Graphs and Charts Describing Different Types of Motion 4(A): Generate and interpret graphs and charts describing different types of motion, including the use of real-time technology such as motion detectors or photogates. Vocabulary displacement: The difference between the final position and initial position of an object. average velocity: The displacement of an object divided by the time interval over which the displacement occurred. acceleration: the change in velocity over time simple harmonic motion: movement that repeats over and over again Key Concepts A moving object travels from one position to another. The length of a straight line between the initial position and the final position is called the displacement. The average velocity of an object is its displacement, or change in position, divided by the time interval over which the displacement occurs. Velocity is associated with direction, while speed is the same measurement without direction. An example of velocity is 4 m/s due east, while an example of speed is 4 m/s. A position-time graph plots position over time. A velocity-time graph plots velocity over time. The shape of either graph provides information about the motion of an object. For example, the slope of a position-time graph represents average velocity. An object can travel at a constant velocity or it can accelerate, meaning that its velocity changes. An accelerating object can be speeding up, slowing down, or changing direction. An object traveling in a circle, even if its speed does not change, is accelerating because its direction is changing. The average velocity of an object can be calculated by measuring the distance it travels and the time during which it travels that distance. Such measurements can sometimes be difficult to obtain by hand, and tools such as motion detectors and photogates can be used to obtain more accurate data. Simple harmonic motion describes the movement of an object whose action is repeated over and over again. If you have ever ridden on a Ferris wheel, then you have experienced simple harmonic motion. Likewise, a bob bouncing up and down on the end of a hanging spring is an example of simple harmonic motion.
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Graphs and Charts Describing Different Types of Motion4(A): Generate and interpret graphs and charts describing different types of motion,
including the use of real-time technology such as motion detectors or photogates.
Vocabulary
displacement: The difference between the final position and initial position of an object.
average velocity: The displacement of an object divided by the time interval over which the displacement
occurred.
acceleration: the change in velocity over time
simple harmonic motion: movement that repeats over and over again
Key Concepts
A moving object travels from one position to another. The length of a straight line between the initial position
and the final position is called the displacement.
The average velocity of an object is its displacement, or change in position, divided by the time interval over
which the displacement occurs. Velocity is associated with direction, while speed is the same measurement
without direction. An example of velocity is 4 m/s due east, while an example of speed is 4 m/s.
A position-time graph plots position over time. A velocity-time graph plots velocity over time. The shape of either
graph provides information about the motion of an object. For example, the slope of a position-time graph
represents average velocity.
An object can travel at a constant velocity or it can accelerate, meaning that its velocity changes. An accelerating
object can be speeding up, slowing down, or changing direction.
An object traveling in a circle, even if its speed does not change, is accelerating because its direction is changing.
The average velocity of an object can be calculated by measuring the distance it travels and the time during
which it travels that distance. Such measurements can sometimes be difficult to obtain by hand, and tools such as
motion detectors and photogates can be used to obtain more accurate data.
Simple harmonic motion describes the movement of an object whose action is repeated over and over again. If
you have ever ridden on a Ferris wheel, then you have experienced simple harmonic motion. Likewise, a bob
bouncing up and down on the end of a hanging spring is an example of simple harmonic motion.
Motion in One Dimension
4(B): Describe and analyze motion in one dimension using equations with the concepts of
distance, displacement, speed, average velocity, instantaneous velocity, and acceleration.
Vocabulary
displacement: the difference between the final position and initial position of an object
instantaneous velocity: the velocity at any given instant while an object is in motion
average velocity: the displacement of an object divided by the time interval over which the displacement
occurred
acceleration: the change in velocity divided by the time interval during which the change occurred
Key Concepts
A moving object travels from one position to another. The length of a straight line drawn from the initial position
to the final position is called the displacement. Displacement can be determined from the following equation:
The average velocity of an object is its displacement, or change in position, divided by the time interval over
which the change occurred. Velocity is associated with direction, while speed is the same measurement without
direction. An example of velocity is 4 m/s due east, while an example of speed is 4 m/s. Average velocity can be
determined from the following equation:
The rate at which velocity changes is known as acceleration. An object's acceleration can be calculated by dividing
the change in velocity by the time during which that change occurred. Acceleration can be determined from the
following equation:
Accelerated Motion in Two Dimensions4(C): Analyze and describe accelerated motion in two dimensions using equations,
including projectile and circular examples.
Vocabulary
projectile motion: free fall with an initial horizontal velocity
trajectory: the path of a moving body, such as a projectile, through space
uniform circular motion: motion of an object in a circle at constant speed
centripetal force: inward force exerted on an object moving in a circle
Key Concepts
The motion of a car traveling along a road or a squirrel climbing a tree is motion in one dimension. Many
examples of motion, however, are in two dimensions. For example, a baseball thrown by a pitcher moves
horizontally toward the batter. The ball also moves vertically as it falls toward the ground.·
The motion of the baseball is an example of projectile motion. An object with projectile motion falls downward
because of gravity, but it also has horizontal velocity. The path, or trajectory, of a projectile is a curve called a
parabola.
An object moving in a circle, even at constant speed, is accelerating because its direction is constantly changing.
The force that causes the object to accelerate in this way, called centripetal force, is directed toward the center of
the circle.
Calculate the Effect of Forces on Objects
4(D): Calculate the effect of forces on objects, including the law of inertia, the relationship
between force and acceleration, and the nature of force pairs between objects.
Vocabulary
law of inertia: the law that states that an object at rest remains at rest and an object in motion stays in motion at
constant speed unless an unbalanced force acts upon it; also known as Newton’s first law of motion
Newton’s second law of motion: the law that states that the acceleration of an object is directly proportional to
the magnitude of the net force acting on it and inversely proportional to the mass of the object
Newton’s third law of motion: the law that states that for every pair of objects that interact, equal but opposite
forces act on the objects
weight: the force that results from the gravitational pull on an object; W = mg
normal: the force that an object in contact with another object exerts on that object, perpendicular to the plane
of contact, so that the second object does not pass through the first
friction: the force that arises between two surfaces in contact with each other and opposes motion along the
surfaces
Key Concepts
An unbalanced force is required to change the motion of an object. Without an unbalanced force, an object at
rest remains at rest and an object in motion remains in motion at constant velocity. This is known as the law of
inertia.
An unbalanced force causes an object to accelerate by speeding up, slowing down, or changing direction. The
magnitude of the acceleration is directly proportional to the force and inversely related to the mass according to
the equation a = F/m , where F is the unbalanced force, m is the mass of the object, and a is the acceleration. This
is explained as Newton’s third law of motion
For every action, there is an equal and opposite reaction. Therefore, if you push against a wall with a force of 8
newtons (N), the wall pushes back on you with a force of 8 N. This is explained as Newton’s third law of motion.
Free Body Diagrams4(E): Develop and interpret free-body force diagrams.
Vocabulary
force: a push or a pull
magnitude: the strength of a force
vector: any quantity that has magnitude and direction
free body diagram: a diagram that shows all the external forces acting on an object
Key Concepts
A force is a push or a pull. The magnitude of a force is its strength. A force is a vector quantity, meaning it is
described by both a magnitude and a direction. Velocity, acceleration, and displacement are also vector
quantities. Vectors are drawn as arrows. The length of the arrow denotes magnitude, and the arrow's angle in
relation to the horizontal or vertical axis denotes direction.
A free body diagram is a diagram of external force vectors acting on an object. The object is usually depicted as a
rectangle, circle, or dot with force vectors pointing at various angles toward or away from it. The diagram often
includes an x-y coordinate grid, with the center of the object placed at the origin. The vectors should be either
drawn to scale or have lengths drawn relative to one another.
In the example shown below, the vectors show three forces acting on an object. Two forces each have a
magnitude of 5 N. The third force has a magnitude of 6 N. The direction of each vector arrow shows the
directions of the force.
A force that points upward or to the right can be described as a positive force. Similarly, a force that points
downward or to the left can be described as a negative force. In the diagram below, positive and negative
magnitudes have been assigned to each force. The net force acting on the object is zero.
Free body force diagrams are useful tools for resolving force vectors in their x and y components and to find the
net force acting on an object. If the net force is greater than zero, there is acceleration in its direction. This
acceleration vector can be drawn as well. In the example shown below, the net force that acts on the object is a
force to the right of 3 N. Notice that the upward and downward forces are equal and opposite, so their effects
cancel each other out.
Frames of Reference4(F): Identify and describe motion relative to different frames of reference.
Vocabulary
frame of reference: a set of axes used to measure the position or motion of an object
inertial frame of reference: a frame of reference in which the observer is either traveling at a constant velocity or
is stationary
noninertial frame of reference: a frame of reference in which the observer is accelerating
special theory of relativity: a description of time, matter, and energy as the speed of particles approach the
speed of light
time dilation: the slowing of time from the frame of reference of an object traveling at nearly the speed of light
length contraction: the contraction of length from the frame of reference of an object traveling at nearly the
speed of light
Key Concepts
You may feel that you are not moving when you are seated in a chair and reading a book, a page, or a computer
screen, such as this one. However, the calculation of movement and position depends on a frame of reference.
You may be at rest with respect to the frame of reference of the school or your house. You are moving, however,
with respect to the solar system. Remember that Earth—and everything upon it—rotates like a top and revolves
around the Sun.
An inertial frame of reference is a system that is stationary or that moves at a constant velocity. An example is a
car, train, or airplane that is traveling at a constant velocity along the ground or in the air. Remember that
velocity is both speed and direction. If you are in a car traveling 60 kilometers per hour on a straight highway, and
if the ride is smooth, then you would feel as motionless as if you were sitting in a chair at school.
If a car suddenly veers to the left or right, if it slows down or speeds up, or if a bump in the road alters the car’s
motion, then the car becomes a noninertial frame of reference. Even if you are strapped in tightly to the seat
behind you, you would feel a force from the car’s acceleration. Remember that acceleration is a change in
velocity and may involve a change in speed, a change in direction, or a change in both speed and direction.
Physicist Albert Einstein (1879–1955) applied ideas about frames of reference to develop the special theory of
relativity, which involves objects in motion that approach the speed of light. The theory depends on two
postulates, or statements that are believed to be true:
1. The speed of light is the same for all observers, regardless of their frame of reference.
2. The laws of physics are the same in every inertial frame of reference.
As a consequence of these postulates, Einstein redefined time, length, mass, and energy as they applied to
particles
moving nearly as fast as the speed of light.
Time dilation involves a difference in time between two frames of reference. For time dilation to be significant,
the frames of reference must differ by nearly the speed of light. For example, if an astronaut travels in a
spaceship that approaches the speed of light, time would pass very slowly on the ship from Earth’s frame of
reference. While the astronaut experiences a one-month journey aboard the ship, half a year or longer might
pass on Earth.
Length contraction involves a difference in observed length between two frames of reference. Aboard the
spaceship, the astronaut would observe distances on Earth or other places to be much shorter than their actual
distances at rest.
As an object’s speed approaches the speed of light, its mass also increases from the frame of reference of a
stationary observer. Kinetic energy depends on mass, so the kinetic energy also increases. At the speed of light,
an object would have infinite mass and infinite kinetic energy, which is why accelerating an object to the speed of
light is not possible.
Historical Development of the Concepts of Different Forces5(A): Research and describe the historical development of the concepts of gravitational,
electromagnetic, weak nuclear, and strong nuclear forces.
Vocabulary
gravitational force: a force of attraction between any two masses in the universe
electromagnetic force: an attractive or repulsive force that acts between charged particles
weak nuclear force: a force that is exerted over the short distances within atoms and is responsible for certain
forms of radioactivity
strong nuclear force: a force that holds the nucleus of an atom together against the repulsion of the protons
Key Concepts
Of all the interactions that occur in the universe, scientists have identified four basic, or fundamental, forces that
can be used to explain physical events.
The first fundamental interaction to be identified and described mathematically was gravitation. Galileo Galilei
first asserted that objects fall at the same rate regardless of their mass. Isaac Newton published his universal law
of gravitation in 1687, which gave a basic understanding of how gravity works. Albert Einstein took Newton’s
ideas a step further in 1916 with his general theory of relativity, which described space and time as curved by the
effects of gravity.
Of the four fundamental forces, the gravitational force has the weakest magnitude, but it can act over long
ranges. It is always an attractive force, and it acts between any two masses in the universe.
People have known about magnets and electrical phenomena, such as lightning, for millennia. The study that led
to the modern understanding of these forces began with William Gilbert around the turn of the seventeenth
century. Later, many scientists, including Charles Augustin de Coulomb, Simeon-Denis Poisson, Carl Friedrich
Gauss, and Michael Faraday, further investigated these forces and identified laws governing electrical or
magnetic force. In 1864, James Clerk Maxwell developed what came to be called Maxwell’s equations, which
mathematically described electromagnetism as a single interaction.
Electromagnetic force acts between particles of matter that carry an electric charge. It can involve attraction or
repulsion, and it can act at a distance. This force can hold atoms together, and it is also the force that can push
two magnets apart.
All matter is made up of atoms. The nucleus of an atom is made up of protons, which have a positive electric
charge, and neutrons, which are electrically neutral. Because particles with the same electric charge repel one
another, a force must exist to hold the nucleus together. Scientists have identified this force as the strong nuclear
force.
The existence of the strong nuclear force was theorized before it was observed. As early as 1934, Hideki Yukawa
theorized the existence of mesons, the particles responsible for the strong nuclear force that holds a nucleus
together. The first actual meson was not detected until 1947. A team at the University of Bristol led by Cecil
Powell found the pi-meson, or pion, in cosmic rays. Since that time, technological advances have given scientists
the ability to produce and detect more mesons. Particle accelerators can propel tiny bits of matter to huge
speeds and smash them apart. Bubble chambers can give pictures of the paths of charged mesons.
Mesons bind together quarks, the particles that make up protons and neutrons. Quarks in neighboring protons
and neutrons can sometimes exchange mesons. This binds protons together inside the nucleus.
The strong nuclear force acts over a very short range. Neutrons increase the amount of strong nuclear force
within the nucleus and thus act to balance the proton-proton electric repulsive forces.
The weak nuclear force is observed when unstable atoms give off certain particles and energy, a process known
as radioactive decay. The weak nuclear force acts across even smaller distances than the strong nuclear force.
Enrico Fermi first postulated the existence of the weak nuclear force in 1933 in order to explain beta decay.
Richard Feynman and Murray Gell-Mann gave a more complete definition of the weak interaction about 25 years
later. Their theory helped scientists predict how the weak nuclear force would affect reactions and particles in
various situations.
Magnitude of the Gravitational Force5(B): Describe and calculate how the magnitude of the gravitational force between two
objects depends on their masses and the distance between their centers.
Vocabulary
Law of Universal Gravitation: a law that states that a force of attraction exists between any two masses in the
universe and that the magnitude of the force is directly proportional to the product of the masses and inversely
proportional to the square of the distance between them
directly proportional relationship: a relationship between two quantities in which one quantity changes in the
same way as the other, either increasing or decreasing as the other quantity does the same
inversely proportional relationship: a relationship between two quantities in which one quantity decreases as
the other quantity increases
gravitational constant: a proportionality constant that is a positive number and has a value of 6.67x10-11
Nm2/kg
2
Key Concepts
In 1687, Isaac Newton proposed the Law of Universal Gravitation, which is based on observations of falling
bodies. According to the law, the gravitational force between two objects is directly proportional to the product
of their masses and inversely proportional to the square of the distance between the centers of their masses:
The Law of Universal Gravitation explains why objects fall toward Earth s surface and why objects such as the
moon and planets can orbit other objects. No one before Newton had described Earth-bound and planetary
motion with the same theory.
As explained by the Law of Universal Gravitation, the gravitational force between two objects increases as the
mass of one object or both objects increases, and it decreases as the distance between the objects increases.
Magnitude of the Electrical Force5(C): Describe and calculate how the magnitude of the electrical force between two objects
depends on their charges and the distance between them.
Vocabulary
electrostatic force: the attractive or repulsive force between two charged objects
electrostatic constant: the constant k used to calculate the magnitude of the electrostatic force:
Coulomb’s law: the electrostatic force between two objects is proportional to the strength of their charges and
the inverse square of the distance between them
conductor: a material through which electrons flow easily
insulator: a material resistant to electron flow
Key Concepts
Opposite charges attract each other, and like charges repel each other.
Coulumb’s law states that the electrostatic force F between two point charges Q1 and Q2 is given by the
equation:
F = ,
in which k is the electrostatic constant, and r is the distance between the two charges.
The electrostatic force is a central force that is directed along an imaginary line joining the two charges.
The force on one charge is equal in magnitude and opposite in direction to the force on the other charge.
Examples of Electric and Magnetic Forces5(D): Identify examples of electric and magnetic forces in everyday life.
Vocabulary
electric field: a region of space in which an electric force has an effect
magnetic field: a region of space in which a magnetic force has an effect
electromagnetic force: the fundamental force of attraction or repulsion due to electric charge
electromagnetic wave (also called electromagnetic radiation): a wave that travels through space as alternating
magnetic and electric fields
static electricity: a charge separation between stationary objects
electrostatic discharge: a brief exchange of electric charge between two objects of different electric potentials
electric current: a flow of electric charge
electromagnet: an item made to temporarily act as a magnet by exposure to an electric current
magnetic domain: a region in a magnetic material with a given magnetization
degauss: to remove a magnetic field from an object by exposure to a higher field
electromagnetic induction: the production of electric potential difference in a conductor as it moves through a
magnetic field
Key Concepts
Electric forces are a result of small charged particles, such as protons and electrons. Protons have a positive
charge, and electrons have a negative charge. Like charges repel one another, while unlike charges attract each
other. An electric field is the region around electric charges that the charges affect.
Magnetic forces result from the motion of charged particles. The forces involve two poles, designated north and
south, that repel and attract one another similarly to opposite electric charges. In a permanent magnet, the
motion of certain electrons aligns in such a way as to create a magnetic field, a region around the magnet that
the magnetic force affects.
The Earth itself acts as a magnet, and compass needles align with the Earth's magnetic field.
Together, electricity and magnetism form the electromagnetic force, one of the four fundamental forces in
nature.
An electromagnetic wave, which is also called electromagnetic radiation, travels as oscillating magnetic and
electric fields. The changing magnetic field induces an electric field, and the changing electric field induces a
magnetic field.
Electrons may accumulate through contact between items, producing static electricity effects, including
electrostatic discharge. Lightning is an example of a very large electrostatic discharge.
An electric current produces a magnetic field. In manmade electromagnets, magnetic domains of iron cores are
aligned with and boost the magnetic field produced by the electric current. Electromagnets are used in many
applications in everyday life, such as spark plugs in a car, transformers, motors, and loudspeakers.
Electromagnets are used to degauss antitheft tags in books in a bookstore after purchase.
An electric current can also be induced in a conductor as it moves through a magnetic field. This is called
electromagnetic induction. By rotating a coil of wire through a magnetic field, electricity can be generated in
power plants and generators.
Characterize Materials as Conductors or Insulators5(E): Characterize materials as conductors or insulators based on their electrical
properties.
Vocabulary
conductor: a material through which electrons flow easily
insulator: a material resistant to electron flow
Key Concepts
Conductors allow an easy flow of electrons between atoms, while insulators resist electron flow.
Whether a material is a conductor or an insulator is intrinsic to its atomic structure.
If the electrons are tightly bound to the atoms of a material, it is likely to be an insulator, whereas materials with
loosely bound atoms are conductors.
Metals are generally good conductors.
ectric Current, Potential, Resistance, and Power5(F): Design, construct, and calculate in terms of current through, potential difference
across, resistance of, and power used by electric circuit elements connected in both series
and parallel combinations.
Vocabulary
current: the rate at which electric charge flows past a given point in an electric circuit, measured in amperes (A),
or amps for short
electric potential: the amount of potential energy per unit charge, measured in volts (V)
resistance: the opposition to the flow of electric charge, measured in ohms (Ω)
electric circuit: a complete loop of conductors through which electric current can flow
series circuit: an electric circuit in which current can flow through a single path
parallel circuit: an electric circuit in which current can flow through two or more distinct paths
power: the rate at which energy is transformed, measured in watts (W)
Key Concepts
Electric current requires a closed conducting path that connects the two terminals of a voltage source. This closed
path is called an electric circuit.
An electric circuit consists of a voltage source (such as a battery), conducting wires, and resistors. The resistors
may be light bulbs, bells, or other devices that oppose the flow of current. In circuit diagrams, a resistor is
indicated by a zigzag line and the letter ‘R.’
Electric circuits can be wired in different ways. In a series circuit, the resistors are arranged in a single path. In a
parallel circuit, the resistors are arranged in separate paths, or branches.
If one resistor in a series circuit is removed from the circuit, such as by unscrewing a bulb, the circuit is broken
and current ceases to flow. As more resistance is added to a series circuit, the overall current through the circuit
decreases.
If one resistor in a parallel circuit is removed from the circuit, current continues to flow through the other paths.
As more resistance is added in one path of a parallel circuit, the overall current through the circuit increases.
Current (I ), voltage (V ), and resistance (R ) are related according to the equation V = IR . This equation holds true
across any two points of a circuit.
Power (P ) is measured in units of watts (W ). One watt is equal to 1 joule per second. In any device connected in
an electric circuit, the power (P ) transformed is equal to the product of the current (I ) and potential difference
across the device (V ). In equation form: P = IV .
For a series circuit, the total resistance of the circuit is the sum of the individual resistors: R T = R 1 + R 2 + R 3
For a parallel circuit, the total resistance of the circuit is given by this formula:
The Relationship between Electric and Magnetic Fields5(G): Investigate and describe the relationship between electric and magnetic fields in
applications such as generators, motors, and transformers.
Vocabulary
electric motor: a device that converts electrical energy into mechanical energy; can be used to do work
electromagnetic induction: the production of voltage in a wire when it moves within a magnetic field
electric generator: a device that converts mechanical energy into electrical energy, such as at an electric power
plant
transformer: a device that uses electromagnetic induction to convert one voltage to another
Key Concepts
In an electric motor, a coil of insulated wire is wrapped around an iron core. The coil is able to rotate freely
between the poles of a permanent magnet. The coil of wire and the iron core form an electromagnet, which
produces a magnetic field that interacts with the magnetic field of the permanent magnet. By attaching the
spinning coil to a shaft, the motor can turn wheels, propellers, or other objects.
In 1831, Michael Faraday discovered that moving a magnet in and out of a coil of wire produces an electric
current in the wire. Moving a coil of wire through a magnetic field also produces an electric current. The process
is known as electromagnetic induction. The current produced is called an induced current.
An electric generator includes a rotating coil of wire through a magnetic field. This induces a current in the wire.
Electric power lines carry electric current across long distances. They do so at high voltage and low current,
conditions that minimize the loss of energy to heat. Near a house or building, the electricity is transformed to low
voltage and high current.
Transformers are devices that apply the principle of magnetic induction to increase or decrease voltage. Step-up