PHYSICS: THE FOUNDATIONAL SCIENCE. Student Supplement. Volume 1. Marc Skwarczynski marcski55.hopto.org/classes/physics

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PHYSICS:

THE FOUNDATIONAL SCIENCE

Student Supplement

Volume 1

Marc Skwarczynski

marcskwarczynski.ccs@gmail.com marcski55.hopto.org/classes/physics

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Course Overview

with scheduled Crash Course Physics (CCP) Videos

Quizzes and Videos without sections noted are over the entire chapter. All pacing is subject to change at the discretion of the teacher.

Test 1

• Chapter 1 - Introduction to Physics | Quiz 1A (1.1-1.4) & Quiz 1B (1.5-1.7)

– CCP 0 - Crash Course Physics Preview • Chapter 2 - Matter | Quiz 2 (2.1-2.3)

– CCP 45 - Nuclear Physics (2.3-2.5)

Test 2

• Chapter 3 - The Liquid State | Quiz 3

– CCP 14 - Fluids at Rest (3.2, 4.2)

– CCP 15 - Fluids in Motion (3.3) • Chapter 4 - The Gaseous State | Quiz 4

– CCP 20 - Temperature (4.3, start at ideal gas law-2:50) • Chapter 5 - The Solid State | Quiz 5 (5.1-5.2, up to Tensile Stress)

– CCP 13 - Statics (open)

Test 3

• Chapter 14 - Heat | Quiz 14

– CCP 20 - Temperature (14.2, stop at ideal gas law-2:50)

– CCP 22 - The Physics of Heat (14.3)

– CCP 21 - Kinetic Theory and Phase Changes (close) • Chapter 15 - The Laws of Thermodynamics | Quiz 15

– CCP 23 - Thermodynamics (15.1-15.2)

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Test 4

• Chapter 6 - Introduction to Motion | Quiz 6

– CCP 1 - Motion in a Straight Line (open)

– CCP 2 - Derivatives (optional, not in class)

– CCP 3 - Integrals (optional, not in class)

• Chapter 7 - Vectors and Projectile Motion | Quiz 7 (7.1-7.4)

– CCP 4 - Vectors and 2D Motion (open)

Test 5

• Chapter 8 (adjusted) - Forces in Nature (8.3-8.5) | Quiz 8 (8.3-8.5)

– CCP 8 - Newtonian Gravity (8.3-8.5)

• Chapter 9 (adjusted) - Concurrent Forces (8.1, 9.1, 8.2, 9.2) | Quiz 9 (8.1, 9.1)

– CCP 5 - Newton’s Laws (8.1, 9.1)

– CCP 6 - Friction (8.2, 9.2)

Test 6

• Chapter 10 - Circular and Periodic Motion | Quiz 10

– CCP 7 - Uniform Circular Motion (10.1)

– CCP 16 - Simple Harmonic Motion (10.2) • Chapter 11 - Work and Machines | Quiz 11

– CCP 9 - Work, Energy, and Power (11.1-12.1)

Test 7

• Chapter 12 - Energy and Momentum | Quiz 12

– CCP 10 - Collisions (12.2-12.3)

• Chapter 13 - Rotary Motion | Quiz 13 (13.1-13.3)

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Test 8

• Chapter 16 - Waves | Quiz 16

– CCP 17 - Traveling Waves (16.1-16.2)

– CCP 19 - The Physics of Music (16.4) • Chapter 17 - Sound | Quiz 17

– CCP 18 - Sound (open)

• Chapter 18 - The Nature of Light | Quiz 18

– CCP 37 - Maxwell’s Equations (optional, not in class)

Test 9

• Chapter 19 - The Reflection of Light | Quiz 19

– CCP 38 - Geometric Optics (ch.19-21 overview) • Chapter 20 - The Refraction of Light | Quiz 20

– CCP 41 - Optical Instruments (20.3, with review) • Chapter 21 - Wave Optics | Quiz 21

– CCP 39 - Light Is Waves (21.1-21.2)

– CCP 40 - Spectra Interference (21.3-21.5)

Test 10

• Chapter 22 - Electrostatics | Quiz 22

– CCP 25 - Electric Charge (22.1)

– CCP 26 - Electric Fields (22.2)

– CCP 27 - Voltage, Electric Energy, and Capacitors (22.3, stop at capacitors-5:30) • Chapter 23 - Magnetism | Quiz 23

– CCP 32 - Magnetism (23.1-23.2)

– CCP 33 - Ampère’s Law (optional, not in class)

• Chapter 24 - Current Generation | Quiz 24

– CCP 34 - Induction - An Introduction (24.1)

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Test 11

• Chapter 25 - Electric Circuits | Quiz 25

– CCP 28 - Electric Current (25.1)

– CCP 29 - DC Resistors & Batteries (25.2)

– CCP 30 - Circuit Analysis (25.3-25.4)

– CCP 31 - Capacitors and Kirchhoff ’s Laws (25.5, stop at capacitors-6:06)

– CCP 36 - AC Circuits (optional, not in class)

• Chapter 26 - Electrical Devices | Quiz 26

– CCP 27 - Voltage, Electric Energy, and Capacitors (26.3, start at capacitors-5:30)

– CCP 31 - Capacitors and Kirchhoff ’s Laws (26.3, start at capacitors-6:06)

Test 12

• Chapter 27 - Advanced Physics Concepts | Quiz 27

– CCP 43 - Quantum Mechanics - Part 1 (27.1-27.2)

– CCP 44 - Quantum Mechanics - Part 2 (27.3-27.4) • Chapter 28 - Relativity | Quiz 28

– CCP 42 - Special Relativity (open)

– CCP 46 - Astrophysics and Cosmology (close)

Expectations for Students

As a teacher, my job description varies, but simplifies as to “teach.” This takes many forms and has many aspects, including preparation. I promise to do my absolute best at my job for your sake. Similarly, as a student, your job description can be simplified as to “learn.” This also takes many forms and has many aspects, including preparation. I sincerely hope that for your sake, you will do your absolute best at your job as well. To make sure we start off right, here is what I expect “learning” to look like in my class.

It is your job to read the textbook outside of class. Homework will contain some material that may not be found in this supplement, and quizzes or tests may also do so minimally. I have provided this supplement to assist your study of physics this year, but I teach from both my slides and the textbook. Stay with me in the book and the supplement throughout each class period. You may catch additional notes you wish to jot down in the

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It is your job to ask questions on material you do not understand. I cannot know you don’t understand unless you tell me! Ask questions in class or during study hall. If you want to ask more in-depth questions, help class will be available weekly, immediately following car line up on .

It is your job to make up missing work and notes. When you miss (even due to illness), it is your job to take care of your notes and homework. If you are unsure what to make up, come ask me. My slides and handouts should be available on the class page: marcski55.

hopto.org/classes/physics. If there is a problem, let me know ASAP so I can fix it.

It is your job to complete homework as the sections are completed. This provides necessary review when material is fresh and will keep you from being overwhelmed the night before each chapter’s homework is due.

It is your job to always show your work! Showing your work should manifest itself by the following:

1. The original formula.

2. The formula solved up until being typed into the calculator, even if just substituting values.

3. An unrounded answer with ellipses (. . . ), if applicable. 4. A final, circled answer with the correct units.

It is your job to report typos (earn bonus points). I give bonus points to thefirststudent to find a typo on something I typed. I do not give bonus points for typos I did not produce.

It is your job to have the following supplies with you, ready to go, each class and lab:

• Usable pencils (and pens, if desired). Pencils are required for tests and quizzes. • Red pens

• 12-inch ruler with centimeters • Loose-leaf paper

• Binder with handouts from this class • Casio fx-9750GII calculator (no phones) • Physics textbook

• Physics lab manual (lab days only) • This supplement

It is your job to contact me with questions/concerns. I always prefer email contact from both parents and students. My email is marcskwarczynski.ccs@gmail.com. Please make sure you state who you are (parents, mention your name and your child’s name) as it is not always obvious from the email address.

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Chapter 1

Introduction to Physics

1.1 - The Nature of Science

science the observation, identification, experimental investigation, and theoretical explanation of phenomena.1

physics science considering matter and energy (thephysicalworld).

Genesis 1:28

And God blessed them [Adam and Eve], and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth.

God’s Revelation

general revelation truth about God discoverable through the study of nature.

Romans 1:20

For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse:

special revelation truth about God discoverable only through His Word.

Romans 5:8

But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us.

Branches of Physics

classical physics subjects studied by physicists from the time of Galileo. Has five branches: mechanics, thermodynamics, sound, light, and electromagnetism.

modern physics subjects developed by physicists since 1900. Has several new branches, such as: quantum mechanics, relativity, solid-state physics, and particle physics.

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1.2 - The Scientific Method

Methods of answering questions:

cogitation thinking deeply, relying solely on whatever facts or insights you can discover within your own mind.

observation the careful watching and recording of events in nature for the purpose of enlarging what you already know.

experimentation the construction of an artificial situation that more clearly shows the way things happen.

1. Question an Observation

2. Research the Topic

3. Consider the Data

4. Create a Hypothesis

5. Design an Experiment

6. Perform the Experiment

7. Analyze the Experiment

8. Report the Data

1.3 - Measurement

Paul Dirac

God chose to make the universe according to very beautiful mathematics.

Lord Kelvin

I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarely, in your thoughts, advanced to the stage of Science,

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Units of Measurement

fundamental unit/quantity the result of direct measurement.

derived unit/quantity the arithmetic combination of fundamental units.

US customary system (FPS system) most commonly used in the US for everyday measurements. (foot, pound, second).

SI system (MKS system) The International System of Measurements used by US scientists and the rest of the world. Often referred to as the metric system. (meter, kilogram, second). The alternate cgs system is also sometimes used for smaller measurements. (centimeter, gram, second).

Standards of Measurement

standard an unalterable fact that, by general agreement, sets the unit value of a fundamental physical quantity; must have a constant value and be accessible to scientists all over the world.

length: meter the distance light travels in _{299 792 458}1 of a second.

mass: kilogram a cylinder of platinum-iridium alloy at the International Bureau in France.

time: second 9 192 631 770_{vibrations of the cesium-133 atom.}

1.4 - Scientific Notation

• The distance from the earth to the sun is93 000 000 mi_or9.3 × 107mi_.

• The charge on an electron is0.000 000 000 000 000 000 16 C_or1.6 × 10−19C_.

To write a number in scientific notation:

1. Move the decimal after the first nonzero digit, dropping extra zeros. All first factors must be between1.0_and9.999 99 …_{to be in scientific notation.}

2. Count how many places the decimal moved and make that number the exponent for ten.

3. Make the exponent positive if the decimal moved left or negative if the decimal moved right.

Examples

1.1) Write6 483 000_{in scientific notation.}

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Computing with Scientific Notation

1. When adding or subtracting, first find a “common power,” then add or subtract the first factors and keep the “common power.” Adjust the decimal and power, if necessary,after calculation.

1.62 × 106+ 3.80 × 105= 1.62 × 106+ 0.380 × 106 = 2.00 × 106

4.875 × 107+ 9.321 × 107= 14.196 × 107= 1.4196 × 108

2. When multiplying, multiply the first factors like usual and add the exponents.

(5.40 × 10−3)(9.00 × 106) = (5.40)(9.00) × (10−3)(106) = 48.6 × 103 = 4.86 × 104

3. When dividing, divide the first factors like usual and subtract the exponents.

2.0 × 109 5.0 × 106 = 2.0 5.0 × 109 106 = 0.40 × 103 = 4.0 × 102

1.5 - Measurement Calculations

Metric-to-Metric Conversions E . . P . . T . . G . . M . . k h d u d c m . . µ . . n . . p . . f Example 1.3 Change: (a) Change0.14 mgtokg. (b) Change53.6 Mstoms. (c) Change430 mto µm.

Calculations with Physical Quantities

1. Unlike quantities cannot be added or subtracted. Like quantities must have (or be given) like units before an operation.

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Example 1.4

Perform, if possible, the following calculations:

a. add300 m_to1.0 km

b. subtract400 g_from1980 m

c. multiply4.00 kgby1.61 s

d. divide336 cmby0.480 m

dimensional analysis the process of converting units by canceling out unwanted units and leaving desired units.

To convert46.5 ft_tom_{, multiply by one so that the feet cancel.}

1 m 3.281 ft ≈ 1 ≈ 3.281 ft 1 m 46.5 ft 1 ⋅ 1 m 3.281 ft = 14.2 m Convert65 mi/hrtom/s.

If using feet to meters,

65 mi 1 hr ⋅ 5280 ft 1 mi ⋅ 0.3048 m 1 ft ⋅ 1 hr 60 min ⋅ 1 min 60 s ≈ 29 m/s

If using miles to (kilo)meters,

65 mi 1 hr ⋅ 1609 m 1 mi ⋅ 1 hr 3600 s ≈ 29 m/s

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1.6 - Significant Digits

significant digits/figures certain digits in a properly stated measurement having accurate physical meaning

Lap # Keith Jennifer 1 56 s 56.10 s

2 55 s 55.25 s

3 55 s 54.60 s

4 57 s 57.20 s

Rules for Determining Significant Digits

1. All nonzero digits are significant.

2. Zeros between nonzero digits are significant.

3. In numbers with a decimal point, all numbers after the first nonzero digit are significant.

4. In numbers without a decimal point, trailing zeros are not significant. Notice that310.

has 3 significant digits while310has only 2.

Rules for Calculations with Significant Digits

Avoid accidentally indicating a higher certainty than actually exists.

1. When adding or subtracting, the answer must be rounded to the place which has the greatest uncertainty.

2. When multiplying or dividing, the answer must be rounded to the same number of significant figures as the factor having the smallest number of significant figures.

3. Exact numbers (those obtained by definition or simple counting) do not influence significant figures in any way.They are considered “infinitely precise.”

4. Postpone rounding until the very last step in the series. Use your calculator’s storage to assist here.

Example 1.5

Perform the following calculations and write the answer, including only significant digits.

a. 25.00 + 26.729

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Example 1.6

Perform the following calculations and write the answer with proper significant digits.

a. 3000 ⋅ 4.55 b. 3.00 × 103⋅ 4.55 c. 3.0 × 103⋅ 4.55 d. 75 ⋅ 133 e. 3681 ÷ 7.98 f. 0.5861 ÷ 0.98725

Accuracy, Precision, and Error

accuracy the closeness of a measurement to the actual (or accepted) value.

precision (tolerance) the closeness of a measurement to other measurement values in the same series.

mean value average.

error of measurement the amount of inaccuracy in a measurement.

systematic error due to some cause that affects every measurement in the same way;

can be eliminated.

random error due to unpredictable and uncontrollable factors in the shifting background of measurement;can be minimized, not eliminated.

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1.7 - Mathematic Techniqes

Example 1.7

a. Find the radius of a sphere that has a volume of54 cm3.

b. Find the sphere’s circumference.

Steps to Solve a Physics Problem

1. Solve the equation for the unknown quantity. (If you have more than one unknown, make sure you are using the best equation for the job.)

2. Substitute values for known variables. (In the case of 𝜋_{, just rewrite} 𝜋 _{and use the}

button on your calculator to avoid rounding issues.)

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Chapter 1 Homework

Date Due: Score:

Directions: Answer questions and problems as content is covered. Your homework will be due after the completion of the chapter; the official due date will be announced in class.

Questions

1.2 - The Scientific Method

1. What are three ways of answering a scientific question? a.

b.

c.

2. What are the steps in the scientific method? a. b. c. d. e. f. g. h.

1.3 - Measurement

3. What are the seven fundamental SI units (names, not abbreviations)? a. b. c. d. e. f. g.

4. What are the standards for the following SI units?

(Write the unit in the blank and its standard in the space below the blank.)

a. length:

b. mass:

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1.6 - Significant Digits

5. When is a zero significant?

6. How do you determine the number of significant digits in an answer obtained by. . .

a. addition or subtraction?

b. multiplication or division?

7. What is the difference between accuracy and precision?

8. What is the difference between systematic error and random error?

1.7 - Mathematic Techniqes

9. What formula shows how to simplify any complex fraction?

10. What are the three steps for solving most physics problems?

a.

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Problems

1.4 - Scientific Notation

1. Write the following numbers in scientific notation:

a. 86 400 ₌ _b. 0.000 004 161 ₌

2. Write the following numbers in decimal notation:

a. 7.03 × 105 ₌ _b. 2.385 × 103 ₌

3. Perform the following additions and subtractions using scientific notation and ignoring significant digits.

a. 3.174 × 10−4+ 1.21 × 10−4

b. 9.84 × 102+ 2.77 × 103

4. Perform the following multiplications and divisions using scientific notation and ignoring significant digits.

a. (3.2 × 104)(6.81 × 107)

b. (4.38 × 10−2) ÷ (6.4 × 104)

1.5 - Measurement Calculations

5. Convert ignoring significant digits.

a. 1 560 000 stoMs

b. 0.000 007 8 s_{to µ}s

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6. Perform, if possible, the following calculations. Place answers into scientific notation and ignore significant digits.

a. Add45.0 sand150 m.

b. Multiply0.0065 g_by14.2 m_.

7. Use dimensional analysis to perform the following conversions. Ignore significant digits and use scientific notation if necessary.

a. 15 wk_tomin_.

b. 45 mi/hrtom/s.

1.6 - Significant Digits

8. Determine the number of significant digits in the following numbers:

a. 70.00 b. 10 005 c. 10 000. d. 7.010 e. 1.8000 × 104 f. 7.500 × 10−4

9. Perform the following calculations and express the answer properly according to the rules for significant digits:

a. 52 + 1.03

b. 13.500 − 23

c. 0.36 ⋅ 4

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1.7 - Mathematic Techniqes

10. Simplify the following:

a. 𝑚 ⋅ 𝑃 𝑄 b. 2𝑚 𝑚+𝑛 2 c. 𝑠𝑠𝑣 + 𝑒𝑎𝑣 𝑙 𝑢𝑣 d. 𝑎2−𝑏2 5𝑥 𝑎+𝑏 𝑥2 e. 2𝑥2⋅ 5𝑦 13𝑧 f. 𝑥 − 𝑦 𝑥 +𝑦 𝑥 −𝑦

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11. Solve each literal equation for the variable in boldboldbold. a. 𝐸𝑝 = 1 2𝑘𝑥 𝑥𝑥2 b. 𝐹 = 𝑚𝑣2 𝑟𝑟𝑟 c. 𝐼 = 𝑚𝑟𝑟𝑟2

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Chapter 2

Matter

2.1 - The Nature of Matter

matter anything that has mass and takes up space.

inertia unless acted upon by an external force, matter at rest will remain at rest, and matter in motion will move persistently in a straight line and at a constant speed.

mass the measure of an object’s inertia.

weight the measure of the exertion of gravity on an object’s mass.

density (𝜌) _{the ratio of an object’s mass to its volume. (}1 cm3 = 1 mL₎ 𝜌 =

𝑚

𝑉

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specific gravity or relative density (𝜌_rel) _{the ratio of a given sample’s density to a standard}

density. For liquids and solids, the standard is water. For gases, the standard is hydrogen gas. 𝜌_rel = 𝜌 𝜌_s (2.2) Example 2.1

A piece of quartz5.0 cm × 2.0 cm × 1.0 cm_{has a mass of}25 g_.

a. Find its density.

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Example 2.2

Silver has a density of10.5 g/cm3_{. What is the mass of a bar of silver} 10.0 cm_long, 2.50 cm

high, and2.00 cm_wide?

2.2 - Pure Substances and Mixtures

molecule a chemical combination of two or more atoms.

elemental molecule a molecule containing only one element.

compound a molecule containing more than one element.

pure substance a substance containing only one kind of atom or molecule.

mixture a physical combination of two or more elements or compounds.

homogeneous a mixture with the particles of each substance uniformly distributed throughout the mixture on a molecule-by-molecule basis.

heterogeneous a mixture which settles into layers of different particles or has large lumps of molecules.

The Four States of Matter

solid has a definite shape and volume and is difficult to compress.

liquid has a definite volume, but not a definite shape and is difficult to compress.

gas has no definite volume or shape and is easy to compress.

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2.3 - The Composition of Matter

atom the basic building block of all matter (the smallest unit of an element).

nucleus a collection of particles (protons and neutrons) at the center of an atom.

proton (𝑝+) _{positively charged (}1.60 × 10−19C_{or “+1”) particle that gives the atom}

its identity as an element.

atomic number the number of protons in a given element; distinguishes one element from another.

neutron (𝑛0) _{neutral (and largest) particle that determines an atom’s mass.}

mass number states the sum of the number of protons and neutrons in the nucleus, not the actual mass of the atom.

isotopes atoms with the same atomic numbers, but different mass numbers.

atomic mass the weighted average of all isotopes of an element, measured in atomic mass units (1 amu = ₁₂1 of a carbon-12 atom).

electron (𝑒−) _{negatively charged (}−1.60 × 10−19C_{or “-1”) particle that determines the}

charge of an atom. If in equal number with protons, an atom is neutral.

ion a charged (unbalanced) atom.

anion a negative ion (having an excess of electrons).

cation a positive ion (having a deficiency of electrons).

element any substance that cannot be broken down by chemical means into a simpler substance. On the periodic table, elements are broken down into periods and groups.

period rows of elements that have the same number of electron shells around the nucleus.

group columns of electrons that have the same number of valence electrons.

valence electrons electrons in the outermost electron shell.

Example 2.3

A certain sample of carbon contains88.43%_{of carbon-12 (}11.75 amu_{) and the rest is carbon-14}

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2.4 - Elementary Particles

𝐸 = 𝑚𝑐2 (2.4)

photons particles of light.

mass gain the principle that the mass of an object should increase if its kinetic energy increases.

nuclear mass defect the mass of every atom is measurably less than the total mass of individual particles due to a release of energy.

subatomic particles particles smaller than an atom

elementary particles particles having no components, no building blocks, and no smaller parts.

quarks particles making up protons and neutrons, explaining their interaction.

hadron substances believed to contain quarks.

meson a hadron containing two quarks.

baryon a hadron containing three quarks.

gluon a massless particle believed to bind the quarks together.

lepton substances not believed to contain quarks. • electron

• neutrino

positron (𝑒+) _{a positively charged electron.}

gamma radiation (𝛾) _{invisible, highly penetrating type of electromagnetic radiation composed}

of short-frequency, high-energy photons.

electromagnetic radiation any type of emitted energy.

pair production the process of an oppositely charged particles appearing seemingly from nowhere.

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2.5 - Particle Reactions

antiparticles particles having the exact same characteristics, but opposite charges.

antimatter the collective term for all antiparticles.

annihilation occurs when a particle and its antiparticle collide and convert their combined masses into a form of energy.

orbital a region of high likelihood for finding an electron as it travels around the nucleus.

electron capture the absorption of an electron by a proton, producing a neutron and a neutrino (𝑣𝑒).

heavy atoms (elements) atoms with a neutron to proton ratio greater than 1:1 (more neutrons than protons).

radioactive decay the release of energy and matter as neutrons and protons collapse into positions of greater stability.

half-life the time required for half of a radioactive substance’s mass to decay into something else.

alpha (𝛼) decay _{the emission of a high-energy particle of two protons and two neutrons}

(helium nucleus).

beta (𝛽) decay the emission of a high-energy electronfrom the nucleusand an antineutrino (𝑣̄𝑒).

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Chapter 2 Homework

Date Due: Score:

Questions

1. How is matter defined?

2. How did Newton describe the property of inertia?

3. Distinguish between mass and weight.

4. Distinguish between density and specific gravity (relative density).

5. In the determination of specific gravity,

a. to what is a liquid or solid compared? b. to what is a gas compared?

2.2 - Pure Substances and Mixtures

6. Name two kinds of pure substances.

a. b.

7. List and describe each of the four states of matter.

a. b.

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2.3 - The Composition of Matter

8. List the identity and location (inside or outside the nucleus) of the three primary particles that compose an atom.

a. b. c.

9. What is the charge (inC_{) of the}

a. neutron? b. electron?

c. proton?

10. Distinguish between atomic number and mass number.

11. What is the difference between isotopes and ions?

12. Define the atomic mass unit.

13. Give two definitions of an element.

2.4 - Elementary Particles

14. What equation relates mass and energy?

15. What particle of energy is found in a beam of light?

16. Explain why an atom’s nucleus composed of positive and neutral particles can remain together according to quark theory.

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18. A particle exists that is virtually massless and travels near the speed of light.

a. What is the particle?

b. How was the particle discovered?

19. Describe pair production. Why is the positron short-lived?

2.5 - Particle Reactions

20. What are antiparticles?

21. Describe the annihilation process.

Problems

Be sure to show all your work, circle your answer, and check your significant figures and units!

1. Gravity on the moon is only 1₆ as strong as on Earth.

a. If a bowling ball weighs71 N_{on the earth, what would be its weight on the moon?}

b. How would being on the moon affect the ball’s mass?

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3. A block of wood measures15 cm × 16 cm × 25 cm_{and has a mass of}960 g_.

a. What is its density?

b. What is its specific gravity?

4. A gold bar is32 cm_long,14 cm_{wide, and}12 cm_{high. Find the mass of the gold bar in. . .}

a. grams.

b. kilograms.

5. An aluminum sheet has a mass of212 g_{. What is its volume?}

6. A cork cylinder is3.2 cm_{high with a radius of}1.8 cm_{. What is its mass? The volume of}

a cylinder is given by the formula𝑉 = 𝜋 𝑟2ℎ.

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Chapter 3

The Liqid State

3.1 - Characteristics of a Liqid

Surface Tension

surface tension a liquid’s resistance to increase its surface area.

• Why a small quantity of liquid turns into a spherical droplet, having the least surface area than any other shape with equivalent volume.

adhesion the electrical attraction betweendifferent kindsof molecules.

cohesion the electrical attraction betweenthe same kindof molecules.

Capillarity

capillary tubes tubes thin enough to allow liquid to rise in the tube when the lower end is below the surface of the liquid.

capillarity (capillary action) the tendency of a liquid to rise in a narrow tube.

meniscus the curved surface inside a narrow tube; may be concave or convex.

3.2 - Hydrostatics

hydrostatics the study of liquids at rest.

Law of Liqid Pressure

force any push or pull on an object. 1 N = 1kg ⋅ m s2

normal perpendicular

• In general, liquid exerts a normal force at each point on any surface inserted into the liquid.

pressure the amount of force brought to bear on a unit area of surface.1 Pa = 1 N m2 = 1 kg m ⋅ s2 𝑃 = 𝐹 ⟹ 𝐹 = 𝐴𝑃 _(3.1)

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weight The force due to the earth’s gravitational attraction to an object’s mass.𝑔 ≈ 9.80 m/s2 𝐹𝑤 = 𝑚𝑔 (3.2) 𝜌 = 𝑚 𝑉 ⟹ 𝑚 = 𝜌𝑉 (3.3) 𝐹_𝑤 = 𝜌𝑉 𝑔 _(3.4) 𝑉 = 𝐴ℎ _(3.5) 𝐹𝑤 = 𝜌𝐴ℎ𝑔 = 𝐴𝜌𝑔 ℎ (3.6) 𝐹 = 𝐴𝜌𝑔 ℎ _(3.7) 𝐹 𝐴 = 𝜌𝑔 ℎ (3.8) 𝑃 = 𝜌𝑔 ℎ _(3.9)

The boxed equation above isthe law of liquid pressure.

Example 3.1

(a) If the density of water is1000 kg/m3_{, what is the pressure at the bottom of a pool filled to}

a depth of2.40 m_?

(b) What is the total force in newtons on the bottom if it is5.50 m_{wide and}10.0 m_long?

Applications of the Law of Liqid Pressure

• At a given depth of liquid (regardless of the shape of container), the downward pressure is everywhere the same. (Fig. 3.7)

• At a given depth of liquid (regardless of the shape of container), the pressure in every direction is everywhere the same. (Fig. 3.8)

• In a multi-level system, the bottom hole has the highest velocity, while the middle hole covers the greatest distance. (Fig. 3.9)

• Water head (ℎ)_{: the distance below the highest level of water in a connected system.}

(Fig. 3.10)

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• Lateral force (Fig 3.13) 𝑃𝑎𝑣 = 1 2𝜌𝑔 ℎ (3.11) 𝐹 = 1 2𝐴𝜌𝑔 ℎ ⟸ 𝐹 = 𝐴𝑃 (3.12) Example 3.2

The wall of a dam is exactly vertical, with a height of35.0 m _{and a width of}176 m_{. What is}

the total force on the wall if the artificial lake behind it has risen to within3.00 m_{of the top?}

Pascal’s Principle

Pascal’s principle the pressure applied to any surface of a confined liquid is transmitted equally in every direction throughout the liquid.

hydraulic device any device that uses a confined liquid to multiply force (at the expense of distance). 𝐹𝐿 𝐹𝑆 = 𝐴𝐿 𝐴𝑆 (3.13) 𝐴_𝐿 𝐴𝑆 = 𝑥_𝑆 𝑥𝐿 (3.14) 𝐹_𝐿 𝐹𝑆 = 𝑥_𝑆 𝑥𝐿 (3.15) Example 3.3

The pistons of a hydraulic device have areas of4.0 cm3_and10. cm3_.

(a) If the smaller is depressed with a force of16 N_{, how much lifting force is applied to the}

other piston?

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Archimedes’ Principle

buoyant force the difference between the downward force and the upward force.

Archimedes’ Principle the buoyant force acting on a body submerged in a liquid is equal to the weight of the liquid displaced by that body.

See Figures 3.19-3.22.

Example 3.4

A solid sphere weighs26.7 Nin air,24.0 Nin a liquid, and23.5 Nin water.

(a) Find the density of the metal.

(b) Find the density of the liquid.

3.3 - Hydrodynamics

hydrodynamics the study of liquids in motion.

Principle of Viscosity

viscosity a liquid’s resistance to flow because of molecular attraction; measured inpoise (P) or centipoise (cP).

See figures 3.23-3.25.

cavitation the production of tiny vapor bubbles within a liquid due to adhesion.

laminar flow an ideal liquid’s tendency to flow in straight lines throughout the cross-sectional area.

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ideal liquid a theoretical liquid that ignores certain real-life conditions to make the study of liquids easier.

• nonviscous • incompressible • uniform in density

volume flow rate measures the total volume of liquid flowing past a point in one second (measured inm3/s)

principle of continuity the volume flow rate at any two points in a pipe must be constant:

𝐴1𝑣1 = 𝐴2𝑣2 (3.16)

Example 3.5

The water supply of a house has three sections with different diameters:1.00 cm_,2.00 cm_{, and} 4.00 cm_{. If the velocity of water is}20.0 m/s_{in the}2.00 cm_pipe,

(a) What is the velocity in the1.00 cmpipe?

(b) What is the velocity in the4.00 cm_pipe?

Bernoulli’s Principle

lateral pressure the pressure at any surface in contact with a moving liquid.

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Chapter 3 Homework

Date Due: Score:

Questions

3.1 - Characteristics of a Liqid

1. How does surface tension explain. . .

a. spherical raindrops?

b. a floating needle?

2. What is the difference between cohesion and adhesion?

3. What is. . .

a. capillarity?

b. a meniscus?

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3.2 - Hydrostatics

5. In what direction does a liquid exert force on a surface exposed to the liquid?

6. What is the difference between force and pressure?

7. State the law of liquid pressure in an equation.

8. How do Pascal’s vases demonstrate that downward pressure depends only on depth?

9. At a given depth in a liquid, how do the pressures in different directions compare?

10. If orifices are placed at different heights of a tank resting on the ground,

a. from which will the flow be the fastest?

b. from which will the flow have the farthest range?

11. In determining pressure at a given point in a connected system of reservoirs and channels,

a. what is the name of the quantity used? b. what is its definition?

12. What is the density of pure water inkg/m3_?

13. What is the formula for the total force exerted by a liquid. . .

a. on the bottom of its container? b. on a wall of its container?

c. What must be assumed for each case?

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15. In a hydraulic device, force is multiplied at the expense of what else?

16. The ratio of the larger piston area to the smaller piston area is equal to what other two ratios?

17. State Archimedes’ principle.

3.3 - Hydrodynamics

18. Define viscosity, and give an example of a liquid with extremely low viscosity and of another with extremely high viscosity.

19. State the principle of continuity in an equation.

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Problems

3.2 - Hydrostatics

1. The bottom of an elevated water tank has an area of 135 m2_{. If the pressure on the}

bottom is1.52 × 104Pa, what is the total force the bottom must support?

2. A column of water exerts a pressure of100. Paand a force of2.40 N. What is the cross-sectional area of the tank?

3. A pipe enters a water tank at a point6.50 m_{below the surface of the contained water.}

What is the water pressure in this pipe?

4. A swimming pool has the dimensions (𝑙 ⋅ 𝑤 ⋅ ℎ_{) of}28.5 m × 10.0 m × 2.30 m_{. When it is}

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5. A hydraulic lift has two cylinders with diameters of2.00 cm_and10.0 cm_{respectively.}

What is the force required on the smaller piston to raise a1.3 × 104N_{car over the larger}

piston?

6. A stone weighs13.2 N_{in air,}10.8 N_{in water, and}11.8 N_{in oil. Find the density of...}

a. the stone

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7. A cedar raft is2.4 m_wide,0.30 m_{high, and}3.0 m_{long. What is the maximum load (in}

newtons) the raft can support? Assume the density of the cedar to be598 kg/m3 _and

ignore the volume of the load.

Hints:The maximum buoyant force equals the weight of the water displaced when the raft is just submerged below the water, and the buoyant force upward equals the weights of the raft and the load.

3.3 - Hydrodynamics

8. A garden hose with an inside diameter of2.5 cmis connected to a nozzle which is closed down to a diameter of0.50 cm_{. If the water in the hose has a speed of}3.0 m/s_{, at what}

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Chapter 4

The Gaseous State

4.1 - Air Pressure

Refer to Table 4.1 in the text.

air pressure the continual bombardment of any surface exposed to the air.

vacuum the total absence of any matter.

Refer to Figures 4.1-4.7 in the text.

atmospheric pressure The pressure exerted by the atmosphere. 14.7 lb/in2₌1.013 × 105Pa

=101.3 kPa

fluid flowing substances (gases and liquids)

• Gases are compressible, while liquids are not.

Liquids Only Liquids and Gases

Law of Liquid Pressure Archimedes’ Principle Pascal’s Principle Bernoulli’s Principle Principle of Continuity

Archimedes’ principle the weight lost by an object suspended in a fluid equals the weight of the displaced fluid.

Bernoulli’s principle lateral pressure decreases as the rate of flow increases. • airfoil: any object with surfaces designed to create lift in air.

• A fluid funneled into a narrower channel gains velocity (adapted continuity).

4.2 - Barometers

horror vacui “nature abhors a vacuum.” The idea that a vacuum is impossible to create because nature immediately fills any empty space with the nearest matter it can find.

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standard atmospheric pressure the pressure that will support a mercury column exactly

760 mm_{tall when the temperature is}0◦C_.

1.0 atm = 760 mmHg = 76 cmHg

1.0 atm = 760 torr

1.0 atm = 1.013 × 105Pa = 101.3 kPa

1.0 atm = 1.013 bar = 1013 mbar

Example 4.1

A scientist wanted to make a new barometer using different liquids. Standard atmospheric pressure is 1.013 × 105Pa_{. What is the shortest tube she could use if her liquid was ethyl}

alcohol𝜌 = 0.789 g/cm3?

Open-end Manometer

guage pressure the reading of an open-end manometer before accounting for atmospheric pressure.

absolute pressure the pressure due only to the gas itself.

Example 4.2

If the gauge pressure indicated by a manometer is10 mmHg, what is the absolute pressure of the gas?

Closed-end Manometer

See figure 4.17.Shows the pressure of a gas solely by the height difference.

Aneroid Barometer aneroid “without liquid”

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4.3 - Gas Laws

Boyle’s Law

inverse proportion one quantity’s increase requires the other’s decrease.

Boyle’s law at constant temperature, the volume of a gas is inversely proportional to its pressure. 𝑉 ∝ 1 𝑃 (4.2) 𝑉 = 𝑘𝐵 𝑃 (4.3) 𝑃 𝑉 = 𝑘𝐵 (4.4) 𝑃1𝑉1 = 𝑃2𝑉2 (4.5) Example 4.3

Air is confined within a cylinder at a pressure of 950 torr; the volume is 54 cm3. What is the volume of the gas if a piston within the cylinder is moved so that pressure is reduced to

1.0 atm_?

Charles’s Law

absolute zero the lowest temperature at which matter can exist.

0 K = −273.15◦C

absolute temperature temperature measured in kelvins (or from absolute zero).

𝑇𝐾 = 𝑇𝐶 + 273.15

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Charles’s law at constant pressure, the volume of a gas is directly proportional to its temperature. 𝑉 ∝ 𝑇 (4.6) 𝑉 = 𝑘𝐶𝑇 (4.7) 𝑉 𝑇 = 𝑘_𝐶 _(4.8) 𝑉1 𝑇1 = 𝑉2 𝑇2 (4.9) Example 4.4

What is the volume of a gas at350 K _{if its volume at} 420 K _is23 L_{? Assume the pressure is}

constant.

Combined Gas Law

Boyle’s law (eq. 4.5) and Charles’s law (eq. 4.9) can be combined to form thecombined gas

law: 𝑃1𝑉1 𝑇1 = 𝑃2𝑉2 𝑇2 (4.10) Example 4.5

If a gas initially at615 torr_and293 K_{shrinks from}15.8 L_to10.8 L_{when cooled to}263 K_{, what}

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Avogadro’s Law

Avogadro’s Law at a given temperature and pressure, two gases of the same volume have the same number of molecules

Avagadro’s Number (𝑁_𝐴) 6.022 × 1023

mole Exactly6.022 × 1023_{of something (usually molecules)}

Ideal Gas Law

𝑉 ∝ 𝑛 _(4.11) 𝑉 ∝ 𝑛𝑇 𝑃 (4.12) 𝑉 = 𝑛𝑅𝑇 𝑃 (4.13) 𝑃 𝑉 = 𝑛𝑅𝑇 _(4.14)

Universal Gas Constant (𝑅) the constant of proportionality for gases0.0821 L ⋅ atm/(K ⋅ mol)

Example 4.6

The pressure of52.1 g_{of chlorine gas (Cl}2) is6.2 atmat320 K. What is the volume of the gas?

𝑃 𝑉 = 𝑛𝑅𝑇 𝑅 = 𝑃 𝑉 𝑛𝑇 𝑃₁𝑉₁ 𝑛1𝑇1 = 𝑃₂𝑉₂ 𝑛2𝑇2 (4.15)

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4.4 - Pneumatic Devices

pneumatic device any device that transports air or that is driven by air pressure

entrained fluid that is caught up and carried along by a fluid stream nearby. • Water Pumps (Fig. 4.24)

• Exhaust Pumps (Fig. 4.24-4.26)

• Compressors (Fig. 4.27)

• Siphons (Fig. 4.28)

Chapter 4 Homework

Date Due: Score:

Questions

4.1 - Air Pressure

1. What are the five main constituents of air when it has maximum concentrations of water vapor and carbon dioxide? List them from highest to lowest concentration.

a. b. c. d. e.

2. What causes air pressure in a container?

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4. What laws pertaining to fluids assume uniform density (not applicable to gases)?

a. b. c.

5. Does something weigh more in air or in a vacuum? Explain.

6. How might Bernoulli’s principle explain the operation of a parasail?

4.2 - Barometers

7. Describehorror vacui.

8. Atmospheric pressure supports:

a. what height of water? b. what height of mercury?

9. How did Pascal confirm Torricelli’s conclusion that mercury is supported at a height of

760 mm_{by atmospheric pressure?}

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4.3 - Gas Laws

11. What is Boyle’s law (equation)?

12. What is Charles’s law (equation)?

13. What temperature scale must be used for temperature in Charles’s law?

14. Write the equation for the combined gas law.

15. How many items are in a mole of something?

16. What is the ideal gas law (equation)?

4.4 - Pneumatic Devices

17. What is entrainment?

Problems

4.2 - Barometers

1. A gas sample is connected to an open-end manometer. The mercury level is 35 mm

lower on the side of the open end. If atmospheric pressure is 764 torr, what is the pressure of the gas?

2. In an open-end manometer, the mercury on the side exposed to a gas sample is7 mm

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4.3 - Gas Laws

3. A tank of compressed oxygen has a volume of0.40 m3_{and a pressure of} 2.76 × 106Pa_.

What is the oxygen’s volume at an atmospheric pressure of 1.013 × 105Pa? Assume constant temperature.

4. A liter (exactly1000 cm3) of oxygen gas at normal atmospheric pressure is compressed to a volume of 250. cm3_{. Find the resulting pressure in torr if there is no change in}

temperature.

5. A tank contains5.00 × 106cm3_{of nitrogen gas at}313 K_{. If the pressure on the piston is}

held constant, what will be its volume when the temperature is lowered to283 K?

6. A balloon filled to a volume of1.65 L_at308 K_{is heated to}325 K_{. What is the new volume}

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7. An automobile tire has a total pressure of2.96 × 105Pa_{when the temperature is}298 K_.

After the tire runs at high speed on hot pavement, its temperature rises to345 K_{. Find}

the pressure at this temperature, assuming the volume has not changed.

8. If a gas has a volume of3.00 m3_{at a pressure of}76 cm_{of mercury and a temperature of} 298 K, what volume will it occupy when the pressure is doubled and the temperature is raised to373 K_?

9. Find the volume of50.4 g_{of oxygen gas (O}₂_{) at}740. torr_and273 K_.

10. Find the pressure of261 gof nitrogen gas (N2) at63.2 Land350. K. The molecular mass

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Chapter 5

The Solid State

Differences between solids and liqids

• A solid has a definiteshapeand volume.

• A solid’s atoms vibrate in place instead of flowing freely.

5.1 - Characteristics of Solids

elasticity the ability of an object to recover its original shape after being deformed by an external force.

rigidity the tendency of an object to resist flexing or deforming.

resilience the amount of deformation required to bring a material to its elastic limit.

elastic limit the point past which a material will not recover its original shape.

plasticity the maximum amount of relative deformation that may bepermanently imposed on it.

mechanical working the various processes used to impose desired shapes upon ingots (solid bars) of newly refined metal.

forging squeezing metal between two dies (half-molds)

rolling pressing metal by a series of paired, heavy rollers into a continuous sheet.

malleability the property of metal that allows it to be rolled or hammered into a sheet.

drawing pulling metal through a single die into a continuous ribbon with the same cross-sectional shape as the interior surface of the die.

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5.2 - Moduli of Deformation

Hooke’s Law

cohesion the attractive force between particles of the same kind.

tensile force the stretching or compressing force of a load.

𝑥 ∝ 𝐹𝑡 (5.1)

𝐹𝑡 = 𝑘 𝑥 (5.2)

restorative force the force acting against the tensile force.

𝐹𝑡 = −𝐹𝑟 (5.3)

𝐹𝑟 = −𝑘 𝑥 (5.4)

Hooke’s law the force of the wire pulling upward is proportional to its displacement downward and that the restorative force acts in the opposite direction of the displacement.

Forces of Deformation

stress (𝜎 ) _{deformative tensile force per unit cross-sectional area.} 𝜎 =

𝐹 𝐴

(5.5)

strain (𝜀 ) _{the relative amount of deformation; the ratio of change compared to the original}

length. 𝜀 = Δ𝓁 𝓁₀ (5.7) 𝜎 = 𝑘 𝜀 (5.8)

Tensile Stress

tensile stress (tension) tensile force applied perpendicular to the cross-sectional area of a stressed object.

Young’s modulus (𝑌) _{the proportionality constant used for tensile stress.}

𝜎 = 𝑌 𝜀 _(5.9)

𝐹 = 𝑌

Δ𝓁

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Example 5.1

Find the elongation of a5.0 cm _{long tendon with a diameter of}0.40 cm_{if it is subjected to a}

force of1470 N.

proportional limit the point past which the restorative force in the wire is no longer a linear function of elongation. (Hooke’s law breaks down.)

elastic limit the maximum stress the material can sustain without being permanently deformed.

ultimate tensilestrength(tensile strength) the maximum stress the material can sustain without breaking.

breaking point the maximumstraintolerated by the material.

brittle material which breaks suddenly without deforming first.

equilibrium the standard relative positions when the particles are stable and unstressed (without repulsion or attraction).

Sign Convention

• Elongation (stretching) is considered positive⊕.

• Compression (squeezing) is considered negative⊝_.

Example 5.2a

A25 cm_{long bone with a cross-sectional area of}3.20 cm2_{supports a load of}2200 N_{. Calculate}

the compression of the bone.

Example 5.2b

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Example 5.3a

A1.0 m_{steel wire has a diameter of}3.8 × 10−4m_{. How much force is required to stretch the}

wire to the elastic limit?

Example 5.3b

A1.0 m_{steel wire has a diameter of}3.8 × 10−4m_{. How much will the wire stretch at its elastic}

limit?

Shear Stress

shear the combination of two oppositely directed forces along parallel lines of action.

𝜀 = Δ𝑥 𝑑 (5.11) 𝜎 = 𝑆 𝜀 𝐹 𝐴 = 𝑆 Δ𝑥 𝑑 (5.12) Example 5.4

A long steel bolt with a cross-sectional area of0.25 cm2hold a metal box0.80 cmoff a post, and the box exerts a shearing force of5.52 × 104N_{. How much is the bolt displaced?}

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Volume Stress

volume stress (bulk stress) the result of the force on a submerged object’s surface to compress it into a smaller volume. There is no elastic limit or ultimate tensile strength for volume

stress. 𝜎 = Δ𝑃 = 𝐹 Δ𝐴 (5.13) 𝜀 = Δ𝑉 𝑉0 (5.14) 𝜎 = 𝐵𝜀 ⟹ Δ𝑃 = −𝐵 Δ𝑉 𝑉0 (5.15) Example 5.5a

Find the change in pressure acting on a2.0 m3_{latex balloon filled with water when it is pulled} 370 mto the bottom of the Dead Sea. The density of the water in the Dead Sea is1240 kg/m3.

Example 5.5b

Find the water balloon’s change in volume at the bottom of the Dead Sea. Ignore any effect of the latex in the balloon. (From part a,Δ𝑃 = 4.496 24 × 106N/m2and𝑉0= 2.0 m

3

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Chapter 5 Homework

Date Due: Score:

Questions

5.1 - Characteristics of Solids

1. Define. a. rigidity b. resilience c. plasticity

2. List and briefly define 3 industrial processes for working metal.

a. b. c.

5.2 - Moduli of Deformation

3. What is Hooke’s law (equation) for...

a. tensile force? b. restorative force?

4. Define.

a. stress

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5. What is the proportionality constant for tensile stress...

a. called?

b. equal to (equation)?

6. Name and briefly define the four points on a graph of stress vs. strain.

a. b. c. d.

7. What kinds of deformations are related...

a. to Young’s modulus? b. to the shear modulus? c. to the bulk modulus?

8. Write the equation for shear modulus.

9. Why is there no elastic limit or ultimate strength for volume stress?

Problems

5.2 - Moduli of Deformation

1. A1.50 kgmass is hung from a vertical spring with𝑘 = 30.0 N/m.

a. What is the magnitude and direction of the tensile force acting on the spring?

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2. Find the magnitude and direction of the spring’s restorative force on a object if it is attached to a spring with𝑘 = 250 N/m_{and compressed}6.0 cm_.

3. A brass wire2.5 mlong has a radius of1.0 mmand hangs from the ceiling. If an object weight12.2 N_{is suspended from the lower end,}

a. What will be the elongation?

b. What is the tension required to reach the elastic limit?

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4. A platform is supported by four solid steel bars, each 54 cm _{long and with a}

cross-sectional area of 3.6 cm2_{. By how much is each compressed if an} 18 000 N _elephant

stands on the platform?Assume each leg supports one fourth of the weight.

5. How much deformation is produced in an aluminum picture nail 1.85 mm2 _in

cross-sectional area when a picture weighing108 Nis hung from it? The picture wire rests at the nail head, which is4.00 mm_{from the wall.}

6. If a steel anchor whose volume is450 cm3is lowered to a depth of1.5 kmin sea water, by how much does the volume decrease? Assume the density of seawater is1030 kg/m3_.

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Chapter 14

Heat

internal energy a measure of an object’s molecular kinetic energy and molecular potential energy.

heat the transfer of internal energy from one object to another.

thermal energy the kinetic energy of an object’s molecules.

14.1 - Thermometry

thermometers instruments used to measure temperature.

thermometry the process of measuring temperature.

thermal equilibrium all objects in contact having reached the same temperature.

Constructing a Temperature Scale

triple point of water the equilibrium established among the three phases of water at a pressure of4.58 mmHgand approximately0◦C. 273.16 K

Fahrenheit scale originally set zero to freezing point of highly concentrated salt water and 96 to normal body temperature; now set pure freezing water to32_°F_{and pure boiling}

water to212°F; used primarily by the American public.

Celsius scale set pure freezing water to0◦C_{and boiling water to}100◦C_{; used by the majority}

of the world and scientists (including American scientists).

Kelvin scale set 0 at absolute zero (−273.15◦C_{); used by scientists when absolute temperature}

is required.

absolute zero the lowest obtainable temperature.

absolute scale a scale which has 0 as the lowest possible value (no negatives).

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𝑁_𝐵 𝑁𝑇 𝑃 = 𝑇_𝐵 𝑇𝑇 𝑃 (14.1) 𝑇_𝐵 = 𝑁_𝐵 𝑁𝑇 𝑃 𝑇_{𝑇 𝑃} _(14.2) 𝑇𝐵 = 𝑁_𝐵 𝑁𝑇 𝑃 (273.16 K) (14.3) Example 14.1

A platinum resistance thermometer has a resistance of 90.35 Ω at the triple point of water. What is the temperature in kelvins if the thermometer has a resistance of97.32 Ω_?

Example 14.2

A constant volume thermometer measures a pressure of10. cmHg_{at the triple point. What is}

the temperature in kelvins if the pressure in the thermometer reads9.5 cmHg?

Temperature Conversions 𝑇𝐶 = 𝑇𝐾 − 273.15 (14.4) 𝑇𝐹 = 9 5𝑇𝐶 + 32 (14.5) 𝑇_𝐶 = 5 9(𝑇𝐹 − 32) (14.6)

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Example 14.3

What is the value of294.2 K_{expressed. . .}

a. in degrees Celsius?

b. in degrees Fahrenheit?

Example 14.4

What is the Celsius temperature when a Fahrenheit thermometer reads72.0_°?

14.2 - Thermal Expansion

linear expansion the expansion along any line through a solid.

Δ𝓁 = 𝛼 𝓁1Δ𝑇 (14.7)

Example 14.5

A single steel span in a bridge is100.00 mlong at0◦C.

a. How long is the span at45◦C?

b. If there are three spans in one bridge, how much will the length of the bridge increase from

0◦C_to45◦C_?

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Δ𝐴 = 𝛾 𝐴1Δ𝑇 (14.8)

volume expansion expansion of a solid in volume.

Δ𝑉 = 𝛽 𝑉1Δ𝑇 (14.9) • 𝛾 = 2𝛼 • 𝛽 = 3𝛼 Δ𝐴 = 2𝛼 𝐴1Δ𝑇 (14.10) Δ𝑉 = 3𝛼 𝑉1Δ𝑇 (14.11) Example 14.6

A hard rubber cube has a volume of 1000. cm3 at0◦C. If the cube is submerged in boiling water (100.◦C_{), what is its volume after reaching thermal equilibrium?}

14.3 - Heat Exchange

calorie (cal) the heat required at1 atm_{to raise}1 g_{of water from}14.5◦C_to15.5◦C_.

Calorie one kilocalorie.

joule (J) metric unit for heat;1 cal = 4.184 J_.

British thermal unit (BTU) the heat required to at1 atm_{to raise}1 lb_{of water from}63_°F_to 64_°F_;1 BTU ≈ 0.25 kcal_.

The Law of Heat Exchange

heat capacity the heat required to raise its temperature by one degree (Celsius).

𝐶 = 𝑄

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𝑐 = 𝑄

𝑚Δ𝑇 (14.13)

law of heat exchange the magnitudes of heat lost and heat gained within the same system are equal.

− 𝑄_lost= 𝑄_gained _(14.14)

𝑄 = 𝑚𝑐 Δ𝑇 _(14.15)

Example 14.7

How much heat is required to raise the temperature of a227 g_{aluminum cooking pot from} 25◦C_to105◦C_?

Example 14.8

A 95 g block of copper (Cu) is taken from a furnace and dropped into a410 g glass beaker containing120 g_{of water. Both the beaker and the water are at}15◦C_{. After the system reaches}

thermal equilibrium, the water is35◦C_{. What was the temperature of the furnace? Assume}

that no heat is lost from the beaker.

Example 14.9

A metal cylinder weighing920 gat100◦Cis dropped into500. gof water contained in a150 g

iron cup, both at13◦C_{. If the temperature rises to}35◦C_{, what is the specific heat of the metal}

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Phase Changes

melting a solid changing into a liquid

endothermic heat-absorbing process

heat of fusion (𝐿𝐹) the heat that must be absorbed per gram to change a solid to a

liquid.For water (ice),𝐿_𝐹 = 333 J/g.

𝑄 = 𝑚𝐿𝐹 (14.17)

freezing a liquid changing into a solid

exothermic heat-evolving (heat-emitting) process.

𝑄 = −𝑚𝐿𝐹 (14.18)

vaporization a liquid changing into a gas.

heat of vaporization (𝐿_𝑉) _{the heat that must be absorbed per gram to change a liquid}

to a gas.For water,𝐿𝑉 = 2260 J/g.

𝑄 = 𝑚𝐿_𝑉 _(14.19)

condensation a gas changing into a liquid.

𝑄 = −𝑚𝐿𝑉 (14.20)

calorimeter an insulated container used in scientific work to determine equilibrium temperature.

calorimetry the use of a calorimeter to measure the equilibrium temperature of a mixture.

Example 14.10

Steam at100◦C_{is added to}400. g_{of ethanol in a calorimeter. The mass of the inner cup, made}

of copper, is 200. g. If the initial temperature of the ethanol and cup is 15◦C and the final temperature of the mixture is45◦C_{, how much steam is added?}

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Heat Transfer

thermal conductor a material that conducts heat efficiently.

thermal insulator a material that does not conduct heat efficiently.

heat flow( 𝑄

𝑡) the amount of heat transferred from one end of a segment to the other per

unit time. 𝑄 𝑡 = 𝑘 𝐴 Δ𝑇 Δ𝑥 (14.21)

thermal conductivity (𝑘) the constant of proportionality for a material.

Example 14.11

Suppose a1.00 m_{brass rod with a cross-sectional area of}1.00 × 10−4m2_conducts2.50 J/s_{. What}

is the temperature difference between the ends of the rod?

Three methods of heat transfer

conduction agitated motion is transmitted between molecules in contact with each other.

convection heat is carried by a moving material.

radiation transmission of heat without a medium, largely in the infrared portion of the spectrum.

Chapter 14 Homework

Date Due: Score:

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Questions

14.1 - Thermometry

1. a. What is the basic reference point for the Kelvin scale of temperature?

b. What is the temperature of this reference point?

2. a. Why is the Kelvin scale called an absolute scale?

b. Why is it an equal-interval scale?

3. If you can measure a property proportional to Kelvin temperature, how may the Kelvin temperature of a body be determined? (equation)

4. On each scale, what is the a. freezing point of water?

i. Kelvin: ii. Celsius: iii. Fahrenheit:

b. boiling point of water? i. Kelvin:

ii. Celsius: iii. Fahrenheit:

5. How much does a gas change volume (compared with its volume at 0◦C_{) when its}

temperature increases or decreases by1◦C?

6. a. How is absolute value defined?

b. What is absolute value on the Kelvin scale? c. What is absolute value on the Celsius scale?

14.3 - Heat Exchange

7. How is each of the following defined?

a. the calorie

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c. the BTU

8. What is the difference between heat capacity (𝐶_{) and specific heat (}𝑐_)?

9. What are the units of. . .

a. heat capacity (𝐶_)?

b. specific heat (𝑐)?

10. What is the heat transferred called. . .

a. at the melting point? b. at the boiling point?

11. For water,

a. What is𝐿_𝐹_?

b. What is𝐿𝑉?

12. What is the difference between endothermic and exothermic?

13. What four factors determine the rate of heat conduction?

a. b. c. d. 14. Define. a. Conduction b. Convection

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c. Radiation

Problems

14.1 - Thermometry

1. A platinum resistance thermometer has a resistance of 95.11 Ω _{at the triple point of}

water. What is the Kelvin temperature if the resistance is93.64 Ω_?

2. Liquid nitrogen has a temperature of77 K_{. Express the temperature on. . .}

a. the Celsius scale.

b. the Fahrenheit scale.

14.2 - Thermal Expansion

3. A standard gauge block made of silver is5.000 cm_{long at}20.00◦C_{. Calculate its length}

when the temperature is30.00◦C_.

4. A gold disk at 20.0◦C _{has a diameter of} 10.0 cm _{and a hole cut in the center that is} 5.0000 cm_{in diameter. Calculate the diameter of the hole when the temperature is raised}

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5. A storage tank made of sheet iron holds4.00 m3_{of rubbing alcohol (}𝛽 = 1.12 × 10−3/◦C₎

when the temperature is−10.0◦C_{. How much alcohol will spill out if the temperature}

is raised to40.0◦C?

a. CalculateΔ𝑉 _{of the storage tank.}

b. CalculateΔ𝑉 _{of the alcohol.}

c. Calculate the amount spilled (𝑉𝑠𝑝 = Δ𝑉𝑎𝑙 − Δ𝑉𝑡 𝑎𝑛𝑘).

14.3 - Heat Exchange

6. How much heat must be added to exactly1.00 Lof water at25◦Cto bring it to the boiling point,100.0◦C_?

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7. Calculate the heat required to change50.0 g_{of ice at}−5.00◦C_{to water at}30.0◦C_.

8. Find the heat necessary to change5.00 kg_{of water at}30.0◦C_{to steam at}100.0◦C_.

9. A small crucible containing400. g_{of gold is heated to the temperature of a small furnace,}

and then the gold is dropped into 1000. gof water at 10.0◦C. If the final temperature comes to20.0◦C_{, find the temperature of the furnace. Neglect heat losses to any container.}

10. A brass rod is6.0 cm_{long and has a radius of}0.50 cm_{. How much heat will flow through}

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Chapter 15

The Laws of Thermodynamics

15.1 - First Law of Thermodynamics

Internal Energy

system any body or collection of bodies that can exchange energy with the surroundings.

surroundings anything outside the system being studied.

closed system sealed off from any mass (or volume) exchange from its surroundings, but work or energy may be exchanged.

open system can exchange both mass and energy with its surroundings.

isolated system cannot exchange either mass or energy with its surroundings.

heat the energy transfer between two bodies caused by a difference in initial temperature.

work the energy transfer between two bodies caused by a force operating over a distance.

equilibrium the state of a system with a net energy transfer of zero.

internal energy(𝐸_int) _{the total molecular energy content of a physical system (potential}

and kinetic).

thermal energy particle’s kinetic energy as they vibrate or rush about (measured as temperature).

𝑊 = 𝑚𝑔 ℎ (15.1)

𝑊 = 𝑄 = 𝑚𝑐 Δ𝑇 (15.2)

1 cal ≈ 4.184 J _(15.3)

mechanical equivalent of heat the amount of work equal to a unit of heat.

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Example 15.1

If you wanted to use the apparatus of Figure 15.2 (textbook) to increase the temperature of

1.0 kgof water by0.10◦C, what total mass should you use? Assume each weight falls a distance of1.0 m_.

First Law of Thermodynamics

The change in internal energy of a system equals the heat added to the system minus the work that the system does on the surroundings.

Δ𝐸_int = 𝑄 − 𝑊 _(15.4)

Example 15.2

The air inside a balloon placed in a refrigerator loses 11.8 Jof heat. At the same time, the shrinking rubber does 0.302 J _{of work in compressing the air. What is the change in the}

internal energy of the air inside the balloon?

adiabatic no heat entering or leaving a system while the system changes.

Δ𝐸_int = −𝑊 _(15.5)

isothermal leaving the temperature of a gas unchanged by compression.

Ideal Gas Law

irreversible process A process that:

• Does not have well-defined values of thermodynamic quantities.

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𝑃 = 𝑘𝐵 𝑉 (15.6) 𝑃 𝑉 = 𝑘𝐵 (15.7) 𝑃𝑖𝑉𝑖 = 𝑃𝑓𝑉𝑓 (15.8)

reversible process A process that:

• Always has well-defined values of thermodynamic quantities.

• Can have an equation written to describe how each quantity varies over time (using calculus).

• Can go through the same changes in reverse to restore each quantity to its original value. 𝑃 𝑉 = 𝑛𝑅𝑇 , 𝑅 = 0.0821L ⋅ atm K ⋅ mol = 8.3145 J K ⋅ mol (15.9) Example 15.3

At a pressure of1.00 atm,1.00 Lof gas is maintained at300. K. Suddenly the gas is compressed to a volume of0.333 L_{. The temperature of the gas is still}300. K_.

a. Is this process reversible or irreversible?

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Example 15.4

Suppose 1.00 mol of a gas undergoes a reversible, isothermal expansion from a volume of

1.00 L_{to a volume of}5.00 L_.

a. Draw the𝑃 − 𝑉 _{diagram for this process at}305 K_.

b. On the same diagram, show the reversi