Transcript A Physics Toolkit
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
Section 1.2
Section 1.3
Section 1.4
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SECTION 1.1
Methods of Science
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 1.1
Methods of Science
Review Vocabulary
•
Control
the standard by which test results in an experiment can be compared.
New Vocabulary
• Physics • Scientific methods • Hypothesis • Model • Scientific theory • 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 1.1
Methods of Science 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 1.1
Methods of Science 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
gravity works.
proposed to explain how the law of
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 1.1
Section Check
“
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 1.2
Mathematics and Physics
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 1.2
Section Check
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.
B.
C.
D.
1 kg·m/s 1 kg ·m/s 2 1 kg ·m 2 /s 1 kg ·m 2 /s 2
SECTION 1.2
Answer
Reason:
Section Check
SECTION 1.2
Section Check
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
× 10 1 m/s
B.
1.5
× 10 3 m/s
C.
2.5 m/s
D.
1.5
× 10 2 m/s
SECTION 1.2
Answer
Reason:
Section Check
SECTION 1.2
Section Check
Which of the following representations is correct when you solve 0.030 kg + 3333 g using scientific notation? A.
B.
C.
D.
3.4
× 10 3 g 3.36
× 10 3 g 3 × 10 3 g 3.363
× 10 3 g
SECTION 1.2
Section Check Answer
Reason:
0.030 kg is the same as 30g and can be written as 3.0 10 1 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 1.3
Measurement
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 1.3
Measurement
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
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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 a different, and less accurate, value.
• The difference in readings is caused by parallax, which is
(b)
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/s 2 ). The following results were obtained: Ronald — 961
±
12 cm/s 2 , Kevin — 953
±
8 cm/s 2 , and Paul — 942
±
4 cm/s 2 . Determine who has the most accurate and precise value.
A.
B.
C.
D.
Kevin got the most precise and accurate value.
Ronald ’ s value is the most accurate, while Kevin ’ s value is the most precise. Ronald ’ s value is the most accurate, while Paul ’ s value is the most precise.
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/s 2 . Hence, Ronald ’ s result is the most accurate. However, Paul ’ s error is only ± 4 cm/s 2 . 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: 1 cm, 2 nd st measuring tape — 99
±
measuring tape — 98
±
0.25 cm, and 3 rd measuring tape — 99
±
0.5 1 cm. Which measuring tape is the most precise?
A.
B.
C.
D.
1 st measuring tape 2 nd measuring tape 3 rd measuring tape Both measuring tapes 1 and 3
SECTION 1.3
Section Check Answer
Reason:
Precision depends on the instrument. The 2 nd measuring tape has an error of only ± 0.25 cm and is therefore the most precise.
SECTION 1.4
Graphing Data
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 1.4
Graphing Data
Review Vocabulary
•
Slope
on a graph, the ratio of vertical change to horizontal change.
New Vocabulary
• Independent variable • Dependent variable • Line of best fit • Linear relationship • Quadratic relationship • 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, Δ
y
, is the difference between the vertical values of A and B. The horizontal change, or run, Δ
x
, 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 and the line slopes downward.
Δ
y
/ Δ
x
is negative, • 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 1 Resources
A Physics Toolkit
Physics Online Study Guide Chapter Assessment Questions Standardized Test Practice
SECTION 1.1
Methods of Science
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 1.1
Methods of Science
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 1.2
Mathematics and Physics
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 1.3
Measurement
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 1.4
Graphing Data
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 1.4
Graphing Data
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 1 Chapter Assessment
A Physics Toolkit
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 Chapter Assessment
A Physics Toolkit
Reason:
1 nm is read as 1 nanometer. The prefix nano stands for 10 -9 .
CHAPTER 1 Chapter Assessment
A Physics Toolkit
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 × 10 2
C.
137
D.
1.37 × 10 2
CHAPTER 1 Chapter Assessment
A Physics Toolkit
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 Chapter Assessment
A Physics Toolkit
Rewrite 3.650 with only 2 significant digits.
A.
3.7
B.
3.6
C.
3.65
D.
0.360 × 10 1
CHAPTER 1 Chapter Assessment
A Physics Toolkit
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 Chapter Assessment
A Physics Toolkit
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 Chapter Assessment
A Physics Toolkit
Reason:
Accuracy describes how well the result of a measurement agrees with the expected value.
CHAPTER 1 Chapter Assessment
A Physics Toolkit
A quadratic relationship between two variables is written as ____.
A.
B.
C.
D.
CHAPTER 1 Chapter Assessment
A Physics Toolkit
Reason:
A quadratic relationship between two variables is written as
y
=
ax
2 +
bx
+
c.
CHAPTER 1 Standardized Test Practice
A Physics Toolkit
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 Standardized Test Practice
A Physics Toolkit
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 Standardized Test Practice
A Physics Toolkit
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 Standardized Test Practice
A Physics Toolkit
What is the slope of the graph?
A.
0.25 m/s 2
B.
0.4 m/s 2
C.
2.5 m/s 2
D.
4.0 m/s 2
CHAPTER 1 Standardized Test Practice
A Physics Toolkit
Which formula is equivalent to A.
B.
C.
D.
CHAPTER 1 Standardized Test Practice
A Physics Toolkit
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 Chapter Resources
A Physics Toolkit
Length of a Spring for Different Masses (1)
CHAPTER 1 Chapter Resources
A Physics Toolkit
Length of a Spring for Different Masses (2)
CHAPTER 1 Chapter Resources
A Physics Toolkit
Graph Indicating a Quadratic, or Parabolic, Relationship
CHAPTER 1 Chapter Resources
A Physics Toolkit
Graph Showing the Inverse Relationship Between Resistance and Current