistry Topic: Acids and Bases
AB1
Introduce the historical development for our understanding of acids and bases (e.g., Arrhenius theory, Lewis
theory). Define and focus on the Bronsted-Lowry theory of acids and bases in terms of proton donors and
acceptors. (Mass. 8.1)
AB2
Relate hydrogen ion concentrations to the pH scale and to acidic, basic, and neutral solutions. Compare and
contrast the strengths of various common acids and bases (e.g., vinegar, baking soda, soap, citrus juice). (Mass.
8.2)
17
Chemistry Topic: Mathematical Skills (Integrated throughout the year)
A. Chemistry students have the opportunity to apply the following mathematical skills: (Mass. III modified
from p. 73)
•
•
•
•
•
•
•
•
•
•
Construct and use tables and graphs to interpret data sets.
Solve simple algebraic expressions.
Measure with accuracy and precision (e.g., length, volume, mass, temperature, time).
Convert within a unit (e.g., centimeters to meters).
Use common prefixes such as milli-, centi-, and kilo-.
Use scientific notation, where appropriate.
Use ratio and proportion to solve problems.
Determine the correct number of significant figures.
Use appropriate metric/standard international (SI) units of measurement for mass (g); length (cm);
and time (s).
Use the Celsius and Kelvin scales.
18
High School Physics Course Objectives
Notations:
9-11 PS_ refers to Washington State Science Learning Standards, June 2009
M._ and H._ standards are taken from Heller, P. and G. Stewart, 2010, “College Ready Physics Standards: A Look to the
Future”
Physics Topic: Electromagnetic Forces
9-11 PS1H
Electricity and magnetism are two aspects of a single electromagnetic force. Moving electric charges produce
magnetic forces, and moving magnets produce electric forces. Demonstrate and explain that an electric current
flowing in a wire will create a magnetic field around the wire (electromagnetic effect). Demonstrate and explain
that moving a magnet near a wire will cause an electric current to flow in the wire (the generator effect).
Physics Topic: Interactions, Systems, and Scale
M.1.1.1
Scientists describe and explain observed changes in terms of interactions. Two objects (which can be a defined
quantity of a solid, liquid or gas) interact when they act on or influence each other to cause some effect. The
evidence of the interaction is usually the effect -- an observed change in one or both objects (e.g., change in the
motion, change in properties such as mass, volume, temperature, shape, and texture).
M.1.1.2
Sometimes an event or process involves a single interaction between two objects; sometimes it involves
complex chains of interactions and/or multiple simultaneous interactions. Some events are very short, while
others are very long.
M.1.1.3
Scientists use the concept of a system to help in their study of processes and events. By defining a system of
interest and a time interval, any inputs, outputs, and changes within the system can be tracked. A real boundary
(e.g., surface of cup) or an imaginary boundary (e.g. food-oxygen system in humans) separates the system of
interest from the surroundings. The system of interest can be a single object, two interacting objects, or a larger
system with subsystems (e.g., car-engine system).
M.1.1.4
The interaction description of the same event is different for different defined systems and/or time intervals.
M.1.1.5
A closed (isolated) system does not interact with its surroundings: materials and energy cannot get into or out
of the system. Most systems of interest in our everyday lives are open systems. Materials and energy can be
transferred into or out of the system. [SSCS, page 101]
M.1.1.6
When defining time intervals and systems of interest, it is convenient to think about three domains of
magnitude in size (distance in meters) and time (in seconds); the macro (human) domain, the cosmic domain,
and the atomic and subatomic domains.
-6
+10
a. The macro (human) domain (distance and time larger than about 10 and smaller than about 10 )
corresponds roughly with what can be perceived and measured with either human senses or simple instruments
(e.g., optical microscopes and telescopes).
+10
b. The cosmic domain (distance and time larger than about 10 ) is so great it is almost beyond imagination,
and requires instruments or procedures that depend on long chains of reasoning to understand how they work.
-6
-14
c. Similarly, the atomic and subatomic domains (distance and time < 10 and < 10 respectively) are tiny
beyond imagination and it requires a great deal of physics knowledge to understand the measurement
instruments.
19
Physics Topic: Interactions and Properties
M.1.2.1
A property of an object is a description, qualitative or quantitative, of how the object interacts with other
objects (e.g., magnetic materials are materials that are attracted to a magnet).
a. In our everyday life, properties of objects are descriptions of how the objects interact with our senses.
b. The interaction of an object with a measuring instrument (e.g., ruler, thermometer, graduated cylinder, mass
balance) provides more reliable information about an object’s properties than our senses alone.
c. A pure substance has a unique set of properties (e.g., melting point, boiling point, density, color, hardness,
thermal conductivity) that can be used to identify it. Under all conditions, these properties do not depend on
the amount (mass or volume) of the substance. [SSCS, page 97]
M.1.2.4
When measurements are performed, a true (or exact) value is never obtained; there is always some uncertainty
associated with a measurement. [SSCS, page 97]
a. An uncertainty (± measurement error) should be estimated and reported with each measured value.
o
Estimations depend on the precision of the instrument (e.g., 20.5 ± 0.5 C).
b. A quantity should be measured several times (trials) and the average (mean) calculated. There is always some
variation in measured values. An uncertainty should be estimated and reported with the average (e.g., 105.4
grams ± 2 grams).
Physics Topic: Conservation of Mass, Energy or Charge
H.2.1.1
For all types of interactions (except nuclear reactions) and for all systems (open and closed), energy is always
conserved. The mathematical form of the conservation of energy principle is the same as the conservation of
mass principle: total energy change within system (∆Esystem) is equal to the total energy transfer into or out of
system (Ein - Eout): ∆Esystem = Ein – Eout where (∆Esystem) is the change in one or more methods of energy storage
within a system, and Ein and Eout) are one or more methods of energy transfer into or out of a system.
H.2.1.2
The energy terms in the conservation of energy principle depend on the defined system and defined time
interval. For any event or process, the terms in the conservation of energy equation will be different for
different defined systems and time intervals.
H.2.1.3
For all types of interactions covered in this standards document (except nuclear interactions), mass and energy
are always conserved separately.
H.2.1.4
Many events and processes involve multiple interactions occurring simultaneously and/or chains of interactions.
When the details of the multiple transfers of energy are unknown or not of interest in a problem, the term
“transformation” can be used (i.e., the initial form of energy is “transformed” into the final form of energy
within the defined closed system). For radiant energy transfers into or out of a system, this description is often
extended to include the transformation of radiant energy (electromagnetic waves or photons) into the final
form(s) of energy within the system (e.g., chemical energy or thermal energy).
H.2.1.6
The conservation of charge, mass, or energy principles are examples of fundamental principles of science
because they cannot be derived from other theories—all scientific theories must be consistent with these
principles.
20
Physics Topic: Constant and Changing Linear Motion
H.3.1.1
The displacement, or change in position, of an object is a vector quantity that can be calculated by subtracting
the initial position from the final position, where initial and final positions can have positive and negative
values (∆x = xf - xi). Displacement is not always equal to the distance traveled. [SSCS, page 143]
H.3.1.2
An object that travels the same displacement in each successive unit time interval has constant velocity.
Constant velocity is a vector quantity and can be represented by and calculated from a position versus time
graph, a motion diagram or the mathematical representation for average velocity. The sign (+ or -) of the
constant velocity indicates the direction of the velocity vector, which is the direction of motion. [SSCS, page
143]
H.3.1.3
The constant velocity an object would travel to achieve the same change in position in the same time interval,
even when the object’s velocity is changing, is the average velocity for the time interval. Average velocity can
be mathematically represented by vave = (xf - xi)/(tf - ti). For straight-line motion, average velocity can be
represented by and calculated from the mathematical representation, a curved position versus time graph and
a motion diagram. [SSCS, page 143]
H.3.1.4
The velocity of an object in straight-line motion changes continuously, from instant to instant while it is
speeding up or slowing down and/or changing direction. The velocity of an object at any instant (clock
reading) is called its instantaneous velocity. The object does not have this velocity over any time interval or
travel any distance with this velocity. Instead, the instantaneous velocity is the constant velocity at which an
object would continue to move if its motion stopped changing at that instant. An object with zero
instantaneous velocity can be accelerating (e.g., motion up a ramp then back down the ramp). [SSCS, page
143]
H.3.1.5
When the change in an object’s instantaneous velocity is the same in each successive unit time interval, the
object has constant acceleration. For straight-line motion, constant acceleration can be represented by and
calculated from a linear instantaneous velocity versus time graph, a motion diagram and the mathematical
representation [a = (vf - vi)/(tf - ti)]. The sign (+ or -) of the constant acceleration indicates the direction of the
change-of-velocity vector. A negative sign does not necessarily mean that the object is traveling in the
negative direction or that it is slowing down. [SSCS, page 144]
H.3.1.6
When the acceleration is not constant, the graph of instantaneous velocity versus time is curved. Average
acceleration over any interval is the constant acceleration an object would have for the same total change in
velocity in the same time interval. Average acceleration can be calculated from the non-linear instantaneous
velocity versus time graph.
H.3.1.7
When the acceleration is constant, the magnitude of the average velocity during a time interval is one-half of
the sum of the initial and final instantaneous velocities [v = (vf + vi)/2]. [SSCS, page 144]
21
Physics Topic: Forces and Changes in Motion
2
H.3.2.1
The force on a 1 kg mass that causes an acceleration of 1 m/s is one Newton (N), where a Newton is defined as
2
kg m/s . Since many events consist of a sequence of interactions, the force diagram for an object/system of
interest can be different for different time intervals.
H.3.2.2
Newton’s second law of motion includes the following ideas:
a. The linear acceleration of an object is directly proportional to the vector sum of all the forces acting on the
object and inversely proportional to the object’s mass (a = ΣF/m). The vector sum of all the forces (net
force) is not a real force caused by an interaction with another object. The single force that could replace
the original multiple forces and cause the same acceleration of the object is the vector sum of forces.
b. A special case of Newton’s second law occurs when the vector sum of all the forces (net force) on an object
is zero. In this case, there is no acceleration and the object remains at rest or maintains a constant speed
and a constant direction of motion.
c. An object moves in a circle when the vector sum of all the forces (net force) is constant in magnitude,
always directed at right angles to the direction of motion and always directed toward the same point in
space, the center of the circle. The speed of the object does not change: the acceleration causes the
continual change in the direction of the change-in-velocity vector.
H.3.2.3
When two interacting objects push or pull on each other, the force on one object is equal in magnitude but
opposite in direction to the force on the other object (Newton’s third law of motion for an interaction pair).
22
Physics Topic: Contact Interaction and Forces
H.3.3.1
The types of interactions of the object/system of interest with its surroundings and the force laws for each type
of interaction must be identified in order to use Newton’s laws to quantitatively explain and predict the
motion of an object or system. [SSCS, page 147]
H.3.3.2
There are empirical force laws for some types of contact interactions. [SSCS, page 147]
a. Elastic materials stretch or compress in proportion to the applied force. The mathematical model (Hooke’s
Law) for the force that a linearly elastic object exerts on another object is Felastic = k∆x, where ∆x is the
displacement of the object from its relaxed position. The direction of the elastic force is always toward the
relaxed position of the elastic object. The constant of proportionality is the same for compression and
extension, and depends on the “stiffness” of the elastic object.
b. The force of kinetic friction always acts in the opposite direction of the relative velocity of the object with
respect to the surface it is sliding over. The magnitude of the kinetic friction depends on the types of
materials that make up the two surfaces sliding past each other and the magnitude of the compression
(normal) force acting on the object. This can be mathematically represented by Fk = μkN.
c. When an external force is applied parallel to two surfaces that are in contact, a force opposes the external
force and keeps the objects from moving relative to each other. This interaction is called static friction,
which is mathematically represented by an inequality: Fs < μsN. The magnitude of the static friction
depends on the types of materials that make up the two surfaces and the magnitude of the compression
(normal) force acting on the object.
H.3.3.3
There are no force laws for some types of contact interactions because the complexity of the interactions does
not allow the magnitude of the forces to be easily represented. [SSCS, page 147]
a. A contact interaction occurs when the surfaces of two solid objects are pressed together because of other
interactions on one or both objects (e.g., a solid sitting on or sliding along a table; a magnet attached to a
refrigerator). This is called a compression interaction. A compression (normal) force applied to an object is
always a push directed at right angles from the surface of the other interacting object.
b. A contact interaction occurs when a cord (e.g., rope, wire, rod) pulls on another object or system and the
cord is not slack. A tension force on an object always points in the direction the cord is pulling.
H.3.3.4
In static friction and drag interactions, one of the interacting systems can be an energy source with a moving
part (e.g., motor moving blades of a helicopter; a person’s moving foot). When the system with an energy
source pushes on another object or system (e.g., the air or the ground), the other object pushes back on the
system with equal and opposite force (Newton’s third law), which can cause a change in motion of the system
with the energy source. [SSCS, page 147]
H.3.3.5
During contact interactions, forces are not transferred to objects (unlike energy) – the interaction stops as
soon as the objects stop touching. Simplifying assumptions are often needed to gain a basic understanding of
a real-world situation or to solve a problem (e.g., for contact interactions, “massless” ropes, “frictionless” sliding
surfaces, maximum static friction and negligible air resistance).
H.3.3.6
At the atomic scale, the interaction between the particles (atoms or molecules) of different substances is an
electric charge interaction. At this scale, there are no “contact” forces. The strength of the attractive forces
between the particles of different substances is different for different pairs of substances, depending on the
electron configurations of the atoms or molecules of the two substances. (See Objective 1.3) [SSCS, page 147]
23
Physics Topic: Gravitational Interaction and Forces
H.3.4.1
Gravitational, magnetic, electrical and electromagnetic interactions occur continually when objects are not
touching, and they do not require an intermediate material (medium). They are called interactions at a
distance, or long-range interactions. (Same as in Objective 5.1)
H.3.4.2
The force law for gravitational interaction, called Newton’s universal law of gravitation, states that the strength
of the gravitational force is proportional to the product of the two masses and inversely proportional to the
2
square of the distance between the centers of the masses [FG = (G m1 m2)/r ]. The proportionality constant is
called a universal constant because it does not depend on any other properties (e.g., chemical composition) of
the objects or whether the object is charged or is a magnet). [SSCS, page 148]
H.3.4.3
When an object’s distance from Earth’s surface is small compared to Earth’s radius, then a simplifying
assumption is that the gravitational force on an object depends only on the mass of the object. In this case,
objects fall with approximately the same acceleration: 9.8 m/sec/sec. [SSCS, page 148]
H.3.4.4
When people are in free fall (e.g., some amusement park rides, sky diving. astronaut orbiting the Earth), they
feel “weightless” because people do not feel the extremely small gravitational force on each atom in their
bodies. When standing, people feel the (normal) force of the ground pushing upwards on their feet, which
produces the sensation of weight.
Physics Topic: Contact Interactions and Energy
H.4.1.1
Energy transfers and energy storage can be measured in many different ways. The units of energy include
Joules, calories, and kilocalories.
H.4.1.2
Mechanical energy transfer (work) is mathematically represented (for constant or average forces) by W = ΣF∆x,
where ΣF is the vector sum of the external forces (net force) in the direction of motion. When an external force
causes a transfer of energy into the system, then W = Win (“work done on the system”). When an external
force causes a transfer of energy out the system, then W = Wout (“work done by the system”). Mechanical
energy transfers (work) within and across the boundaries of a system can result in changes in the kinetic,
elastic, chemical or thermal energy of the interacting objects. [SSCS, page 158]
H.4.1.3
If the only significant transfers of energy into or out of a system are caused by contact interactions, then the
conservation of energy principle is:
∆Esystem = Ein - Eout
∆Ekinetic + ∆Eelastic + ∆Ethermal + ∆Echemical + ∆Eother = Win - Wout
where ∆Eother includes changes in other methods of energy storage (such as “deformation energy”
associated with a permanent change in shape of an object).
H.4.1.4
Depending on the system of interest in a problem, one or more of the energy transfers across the system
boundary could be applicable, not applicable, or too small of an effect to be measurable. [SSCS, page 158]
H.4.1.5
The empirical approximation for the change in the stored elastic energy of an object made of elastic material
2
(such as a spring) is ∆Eelastic = 1/2 k∆x , where ∆x is the distance the elastic object is compressed or stretched
from its relaxed length. [SSCS, page 158]
H.4.1.6
Kinetic energy is the energy of motion and can be mathematically represented by Ekinetic = 1/2 mv , where v
is the magnitude of the instantaneous velocity of the object. [SSCS, page 158]
2
24
Physics Topic: Mechanical Wave Interactions and Energy
H.4.3.1
When the mechanical wave material (medium) is two-dimensional (e.g., surface water waves, surface seismic
waves) or three-dimensional (e.g., sound), then the interaction between a wave and another object or
boundary with a different material causes the path of the wave to change (bend or change direction). The
change in the path of the wave can be represented with ray diagrams.
a. Mechanical waves can bounce off of solid barriers. This interaction is called reflection. The law of reflection
states that the angle at which a wave approaches the barrier (angle of incidence) equals the angle at which
the wave reflects off the barrier (angle of reflection).
b. When a mechanical wave travels from one material (medium) into another material, its direction changes.
This interaction is called refraction. Since the speed of a wave depends on the material through which the
wave travels, both the speed and the wavelength of the refracted wave change.
c. Mechanical waves bend around small obstacles or openings. This interaction is called diffraction. The
amount of diffraction (bending) increases with decreasing wavelength. When the wavelength is smaller
than the obstacle or opening, no noticeable diffraction occurs.
H.4.3.2
When energy in a mechanical wave (Eincident) reaches a barrier or boundary to another material, a portion of
its energy is reflected at the boundary (Ereflected), and a portion of the energy passes through the boundary
into the material (Etransmitted). For a system consisting of two materials and incident, reflected, and
transmitted waves, the conservation of energy principle can be mathematically represented by:
∆Esystem = Ein - Eout
Eincident - Ereflected - Etransmitted = Edissipated
where Edissipated is the energy “dissipated,” absorbed by the material or transferred out of the system due to
the interaction of the system with surrounding objects, assuming no other transfers of energy have taken
place. When the dissipated energy is so small that it can be neglected, then:
Eincident - Ereflected = Etransmitted
H.4.3.3
When two waves traveling in the same material meet, they pass through each other. When the waves pass
through each other, the displacements caused by the two waves add algebraically. This phenomenon is called
the superposition of waves.
a. When the two displacements are in the same direction (same sign), the total displacement of the material
is larger than the displacement of either wave (constructive interference).
b. When the two displacements are in opposite directions (opposite signs), the total displacement of the
material is less than the displacement of the largest amplitude wave (destructive interference).
H.4.3.4
When an observer and a mechanical wave source move toward each other, the observed frequency is higher;
when they move away from each other, the observed frequency is lower. This phenomenon is called the
Doppler effect.
25
Physics Topic: Radiant Energy Interactions
H.4.4.1
Light energy interactions with solid barriers or the interface between two materials exhibit patterns of
reflection, refraction, diffraction, and interference similar to the interactions of mechanical waves with barriers
and interfaces.
H.4.4.2
When light energy from a source (Eincident) reaches a boundary between materials with different optical
properties (such as air to water), a portion of the energy is reflected at the boundary (Ereflected), and a portion
of the energy passes through the boundary into the material (Ematerial). At such a boundary, the conservation
of energy principle can be mathematically represented by: [SSCS page 163]
∆Esystem = Ein - Eout
Eincident - Ereflected - Ematerial = 0
Eincident - Ereflected = Ematerial
H.4.4.3
The light energy that goes into the material (Ematerial) can be absorbed by the material and transmitted
through the material.
Ematerial = Eabsorbed + Etransmitted
The amount of energy that is absorbed into the material depends primarily on the properties of the material
object. For example, the visible light energy that is absorbed into opaque objects (e.g., paper, a chair, an
apple) usually results in a small increase in the object’s thermal energy. Transparent materials transmit most of
the energy through the material.
Physics Topic: Energy and Fields
H.5.2.1
The energy stored in the field around two mutually attracting or repelling objects is called potential energy
(e.g., gravitational potential energy, electric potential energy). A single object does not have potential energy.
Only the system consisting of two or more attracting or repelling objects can have potential energy.
H.5.2.5
Whenever mechanical energy is transferred to a system of charged objects and there is no change in kinetic
energy and no energy is transferred out of the system, the electric potential energy stored in the system must
increase for energy to be conserved. The change in electric potential energy per unit charge is called the
potential difference (∆V):
∆Esystem = Ein - Eout
∆PEelectric = Win
∆V = ∆PEelectric/q
26