PHYSICS
Principles and Problems
Chapter 1: A Physics Toolkit
CHAPTER
1
A Physics Toolkit
BIG IDEA
Physicists use scientific methods to investigate
energy and matter.
CHAPTER
1
Table Of Contents
Section 1.1 Methods of Science
Section 1.2 Mathematics and Physics
Section 1.3 Measurement
Section 1.4 Graphing Data
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SECTION
Methods of Science
1.1
MAIN IDEA
Scientific investigations do not always proceed with
identical steps but do contain similar methods.
Essential Questions
•
What are the characteristics of scientific methods?
•
Why do scientists use models?
•
What is the difference between a scientific theory and
a scientific law?
•
What are some limitations of science?
SECTION
Methods of Science
1.1
Review Vocabulary
• Control the standard by which test results in an
experiment can be compared.
New Vocabulary
• Physics
• Model
• Scientific methods
• Scientific theory
• Hypothesis
• Scientific law
SECTION
1.1
Methods of Science
What is Physics?
Physics is a branch of science that involves the
study of the physical world: energy, matter, and
how they are related.
Learning physics will help you to understand
the physical world.
SECTION
1.1
Methods of Science
Scientific Methods
• Although physicists do not
always follow a rigid set of
steps, investigations often
follow similar patterns called
scientific methods.
• Depending on the particular
investigation, a scientist might
add new steps, repeat some
steps or skip steps altogether.
SECTION
1.1
Methods of Science
Scientific Methods (cont.)
• Many investigations begin when someone
observes an event in nature and wonders why or
how it occurs.
• The question of “why” or “how” is the problem.
– Many questions have been asked throughout history:
why objects fall to Earth, what causes day and night,
how to generate electricity…
– Often the investigation into one problem may lead to
more questions and more investigations.
SECTION
1.1
Methods of Science
Scientific Methods (cont.)
• Researching already known information about a
problem, helps to fine-tune the question and
form it into a hypothesis.
– Hypothesis is a possible explanation for a problem
using what you know and have observed.
SECTION
Methods of Science
1.1
Scientific Methods (cont.)
• Hypotheses can be tested by different means:
– Observations
– Models
– Experiments
• Test the effect of one thing on another, using a control.
SECTION
1.1
Methods of Science
Scientific Methods (cont.)
• An important part of every investigation includes
recording observations and organizing data into
easy-to-read tables and graphs.
• Based on the analysis of the data, the next step is
to decide whether the hypothesis is supported.
– If supported, the data must be reproducible many times.
– If not supported, the hypothesis must be reconsidered.
SECTION
1.1
Methods of Science
Models
• Sometimes, scientists cannot see everything they
are testing. They might be observing an object
that is too large or too small, a process that takes
too much time to see completely, or a material that
is hazardous.
• A model is a representation of an idea, event,
structure, or object that helps people better
understand it.
SECTION
1.1
Methods of Science
Scientific Theories and Laws
• A scientific theory is an explanation of things or
events based on knowledge gained from many
observations and investigations.
– This is not a hypothesis, this is what a hypothesis
becomes after numerous trials of data supporting the
hypothesis.
– A theory is never permanent, it can change as new data
and information becomes available.
SECTION
Methods of Science
1.1
Scientific Theories and Laws (cont.)
• A scientific law is a statement about what
happens in nature and seems to be true all the
time.
– Laws tell you what will happen under certain conditions,
but they do not explain why or how something happens.
Ex. Gravity
• The law of gravity states that any one mass will attract another
mass.
• There are many theories proposed to explain how the law of
gravity works.
SECTION
1.1
Methods of Science
The Limitations of Science
• Science cannot explain or solve every question.
• A scientific question must be testable and
verifiable.
– Questions about opinions, values or emotions are not
scientific because they cannot be tested.
SECTION
1.1
Section Check
The similar patterns used, by all branches of
science, in an investigation are called?
A.
B.
C.
D.
Hypotheses
Scientific theories
Scientific methods
Scientific laws
SECTION
Section Check
1.1
“In a closed-system, mass is always
conserved” is an example of which of the
following?
A.
B.
C.
D.
Scientific law
Scientific theory
Hypothesis
Model
SECTION
Mathematics and Physics
1.2
MAIN IDEA
We use math to express concepts in physics.
Essential Questions
•
Why do scientists use the metric system?
•
How can dimensional analysis help evaluate answers?
•
What are significant figures?
SECTION
1.2
Mathematics and Physics
Review Vocabulary
• SI International System of Units – the improved,
universally accepted version of the metric system that
is based on multiples of ten.
New Vocabulary
• Dimensional analysis
• Significant figures
SECTION
1.2
Mathematics and Physics
Mathematics in Physics
• Physicists often use the language of mathematics.
• Physicists rely on theories and experiments with
numerical results to support their conclusions.
SECTION
1.2
Mathematics and Physics
SI Units
• In order to communicate
results that everyone can
understand, the worldwide
scientific community uses
an adaptation of the metric
system called Systeme
International d’Unites or SI.
• The SI system of
measurement uses seven
base quantities.
SECTION
1.2
Mathematics and Physics
SI Units (cont.)
• The base quantities were originally defined in terms of
direct measurements. Other units, called derived units, are
created by combining the base units in various ways.
• The SI system is regulated by the International Bureau of
Weights and Measures in Sèvres, France.
• This bureau and the National Institute of Science and
Technology (NIST) in Gaithersburg, Maryland, keep the
standards of length, time, and mass against which our
metersticks, clocks, and balances are calibrated.
SECTION
1.2
Mathematics and Physics
SI Units (cont.)
• Another feature in the SI
system is the ease of
converting units.
• To convert between
units, multiply or divide
by the appropriate power
of 10.
• Prefixes are used to
change SI base units to
powers of 10.
SECTION
1.2
Mathematics and Physics
Dimensional Analysis
• You will often need to use different versions of a
formula, or use a string of formulas, to solve a
physics problem.
• To check that you have set up a problem correctly,
write the equation or set of equations you plan to
use with the appropriate units.
SECTION
1.2
Mathematics and Physics
Dimensional Analysis (cont.)
• Before performing calculations, check that the
answer will be in the expected units.
• For example, if you are finding a speed and you see
that your answer will be measured in s/m, you know
you have made an error in setting up the problem.
• This method of treating the units as algebraic
quantities, which can be cancelled, is called
dimensional analysis.
SECTION
1.2
Mathematics and Physics
Dimensional Analysis (cont.)
• Dimensional analysis is also used in choosing
conversion factors.
• A conversion factor is a multiplier equal to 1. For
example, because 1 kg = 1000 g, you can
construct the following conversion factors:
SECTION
1.2
Mathematics and Physics
Dimensional Analysis (cont.)
• Choose a conversion factor that will make the units
cancel, leaving the answer in the correct units.
• For example, to convert 1.34 kg of iron ore to
grams, do as shown below:
SECTION
1.2
Mathematics and Physics
Significant Figures
• A meterstick is used to measure a pen and you find the end
of the pen is in between 138 and 139mm. You estimate
that the pen is two-tenths of a millimeter past the 138 mark
and record the measurement as 138.2mm.
• This measurement has four valid digits: three you are sure
of, and one you estimated.
• The valid digits in a measurement are called significant
figures.
• However, the last digit given for any measurement is the
uncertain digit.
SECTION
1.2
Mathematics and Physics
Significant Figures (cont.)
• All nonzero digits in a measurement are
significant, but not all zeros are significant.
• Consider a measurement such as 0.0860 m. Here
the first two zeros serve only to locate the decimal
point and are not significant.
• The last zero, however, is the estimated digit and
is significant.
SECTION
1.2
Mathematics and Physics
Significant Figures (cont.)
• When you perform any arithmetic operation, it is
important to remember that the result can never be
more precise than the least-precise measurement.
• To add or subtract measurements:
–First perform the operation, then round off the result to
correspond to the least-precise value involved. Ex.
3.86m + 2.4m = 6.3m
SECTION
1.2
Mathematics and Physics
Significant Figures (cont.)
• To multiply or divide measurements:
–Perform the calculation and then round to the same
number of significant digits as the least-precise
measurement. Ex. 409.2km/11.4L = 35.9km/L
• Note: Significant digits are considered only when
calculating with measurements. There is no
uncertainty associated with counting (4 washers)
or exact conversion factors (24 hours in 1 day).
SECTION
Section Check
1.2
The potential energy, PE, of a body of mass, m, raised
to a height, h, is expressed mathematically as PE = mgh,
where g is the gravitational constant. If m is measured
in kg, g in m/s2, h in m, and PE in joules, then what is 1
joule described in base units?
A. 1 kg·m/s
B. 1 kg·m/s2
C. 1 kg·m2/s
D. 1 kg·m2/s2
SECTION
1.2
Answer
Reason:
Section Check
SECTION
Section Check
1.2
A car is moving at a speed of 90 km/h. What is
the speed of the car in m/s? (Hint: Use
Dimensional Analysis)
A. 2.5×101 m/s
B. 1.5×103 m/s
C. 2.5 m/s
D. 1.5×102 m/s
SECTION
1.2
Answer
Reason:
Section Check
SECTION
Section Check
1.2
Which of the following representations is correct
when you solve 0.030 kg + 3333 g using
scientific notation?
A. 3.4×103 g
B. 3.36×103 g
C. 3×103 g
D. 3.363×103 g
SECTION
1.2
Section Check
Answer
Reason: 0.030 kg is the same as 30g and can be
written as 3.0 101 g which has 2
significant digits, the number 3 and the
zero after 3.
3333 has four significant digits; all four
threes.
Therefore, our answer should contain
only 2 significant digits.
SECTION
Measurement
1.3
MAIN IDEA
Making careful measurements allows scientists to repeat
experiments and compare results.
Essential Questions
•
Why are the results of measurements often reported
with an uncertainty?
•
What is the difference between precision and
accuracy?
•
What is a common source of error when making a
measurement?
SECTION
Measurement
1.3
Review Vocabulary
• Parallax the apparent shift in the position of an object
when it is viewed from different angles.
New Vocabulary
• Measurement
• Precision
• Accuracy
SECTION
1.3
Measurement
What is a Measurement?
• A measurement is a comparison between an
unknown quantity and a standard.
–Ex. Measuring the mass of a rolling cart. The
unknown quantity is the cart, the standard is the gram
as defined the instrument being used.
• Measurements quantify observations.
• Careful measurements enable you to derive the
relationship between any two quantities.
SECTION
1.3
Measurement
Comparing Results
• When a measurement is made, the results are
often reported with uncertainty.
• Therefore, before fully accepting new data, other
scientists examine the experiment, looking for
possible sources of errors, and try to reproduce
the results.
• A new measurement that is within the margin of
uncertainty confirms the old measurement.
SECTION
1.3
Measurement
Precision Versus Accuracy
Click image to view the movie.
SECTION
1.3
Measurement
Techniques of Good Measurement
• To assure precision and accuracy, instruments
used to make measurements need to be used
correctly.
• This is important because one common source of
error comes from the angle at which an instrument
is read.
SECTION
1.3
Measurement
Techniques of Good Measurement
• Scales should be read with one’s
eye straight in front of the measure.
(a)
• If the scale is read from an angle,
as shown in figure (b), you will get
(b)
a different, and less accurate,
value.
• The difference in readings is
caused by parallax, which is
the apparent shift in the position of an object when it is
viewed from different angles.
SECTION
1.3
Measurement
Ronald, Kevin, and Paul perform an experiment to determine
the value of acceleration due to gravity on Earth (which most
scientists agree is about 980 cm/s2). The following results
were obtained: Ronald — 961 ± 12 cm/s2, Kevin — 953 ± 8
cm/s2, and Paul — 942 ± 4 cm/s2. Determine who has the
most accurate and precise value.
A. Kevin got the most precise and accurate value.
B. Ronald’s value is the most accurate, while Kevin’s value is the
most precise.
C. Ronald’s value is the most accurate, while Paul’s value is the
most precise.
D. Paul’s value is the most accurate, while Ronald’s value is the
most precise.
SECTION
1.3
Section Check
Answer
Reason: Ronald’s answer is closest to 980 cm/s2.
Hence, Ronald’s result is the most
accurate. However, Paul’s error is only
±4 cm/s2. Hence, Paul’s result is the
most precise.
SECTION
1.3
Section Check
What is the precision of an instrument?
A. the smallest divisions marked on the instrument
B. the least count written on the instrument
C. one-half the least count written on the instrument
D. one-half the smallest division written on the
instrument
SECTION
1.3
Section Check
Answer
Reason: Precision depends on the instrument and
the technique used to make the
measurement. Generally, the device with
the finest division on its scale produces
the most precise measurement. The
precision of a measurement is one-half of
the smallest division of the instrument.
SECTION
1.3
Section Check
A 100-cm long rope was measured with three different
measuring tapes. The answer obtained with the three
measuring tapes were: 1st measuring tape — 99 ± 0.5
cm, 2nd measuring tape — 98 ± 0.25 cm, and 3rd
measuring tape — 99 ± 1 cm. Which measuring tape is
the most precise?
A. 1st measuring tape
B. 2nd measuring tape
C. 3rd measuring tape
D. Both measuring tapes 1 and 3
SECTION
1.3
Section Check
Answer
Reason: Precision depends on the instrument. The
2nd measuring tape has an error of only
±0.25 cm and is therefore the most
precise.
SECTION
Graphing Data
1.4
MAIN IDEA
Graphs make it easier to interpret data, identify trends and
show relationships among a set of variables.
Essential Questions
•
What can be learned from graphs?
•
What are some common relationships in graphs?
•
How do scientists make predictions?
SECTION
Graphing Data
1.4
Review Vocabulary
• Slope on a graph, the ratio of vertical change to
horizontal change.
New Vocabulary
• Independent variable
• Linear relationship
• Dependent variable
• Quadratic relationship
• Line of best fit
• Inverse relationship
SECTION
1.4
Graphing Data
Identifying Variables
• A variable is any factor that might affect the
behavior of an experimental setup.
• The independent variable is the factor that is
changed or manipulated during the experiment.
• The dependent variable is the factor that
depends on the independent variable.
SECTION
1.4
Graphing Data
Identifying Variables (cont.)
Click image to view the movie.
SECTION
1.4
Graphing Data
Linear Relationships
• Scatter plots of data may take many different
shapes, suggesting different relationships.
• Three of the most common relationships include
linear relationships, quadratic relationships and
inverse relationships.
SECTION
1.4
Graphing Data
Linear Relationships
• When the line of best fit is a
straight line, as in the figure,
the dependent variable varies
linearly with the independent
variable. This relationship
between the two variables is
called a linear relationship.
• The relationship can be written
as an equation.
SECTION
1.4
Graphing Data
Linear Relationships
• The slope is the ratio of the
vertical change to the
horizontal change. To find the
slope, select two points, A and
B, far apart on the line. The
vertical change, or rise, Δy, is
the difference between the
vertical values of A and B. The
horizontal change, or run, Δx, is
the difference between the
horizontal values of A and B.
SECTION
1.4
Graphing Data
Linear Relationships
• As presented in the previous slide, the slope of a line is
equal to the rise divided by the run, which also can be
expressed as the change in y divided by the change in x.
• If y gets smaller as x gets larger, then Δy/Δx is negative,
and the line slopes downward.
• The y-intercept, b, is the point at which the line crosses the
y-axis, and it is the y-value when the value of x is zero.
SECTION
1.4
Graphing Data
Nonlinear Relationships
• When the graph is not a straight line, it means that
the relationship between the dependent variable
and the independent variable is not linear.
• There are many types of nonlinear relationships in
science. Two of the most common are the
quadratic and inverse relationships.
SECTION
1.4
Graphing Data
Nonlinear Relationships
• The graph shown in the
figure is a quadratic
relationship.
• A quadratic
relationship exists when
one variable depends on
the square of another.
SECTION
1.4
Graphing Data
Nonlinear Relationships
• A quadratic relationship can be represented by the
following equation:
SECTION
1.4
Graphing Data
Nonlinear Relationships
• The graph in the figure shows
how the current in an electric
circuit varies as the resistance is
increased. This is an example of
an inverse relationship.
• In an inverse relationship, a
hyperbola results when one
variable depends on the inverse
of the other.
SECTION
1.4
Graphing Data
Nonlinear Relationships
• An inverse relationship can be represented by the
following equation:
SECTION
1.4
Graphing Data
Nonlinear Relationships
• There are various mathematical models available
apart from the three relationships you have
learned. Examples include sinusoids, which are
used to model cyclical phenomena, and
exponential decay curves, which are used to
model radioactivity.
• Combinations of different mathematical models
represent even more complex phenomena.
SECTION
1.4
Graphing Data
Predicting Values
• Relations, either learned as formulas or developed
from graphs, can be used to predict values you have
not measured directly.
• Physicists use models to accurately predict how
systems will behave: what circumstances might lead
to a solar flare, how changes to a circuit will change
the performance of a device, or how electromagnetic
fields will affect a medical instrument.
SECTION
1.4
Section Check
Which type of relationship is shown by the
following graph?
A. Linear
B. Inverse
C. Parabolic
D. Quadratic
SECTION
1.4
Section Check
Answer
Reason: In an inverse relationship, a hyperbola
results when one variable depends on the
inverse of the other.
SECTION
1.4
Section Check
What is a line of best fit?
A. the line joining the first and last data points in a graph
B. the line joining the two center-most data points in a
graph
C. the line drawn as close to all the data points as
possible
D. the line joining the maximum data points in a graph
SECTION
1.4
Section Check
Answer
Reason: The line drawn closest to all data points as
possible is called the line of best fit. The
line of best fit is a better model for
predictions than any one or two points that
help to determine the line.
SECTION
1.4
Section Check
Which relationship can be written as y = mx + b?
A. Linear relationship
B. Quadratic relationship
C. Parabolic relationship
D. Inverse relationship
SECTION
1.4
Section Check
Answer
Reason: A linear relationship can be written as y =
mx + b, where m is the slope and b is the
y-intercept.
CHAPTER
A Physics Toolkit
1
Resources
Physics Online
Study Guide
Chapter Assessment Questions
Standardized Test Practice
SECTION
Methods of Science
1.1
Study Guide
•
Scientific methods include making observations and
asking questions about the natural world.
•
Scientists use models to represent things that may be
too small or too large, processes that take too much
time to see completely, or a material that is
hazardous.
SECTION
Methods of Science
1.1
Study Guide
•
A scientific theory is an explanation of things or
events based on knowledge gained from
observations and investigations. A scientific law is a
statement about what happens in nature, which
seems to be true all the time.
•
Science can not explain or solve everything.
Questions about opinions or values can not be
tested.
SECTION
Mathematics and Physics
1.2
Study Guide
•
Using the metric system helps scientists around the
world communicate more easily.
•
Dimensional analysis is used to check that an answer
will be in the correct units.
•
Significant figures are the valid digits in a
measurement.
SECTION
Measurement
1.3
Study Guide
•
Measurements are reported with uncertainty because a
new measurement that is within the margin of
uncertainty confirms the old measurement.
•
Precision is the degree of exactness with which a
quantity is measured. Accuracy is the extent to which a
measurement matches the true value.
•
A common source of error that occurs when making a
measurement is the angle at which an instrument is
read. If the scale of an instrument is read an angle, as
opposed to eye level, the measurement will be less
accurate.
SECTION
Graphing Data
1.4
Study Guide
•
Graphs contain information about the relationships
among variables. Patterns that are not immediately
evident in a list of numbers are seen more easily when
the data are graphed.
SECTION
Graphing Data
1.4
Study Guide
•
Common relationships shown in graphs include linear
relationships, quadratic relationships and inverse
relationships. In a linear relationship, the dependent
variable varies linearly with the independent variable. A
quadratic relationship occurs when one variable
depends on the square of an another. In an inverse
relationship, one variable depends on the inverse of the
other variable.
•
Scientists use models and relationships between
variables to make predictions.
CHAPTER
A Physics Toolkit
1
Chapter Assessment
How will you express 1 nm in m?
A. 1×10-3 m
B. 1×10-6 m
C. 1×10-9 m
D. 1×10-1 m
CHAPTER
1
A Physics Toolkit
Chapter Assessment
Reason: 1 nm is read as 1 nanometer. The prefix
nano stands for 10-9.
CHAPTER
1
A Physics Toolkit
Chapter Assessment
Add the following numbers and write the
answer using the proper number of significant
digits: 12.3 + 1.2 + 123.
A. 136.5
B. 1.4 × 102
C. 137
D. 1.37 × 102
CHAPTER
1
A Physics Toolkit
Chapter Assessment
Reason: The last digit in 12.3 and 1.2 are both
in the tenth’s place. However, the last
digit in 123 is in the one’s place.
Therefore, the last digit of the answer
should be in the one’s place.
CHAPTER
1
A Physics Toolkit
Chapter Assessment
Rewrite 3.650 with only 2 significant digits.
A. 3.7
B. 3.6
C. 3.65
D. 0.360 × 101
CHAPTER
1
A Physics Toolkit
Chapter Assessment
Reason: The last reported digit would be the 6.
The digit to the right is a 5 followed
by a zero. Therefore since the 6 is
even it remains so and the answer
would be 3.6.
CHAPTER
1
A Physics Toolkit
Chapter Assessment
If 15 different individuals perform an experiment, and
15 answers are obtained, which answer will be
accepted as the most accurate?
A. the answer obtained by the highest number of persons
B. the eighth number if all the numbers are arranged in an
ascending order
C. the answer nearest to the expected answer
D. the average of all 15 answers
CHAPTER
1
A Physics Toolkit
Chapter Assessment
Reason: Accuracy describes how well the result
of a measurement agrees with the
expected value.
CHAPTER
1
A Physics Toolkit
Chapter Assessment
A quadratic relationship between two variables
is written as ____.
A.
B.
C.
D.
CHAPTER
1
A Physics Toolkit
Chapter Assessment
Reason: A quadratic relationship between two
variables is written as
y = ax2 + bx + c.
CHAPTER
A Physics Toolkit
1
Standardized Test Practice
Two laboratories use radiocarbon dating to measure the
age of two wooden spear handles found in the same
grave. Lab A finds an age of 2250  40 years for the first
object; lab B finds an age of 2215  50 years for the
second object. Which of the following is true?
A. Lab A’s reading is more accurate than lab B’s.
B. Lab A’s reading is less accurate than lab B’s.
C. Lab A’s reading is more precise than lab B’s.
D. Lab A’s reading is less precise than lab B’s.
CHAPTER
1
A Physics Toolkit
Standardized Test Practice
Which of the following is equal to 86.2 cm?
A. 8.62 m
B. 0.862 mm
C. 8.62×10-4 km
D. 862 dm
CHAPTER
1
A Physics Toolkit
Standardized Test Practice
Jario has a homework problem to do involving time,
distance, and velocity, but he has forgotten the formula.
The question asks him for a measurement in seconds,
and the numbers that are given have units of m/s and km.
What could Jario do to get the answer in seconds?
A. Multiply the km by the m/s, then multiply by 1000.
B. Divide the km by the m/s, then multiply by 1000.
C. Divide the km by the m/s, then divide by 1000.
D. Multiply the km by the m/s, then divide by 1000.
CHAPTER
1
A Physics Toolkit
Standardized Test Practice
What is the slope of the graph?
A. 0.25 m/s2
B. 0.4 m/s2
C. 2.5 m/s2
D. 4.0 m/s2
CHAPTER
1
A Physics Toolkit
Standardized Test Practice
Which formula is equivalent to
A.
B.
C.
D.
CHAPTER
A Physics Toolkit
1
Standardized Test Practice
Test-Taking Tip
Skip Around if You Can
You may want to skip over difficult questions and
come back to them later, after you’ve answered
the easier questions. This will guarantee more
points toward your final score. In fact, other
questions may help you answer the ones you
skipped. Just be sure you fill in the correct ovals
on your answer sheet.
CHAPTER
1
A Physics Toolkit
Chapter Resources
Length of a Spring for Different Masses (1)
CHAPTER
1
A Physics Toolkit
Chapter Resources
Length of a Spring for Different Masses (2)
CHAPTER
1
A Physics Toolkit
Chapter Resources
Graph Indicating a Quadratic, or Parabolic,
Relationship
CHAPTER
1
A Physics Toolkit
Chapter Resources
Graph Showing the Inverse Relationship
Between Resistance and Current