Chapter 1
Section 1 What Is Physics?
The Branches of Physics
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Chapter 1
Section 1 What Is Physics?
The Branches of Physics
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Chapter 1
Section 1 What Is Physics?
Physics
• The goal of physics is to use a small number of
basic concepts, equations, and assumptions to
describe the physical world.
• These physics principles can then be used to make
predictions about a broad range of phenomena.
• Physics discoveries often turn out to have
unexpected practical applications, and advances in
technology can in turn lead to new physics
discoveries.
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Chapter 1
Section 1 What Is Physics?
Physics and Technology
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Chapter 1
Section 1 What Is Physics?
The Scientific Method
• There is no single
procedure that scientists
follow in their work.
However, there are
certain steps common to
all good scientific
investigations.
• These steps are called
the scientific method.
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Chapter 1
Section 1 What Is Physics?
Models
• Physics uses models that describe phenomena.
• A model is a pattern, plan, representation, or
description designed to show the structure or
workings of an object, system, or concept.
• A set of particles or interacting components
considered to be a distinct physical entity for the
purpose of study is called a system.
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Chapter 1
Section 1 What Is Physics?
Hypotheses
• Models help scientists develop hypotheses.
• A hypothesis is an explanation that is based on prior
scientific research or observations and that can be
tested.
• The process of simplifying and modeling a situation
can help you determine the relevant variables and
identify a hypothesis for testing.
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Chapter 1
Section 1 What Is Physics?
Hypotheses, continued
Galileo modeled the behavior of falling objects in
order to develop a hypothesis about how objects fall.
If heavier objects fell faster
than slower ones,would two
bricks of different masses
tied together fall slower (b) or
faster (c) than the heavy
brick alone (a)? Because of
this contradiction, Galileo
hypothesized instead that all
objects fall at the same rate,
as in (d).
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Chapter 1
Section 2 Measurements in
Experiments
Preview
• Numbers as Measurements
• Dimensions and Units
• Accuracy and Precision
• Significant Figures
• Vectors
• Distance/Displacement Speed\Velocity
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Chapter 1
Section 2 Measurements in
Experiments
Objectives
• List basic SI units and the quantities they describe.
• Convert measurements into scientific notation.
• Distinguish between accuracy and precision.
• Use significant figures in measurements and
calculations.
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Chapter 1
Section 2 Measurements in
Experiments
Numbers as Measurements
• In SI, the standard measurement system for science,
there are seven base units.
• Each base unit describes a single dimension, such
as length, mass, or time.
• The units of length, mass, and time are the meter
(m), kilogram (kg), and second (s), respectively.
• Derived units are formed by combining the seven
base units with multiplication or division. For
example, speeds are typically expressed in units of
meters per second (m/s).
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Chapter 1
Section 2 Measurements in
Experiments
SI Standards
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Chapter 1
Section 2 Measurements in
Experiments
SI Prefixes
In SI, units are
combined with
prefixes that
symbolize certain
powers of 10.
The most
common prefixes
and their
symbols are
shown in the
table.
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Chapter 1
Section 2 Measurements in
Experiments
Accuracy and Precision
• Accuracy is a description of how close a
measurement is to the correct or accepted value of
the quantity measured.
• Precision is the degree of exactness of a
measurement.
• A numeric measure of confidence in a measurement
or result is known as uncertainty. A lower
uncertainty indicates greater confidence.
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Chapter 1
Section 2 Measurements in
Experiments
Accuracy and Precision
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Chapter 1
Section 2 Measurements in
Experiments
Measurement and Parallax
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Chapter 1
Section 2 Measurements in
Experiments
Significant Figures
• It is important to record the precision of your
measurements so that other people can understand
and interpret your results.
• A common convention used in science to indicate
precision is known as significant figures.
• Significant figures are those digits in a
measurement that are known with certainty plus the
first digit that is uncertain.
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Chapter 1
Section 2 Measurements in
Experiments
Significant Figures, continued
Even though this ruler is
marked in only centimeters
and half-centimeters, if you
estimate, you can use it to
report measurements to a
precision of a millimeter.
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Chapter 1
Section 2 Measurements in
Experiments
Rules for Determining Significant Zeroes
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Chapter 1
Section 2 Measurements in
Experiments
Rules for Determining Significant Zeros
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Chapter 1
Section 2 Measurements in
Experiments
Rules for Calculating with Significant Figures
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Chapter 1
Section 2 Measurements in
Experiments
Rules for Rounding in Calculations
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Chapter 1
Section 2 Measurements in
Experiments
Rules for Rounding in Calculations
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Chapter 1
Section 3 The Language of
Physics
Preview
• Objectives
• Mathematics and Physics
• Physics Equations
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Chapter 1
Section 3 The Language of
Physics
Objectives
• Interpret data in tables and graphs, and recognize
equations that summarize data.
• Distinguish between conventions for abbreviating
units and quantities.
• Use dimensional analysis to check the validity of
equations.
• Perform order-of-magnitude calculations.
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Chapter 1
Section 3 The Language of
Physics
Mathematics and Physics
• Tables, graphs, and equations can make data
easier to understand.
• For example, consider an experiment to test Galileo’s
hypothesis that all objects fall at the same rate in the
absence of air resistance.
– In this experiment, a table-tennis ball and a golf ball are
dropped in a vacuum.
– The results are recorded as a set of numbers corresponding
to the times of the fall and the distance each ball falls.
– A convenient way to organize the data is to form a table, as
shown on the next slide.
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Chapter 1
Section 3 The Language of
Physics
Data from Dropped-Ball Experiment
A clear trend can be seen in the data. The more time that
passes after each ball is dropped, the farther the ball falls.
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Chapter 1
Section 3 The Language of
Physics
Graph from Dropped-Ball Experiment
One method for analyzing the data is to construct a
graph of the distance the balls have fallen versus the
elapsed time since they were released. a
The shape of the
graph provides
information about
the relationship
between time and
distance.
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Chapter 1
Section 3 The Language of
Physics
Physics Equations
• Physicists use equations to describe measured or
predicted relationships between physical quantities.
• Variables and other specific quantities are abbreviated
with letters that are boldfaced or italicized.
• Units are abbreviated with regular letters, sometimes
called roman letters.
• Two tools for evaluating physics equations are
dimensional analysis and order-of-magnitude
estimates.
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Chapter 1
Section 3 The Language of
Physics
Equation from Dropped-Ball Experiment
• We can use the following equation to describe the relationship
between the variables in the dropped-ball experiment:
(change in position in meters) = 4.9  (time in seconds)2
• With symbols, the word equation above can be written as follows:
y = 4.9(t)2
• The Greek letter  (delta) means “change in.” The abbreviation
y indicates the vertical change in a ball’s position from its
starting point, and t indicates the time elapsed.
• This equation allows you to reproduce the graph and make
predictions about the change in position for any time.
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Chapter 3
Section 1 Introduction to Vectors
Preview
• Objectives
• Scalars and Vectors
• Graphical Addition of Vectors
• Triangle Method of Addition
• Properties of Vectors
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Chapter 3
Section 1 Introduction to Vectors
Scalars and Vectors
• A scalar is a physical quantity that has magnitude
but no direction.
– Examples: speed, volume, the number of pages
in your textbook
• A vector is a physical quantity that has both
magnitude and direction.
– Examples: displacement, velocity, acceleration
• In this book, scalar quantities are in italics. Vectors
are represented by boldface symbols.
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Chapter 3
Section 1 Introduction to Vectors
Graphical Addition of Vectors
• A resultant vector represents the sum of two or
more vectors.
• Vectors can be added graphically.
A student walks from his
house to his friend’s house
(a), then from his friend’s
house to the school (b). The
student’s resultant
displacement (c) can be
found by using a ruler and a
protractor.
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Chapter 3
Section 1 Introduction to Vectors
Triangle Method of Addition
• Vectors can be moved parallel to themselves in a
diagram.
• Thus, you can draw one vector with its tail starting at
the tip of the other as long as the size and direction of
each vector do not change.
• The resultant vector can then be drawn from the tail
of the first vector to the tip of the last vector.
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Chapter 3
Section 1 Introduction to Vectors
Triangle Method of Addition
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Chapter 3
Section 1 Introduction to Vectors
Properties of Vectors
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Visual Concept
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Chapter 3
Section 2 Vector Operations
Coordinate Systems in Two Dimensions
• One method for diagraming the
motion of an object employs
vectors and the use of the xand y-axes.
• Axes are often designated
using fixed directions.
• In the figure shown here, the
positive y-axis points north
and the positive x-axis points
east.
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Chapter 3
Section 2 Vector Operations
Determining Resultant Magnitude and
Direction
• In Section 1, the magnitude and direction of a
resultant were found graphically.
• With this approach, the accuracy of the answer
depends on how carefully the diagram is drawn
and measured.
• A simpler method uses the Pythagorean theorem
and the tangent function.
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Section 2 Vector Operations
Chapter 3
Determining Resultant Magnitude and
Direction, continued
The Pythagorean Theorem
• Use the Pythagorean theorem to find the magnitude of the
resultant vector.
• The Pythagorean theorem states that for any right triangle,
the square of the hypotenuse—the side opposite the right
angle—equals the sum of the squares of the other two
sides, or legs.
c  a b
2
2
2
(hypotenuse)2  (leg 1)2  (leg 2)2
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Chapter 3
Section 2 Vector Operations
Determining Resultant Magnitude and
Direction, continued
The Tangent Function
• Use the tangent function to find the direction of the
resultant vector.
• For any right triangle, the tangent of an angle is defined as
the ratio of the opposite and adjacent legs with respect to
a specified acute angle of a right triangle.
opposite leg
tangent of angle  =
adjacent leg
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Chapter 3
Section 2 Vector Operations
Resolving Vectors into Components
• You can often describe an object’s motion more
conveniently by breaking a single vector into two
components, or resolving the vector.
• The components of a vector are the projections
of the vector along the axes of a coordinate
system.
• Resolving a vector allows you to analyze the
motion in each direction.
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Chapter 3
Section 2 Vector Operations
Resolving Vectors into Components, continued
Consider an airplane flying at 95 km/h.
• The hypotenuse (vplane) is the resultant vector
that describes the airplane’s total velocity.
• The adjacent leg represents the x component
(vx), which describes the airplane’s horizontal
speed.
•
The opposite leg represents
the y component (vy),
which describes the
airplane’s vertical speed.
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Chapter 3
Section 2 Vector Operations
Resolving Vectors into Components, continued
• The sine and cosine functions can be used to
find the components of a vector.
• The sine and cosine functions are defined in terms
of the lengths of the sides of right triangles.
opposite leg
sine of angle  =
hypotenuse
adjacent leg
cosine of angle  =
hypotenuse
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Section 2 Vector Operations
Chapter 3
Adding Vectors That Are Not Perpendicular
• Suppose that a plane travels first 5 km at an angle
of 35°, then climbs at 10° for 22 km, as shown
below. How can you find the total displacement?
• Because the original displacement vectors do not
form a right triangle, you can not directly apply the
tangent function or the Pythagorean theorem.
d2
d1
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Chapter 3
Section 2 Vector Operations
Adding Vectors That Are Not Perpendicular,
continued
• You can find the magnitude and the direction of
the resultant by resolving each of the plane’s
displacement vectors into its x and y components.
• Then the components along each axis can be
added together.
As shown in the figure, these sums will
be the two perpendicular components
of the resultant, d. The resultant’s
magnitude can then be found by using
the Pythagorean theorem, and its
direction can be found by using the
inverse tangent function.
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Chapter 3
Section 4 Relative Motion
Objectives
• Describe situations in terms of frame of reference.
• Solve problems involving relative velocity.
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Chapter 3
Section 4 Relative Motion
Frames of Reference
• If you are moving at 80 km/h north and a car
passes you going 90 km/h, to you the faster car
seems to be moving north at 10 km/h.
• Someone standing on the side of the road would
measure the velocity of the faster car as 90 km/h
toward the north.
• This simple example demonstrates that velocity
measurements depend on the frame of reference
of the observer.
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Chapter 3
Section 4 Relative Motion
Frames of Reference, continued
Consider a stunt dummy dropped from a plane.
(a) When viewed from the plane, the stunt dummy falls straight
down.
(b) When viewed from a stationary position on the ground, the
stunt dummy follows a parabolic projectile path.
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Chapter 3
Section 4 Relative Motion
Relative Motion
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Chapter 3
Section 4 Relative Motion
Relative Velocity
• When solving relative velocity problems, write down the
information in the form of velocities with subscripts.
• Using our earlier example, we have:
• vse = +80 km/h north (se = slower car with respect to
Earth)
• vfe = +90 km/h north (fe = fast car with respect to Earth)
• unknown = vfs (fs = fast car with respect to slower car)
• Write an equation for vfs in terms of the other velocities. The
subscripts start with f and end with s. The other subscripts
start with the letter that ended the preceding velocity:
• vfs = vfe + ves
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Section 1 Displacement and Velocity
Chapter 2
Preview
•
•
•
•
•
•
Objectives
One Dimensional Motion
Displacement
Average Velocity
Velocity and Speed
Interpreting Velocity Graphically
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Section 1 Displacement and Velocity
Chapter 2
Objectives
• Describe motion in terms of frame of reference,
displacement, time, and velocity.
• Calculate the displacement of an object traveling at a
known velocity for a specific time interval.
• Construct and interpret graphs of position versus
time.
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Section 1 Displacement and Velocity
Chapter 2
One Dimensional Motion
• To simplify the concept of motion, we will first
consider motion that takes place in one
direction.
• One example is the motion of a commuter train on
a straight track.
• To measure motion, you must choose a frame of
reference. A frame of reference is a system for
specifying the precise location of objects in space
and time.
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Section 1 Displacement and Velocity
Chapter 2
Frame of Reference
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Section 1 Displacement and Velocity
Chapter 2
Displacement
•
•
•
Displacement is a change in position.
Displacement is not always equal to the distance traveled.
The SI unit of displacement is the meter, m.
x = xf – xi
displacement = final position – initial position
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Section 1 Displacement and Velocity
Chapter 2
Displacement
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Section 1 Displacement and Velocity
Chapter 2
Positive and Negative Displacements
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Section 1 Displacement and Velocity
Chapter 2
Average Velocity
• Average velocity is the total displacement
divided by the time interval during which the
displacement occurred.
vavg
x x f  xi


t
t f  ti
change in position
displacement
average velocity =
=
change in time
time interval
•
In SI, the unit of velocity is meters per second, abbreviated as m/s.
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Section 1 Displacement and Velocity
Chapter 2
Average Velocity
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Section 1 Displacement and Velocity
Chapter 2
Velocity and Speed
• Velocity describes motion with both a direction
and a numerical value (a magnitude).
• Speed has no direction, only magnitude.
• Average speed is equal to the total distance
traveled divided by the time interval.
distance traveled
average speed =
time of travel
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Section 1 Displacement and Velocity
Chapter 2
Interpreting Velocity Graphically
•
•
For any position-time graph, we can determine the average velocity by
drawing a straight line between any two points on the graph.
If the velocity is constant, the graph of position versus
time is a straight line. The slope indicates the velocity.
– Object 1: positive slope = positive
velocity
– Object 2: zero slope= zero velocity
– Object 3: negative slope = negative
velocity
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Section 1 Displacement and Velocity
Chapter 2
Interpreting Velocity Graphically, continued
The instantaneous velocity is the velocity of an object at some instant
or at a specific point in the object’s path.
The instantaneous
velocity at a given time
can be determined by
measuring the slope of
the line that is tangent
to that point on the
position-versus-time
graph.
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Section 1 Displacement and Velocity
Chapter 2
Sign Conventions for Velocity
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