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... 1523 A Atomic Masses.................................................... 1531 B Selected Radioactive Isotopes............................................ 1537 C Useful Information.................................................. 1541 D Glossary of Key Symbols and Notation....................................... 154... |
resources provide quality academic instruction. Three key features set our materials apart from others: they can be customized by instructors for each class, they are a “living” resource that grows online through contributions from science educators, and they are available for free or at minimal cost. Customization Op... |
fast-paced survey of physics facts and formulas that did not provide in-depth conceptual understanding of major physics ideas and the connections between them. The new AP® Physics 1 and 2 courses focus on the big ideas typically included in the first and second semesters of an algebrabased, introductory college-level ... |
is organized such that topics are introduced conceptually with a steady progression to precise definitions and analytical applications. The analytical aspect (problem solving) is tied back to the conceptual before moving on to another topic. Each introductory chapter, for example, opens with an engaging photograph rel... |
to OpenStax College Physics: AP® Edition This content is available for free at http://cnx.org/content/col11844/1.13 Preface Senior Contributors 3 Irna Lyublinskaya CUNY College of Staten Island, Staten Island, NY Gregg Wolfe Avonworth High School, Pittsburgh, PA Douglas Ingram TCU Department of Physics and Astronomy, ... |
® Physics Student The fundamental goal of physics is to discover and understand the “laws” that govern observed phenomena in the world around us. Why study physics? If you plan to become a physicist, the answer is obvious—introductory physics provides the foundation for your career; or if you want to become an engineer... |
spark you get from walking across a wool carpet, for example. Similarly, lightning results from air movements under certain weather conditions. In AP® Physics 2 course you will continue your journey by studying fluid dynamics, which explains why rising smoke curls and twists and how the body regulates blood flow. The ... |
the focus of each Big Idea. • Big Idea 1: Objects and systems have properties. • Big Idea 2: Fields explain interactions. • Big Idea 3: The interactions are described by forces. • Big Idea 4: Interactions result in changes. • Big Idea 5: Changes are constrained by conservation laws. • Big Idea 6: Waves can transfer en... |
44/1.13 Preface 5 OpenStax College Physics: AP® Edition has been written to engage students in their exploration of physics and help them relate what they learn in the classroom to their lives outside of it. Physics underlies much of what is happening today in other sciences and in technology. Thus, the book content in... |
dust. Two smaller galaxies are also visible as bright blue spots in the background. At a staggering 2.5 million light years from Earth, this galaxy is the nearest one to our own galaxy (which is called the Milky Way). The stars and planets that make up Andromeda might seem to be the furthest thing from most people's r... |
accurate and precise, and the reasons scientists go to painstaking lengths to be as clear as possible regarding their own limitations. 8 Chapter 1 | Introduction: The Nature of Science and Physics Chapter 1 introduces many fundamental skills and understandings needed for success with the AP® Learning Objectives. While... |
? Both contain energy that can be converted to other forms. The law of conservation of energy (which says that energy can change form but is never lost) ties together such topics as food calories, batteries, heat, light, and watch springs. Understanding this law makes it easier to learn about the various forms energy t... |
utilizes these physics equations to determine the travel time from one location to another. Figure 1.3 The Apple “iPhone” is a common smart phone with a GPS function. Physics describes the way that electricity flows through the circuits of this device. Engineers use their knowledge of physics to construct an iPhone wi... |
, such as how musical instruments make sound, how the eye detects color, and how lasers can transmit information. It is not necessary to formally study all applications of physics. What is most useful is knowledge of the basic laws of physics and a skill in the analytical methods for applying them. The study of physics... |
it to be. This content is available for free at http://cnx.org/content/col11844/1.13 Chapter 1 | Introduction: The Nature of Science and Physics 11 Figure 1.8 Isaac Newton (1642–1727) was very reluctant to publish his revolutionary work and had to be convinced to do so. In his later years, he stepped down from his aca... |
Some theories include models to help visualize phenomena, whereas others do not. Newton's theory of gravity, for example, does not require a model or mental image, because we can observe the objects directly with our own senses. The kinetic theory of gases, on the other hand, is a model in which a gas is viewed as bei... |
and tributes to the power of science. It is the underlying order in the universe that enables scientists to make such spectacular predictions. However, if experiment does not verify our predictions, then the theory or law is wrong, no matter how elegant or convenient it is. Laws can never be known with absolute certai... |
times through the Renaissance, natural philosophy encompassed many fields, including astronomy, biology, chemistry, physics, mathematics, and medicine. Over the last few centuries, the growth of knowledge has resulted in ever-increasing specialization and branching of natural philosophy into separate fields, with phys... |
picture phenomena we cannot see. In fact, new instrumentation has allowed us in recent years to actually “picture” the atom. 14 Chapter 1 | Introduction: The Nature of Science and Physics Limits on the Laws of Classical Physics For the laws of classical physics to apply, the following criteria must be met: Matter must... |
? Solution Without knowing the details of the law, you can still infer that the information your friend has learned conforms to the requirements of all laws of nature: it will be a concise description of the universe around us; a statement of the underlying rules that all natural processes follow. If the information ha... |
measurements. For example, we define distance and time by specifying methods for measuring them, whereas we define average speed by stating that it is calculated as distance traveled divided by time of travel. Measurements of physical quantities are expressed in terms of units, which are standardized values. For examp... |
ogram The Second The SI unit for time, the second(abbreviated s), has a long history. For many years it was defined as 1/86,400 of a mean solar day. More recently, a new standard was adopted to gain greater accuracy and to define the second in terms of a non-varying, or constant, physical phenomenon (because the solar ... |
the old meter standard at the International Bureau of Weights and Measures near Paris. Exact replicas of the standard kilogram are also kept at the United States' National Institute of Standards and Technology, or NIST, located in Gaithersburg, Maryland outside of Washington D.C., and at other locations around the wor... |
, the number 800 can be written as 8×102, and the number 450 can be written as 4.5×102. Thus, the numbers 800 and 450 are of the same order of magnitude: 102. Order of magnitude can be thought of as a ballpark estimate for the scale of a value. The diameter of an atom is on the order of 10−9 m, while the diameter of th... |
Ci high radioactivity kilometer km 103 m about 6/10 mile hectoliter hL 102 L 26 gallons dekagram dag 101 g teaspoon of butter deciliter dL 10−1 L less than half a soda centimeter cm 10−2 m fingertip thickness millimeter mm 10−3 m flea at its shoulders micrometer µm 10−6 m detail in microscope nanogram ng 10−9 g small ... |
is to list the units that you have and the units that you want to convert to. In this case, we have units in meters and we want to convert to kilometers. Next, we need to determine a conversion factor relating meters to kilometers. A conversion factor is a ratio expressing how many of one unit are equal to another uni... |
1 Recorded history 1 105 107 109 Time for one heartbeat One day 8.64×104 s One year (y) 3.16×107 s About half the life expectancy of a human 1017 1018 Age of the Earth Age of the universe 1 102 104 107 1011 Distance from the Earth to the Sun 1023 Mass of the Moon 7.35×1022 kg 1016 Distance traveled by light in 1 year (... |
3) (1.4) (1) Be sure that you have properly cancelled the units in the unit conversion. If you have written the unit conversion factor upside down, the units will not cancel properly in the equation. If you accidentally get the ratio upside down, then the units will not cancel; rather, they will give you the wrong unit... |
that we are all familiar with, there are others that are much more obscure. For example, a firkin is a unit of volume that was once used to measure beer. One firkin equals about 34 liters. To learn more about nonstandard units, use a dictionary or encyclopedia to research different “weights and measures.” Take note of... |
to: Learning Objectives • Determine the appropriate number of significant figures in both addition and subtraction, as well as multiplication and division calculations. • Calculate the percent uncertainty of a measurement. Accuracy and Precision of a Measurement Science is based on observation and experiment—that is, ... |
the restaurant at the center of the target. This indicates a low precision, high accuracy measuring system. However, in Figure 1.25, the GPS measurements are concentrated quite closely to one another, but they are far away from the target location. This indicates a high precision, low accuracy measuring system. Figure... |
In our example, such factors contributing to the uncertainty could be the following: the smallest division on the ruler is 0.1 in., the person using the ruler has bad eyesight, or one side of the paper is slightly longer than the other. At any rate, the uncertainty in a measurement must be based on a careful considera... |
but the uncertainty in the weight remained the same. Hint for future calculations: when calculating percent uncertainty, always remember that you must multiply the fraction by 100%. If you do not do this, you will have a decimal quantity, not a percent value. Uncertainties in Calculations There is an uncertainty in an... |
imeter. The caliper is a more precise measuring tool because it can measure extremely small differences in length. The more precise the measuring tool, the more precise and accurate the measurements can be. When we express measured values, we can only list as many digits as we initially measured with our measuring tool... |
that a measurement was made to the 0.1 decimal point, so the zeros are significant (c) 1; the value 103 signifies the decimal place, not the number of measured values (d) 5; the final zero indicates that a measurement was made to the 0.001 decimal point, so it is significant (e) 4; any zeros located in between signifi... |
so our final answer must also be expressed to the 0.1 decimal place. Thus, the answer is rounded to the tenths place, giving us 15.2 kg. Significant Figures in this Text In this text, most numbers are assumed to have three significant figures. Furthermore, consistent numbers of significant figures are used in all work... |
imations or “guesstimates” for a particular quantity. What is the distance to a certain destination? What is the approximate density of a given item? About how large a current will there be in a circuit? Many approximate numbers are based on formulae in which the input quantities are known only to a limited accuracy. A... |
used them to evenly cover a football field (between the end zones), make an approximation of how high the money pile 28 Chapter 1 | Introduction: The Nature of Science and Physics would become. (We will use feet/inches rather than meters here because football fields are measured in yards.) One of your friends says 3 i... |
bill stacks is 9 in.3 / stack×108 stacks = 9×108 in.3. (5) Calculate the height. To determine the height of the bills, use the equation: = area of field×height of money: volume of bills Height of money = volume of bills area of field Height of money = 9×108in.3 6×106in.2 = 1.33×102 in., Height of money ≈ 1×102 in. = 10... |
: the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation metric system: a system in which values can be calculated in factors of 10 model: representation of something that is often too difficult (or impossible) to ... |
from other measurements. • Units are standards for expressing and comparing the measurement of physical quantities. All units can be expressed as combinations of four fundamental units. • The four fundamental units we will use in this text are the meter (for length), the kilogram (for mass), the second (for time), and... |
compare to the required validity of a theory or a law? 7. Classical physics is a good approximation to modern physics under certain circumstances. What are they? 8. When is it necessary to use relativistic quantum mechanics? 9. Can classical physics be used to accurately describe a satellite moving at a speed of 7500 ... |
? (Assume that 1 kilometer equals 3,281 feet.) 8. The speed of sound is measured to be 342 m/s on a certain day. What is this in km/h? 9. Tectonic plates are large segments of the Earth's crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at th... |
percent uncertainty? (b) If it has the same percent uncertainty when it reads 60 km/h, what is the range of speeds you could be going? 20. (a) A person's blood pressure is measured to be 120 ± 2 mm Hg. What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressu... |
) By what amount is the gas decreased in volume in cubic centimeters? (b) Find the uncertainty in this volume. 16. A can contains 375 mL of soda. How much is left after 308 mL is removed? 1.4 Approximation 17. State how many significant figures are proper in the results of the following calculations: (a) 29. How many h... |
be one dimensional. (credit: Vince Maidens, Wikimedia Commons) Chapter Outline 2.1. Displacement 2.2. Vectors, Scalars, and Coordinate Systems 2.3. Time, Velocity, and Speed 2.4. Acceleration 2.5. Motion Equations for Constant Acceleration in One Dimension 2.6. Problem-Solving Basics for One Dimensional Kinematics 2.7... |
3 The interactions of an object with other objects can be described by forces. 34 Chapter 2 | Kinematics Enduring Understanding 3.A All forces share certain common characteristics when considered by observers in inertial reference frames. Essential Knowledge 3.A.1 An observer in a particular reference frame can descri... |
.) Displacement If an object moves relative to a reference frame (for example, if a professor moves to the right relative to a white board or a passenger moves toward the rear of an airplane), then the object's position changes. This change in position is known as displacement. The word “displacement” implies that an o... |
f = 3.5 m. Thus her displacement is Δ = f −0 = 3.5 m − 1.5 m = + 2.0 m. (2.2) In this coordinate system, motion to the right is positive, whereas motion to the left is negative. Similarly, the airplane passenger's initial position is 0 = 6.0 m and his final position is f = 2.0 m, so his displacement is 36 Chapter 2 | ... |
she ride? (c) What is the magnitude of her displacement? Solution Figure 2.5 (a) The rider's displacement is Δ = f − 0 = −1 km. (The displacement is negative because we take east to be positive and west to be negative.) (b) The distance traveled is 3 km + 2 km = 5 km. (c) The magnitude of the displacement is 1 km. Thi... |
direction or none is specified. A scalar is any quantity that has a magnitude, but no direction. For example, a 20ºC temperature, the 250 kilocalories (250 Calories) of energy in a candy bar, a 90 km/h speed limit, a person's 1.8 m height, and a distance of 2.0 m are all scalars—quantities with no specified direction.... |
and by an observer standing on the sidewalk. Both the bus passenger and sidewalk observer will be able to collect information about you. They can determine how far you moved and how much time it took you to do so. However, while you moved at a consistent pace, both observers will get different results. To the passenge... |
. time. The information presented in this section supports the following AP® learning objectives and science practices: • 3.A.1.1 The student is able to express the motion of an object using narrative, mathematical, and graphical representations. (S.P. 1.5, 2.1, 2.2) • 3.A.1.3 The student is able to analyze experimenta... |
4) where Δ is the change in time or elapsed time, f is the time at the end of the motion, and 0 is the time at the beginning of the motion. (As usual, the delta symbol, Δ, means the change in the quantity that follows it.) Life is simpler if the beginning time 0 is taken to be zero, as when we use a stopwatch. If we we... |
to the back of the plane. To get more details, we must consider smaller segments of the trip over smaller time intervals. Figure 2.9 A more detailed record of an airplane passenger heading toward the back of the plane, showing smaller segments of his trip. The smaller the time intervals considered in a motion, the mor... |
. For example, if you drive to a store and return home in half an hour, and your car's odometer shows the total distance traveled was 6 km, then your average speed was 12 km/h. Your average velocity, however, was zero, because your displacement for the round trip is zero. (Displacement is change in position and, thus, ... |
minutes. The distance between the two stations is approximately 40 miles. What is (a) the average velocity of the train, and (b) the average speed of the train in m/s? Solution (a) The average velocity of the train is zero because f = 0 ; the train ends up at the same place it starts. (b) The average speed of the trai... |
that velocity is a vector—it has both magnitude and direction. This means that a change in velocity can be a change in magnitude (or speed), but it can also be a change in direction. For example, if a car turns a corner at constant speed, it is accelerating because its direction is changing. The quicker you turn, the ... |
/s, it is finishing with a speed less than that, like +5 m/s. Because the change in velocity is negative, the acceleration will be as well.) Figure 2.17 Car C has a constant speed. Because the positive direction is considered to the right of the paper, Car C is moving with a positive velocity. Because all arrows are of... |
time (shaded grey) the position of the object does not change much, resulting in a small positive velocity. During a later portion of time (shaded green) the position of the object changes more, resulting in a larger positive velocity. Because this positive velocity is increasing over time, the acceleration of the obj... |
this problem by identifying Δ and Δ from the given information and then calculating the average f − 0 f − 0 acceleration directly from the equation - = Δ Δ =. Solution 1. Identify the knowns. 0 = 0, f = −15.0 m/s (the minus sign indicates direction toward the west), Δ = 1.80 s. 2. Find the change in velocity. Since th... |
s2 and –2.0 m/s2, respectively. 50 Chapter 2 | Kinematics Figure 2.29 Graphs of instantaneous acceleration versus time for two different one-dimensional motions. (a) Here acceleration varies only slightly and is always in the same direction, since it is positive. The average over the interval is nearly the same as the ... |
straightforward since the initial and final positions are given. Solution 1. Identify the knowns. In the figure we see that f = 6.70 km and 0 = 4.70 km for part (a), and ′f = 3.75 km and ′0 = 5.25 km for part (b). 2. Solve for displacement in part (a). Δ = f − 0 = 6.70 km − 4.70 km= +2.00 km 3. Solve for displacement ... |
involves three steps. First we must determine the change in velocity, then we must determine the change in time, and finally we use these values to calculate the acceleration. Solution 52 Chapter 2 | Kinematics 1. Identify the knowns. 0 = 0 (the trains starts at rest), f = 30.0 km/h, and Δ = 20.0 s. 2. Calculate Δ. Si... |
/h 8.00 s 103 m 1 km 1 h 3600 s = −1.04 m/s2. (2.16) (2.17) (2.18) Discussion The minus sign indicates that acceleration is to the left. This sign is reasonable because the train initially has a positive velocity in this problem, and a negative acceleration would oppose the motion. Again, acceleration is in the same di... |
.00 min. 2. Determine displacement, Δ′. We found Δ′ to be − 1.5 km in Example 2.2. 3. Solve for average velocity. 4. Convert units. - = Δ′ Δ = −1.50 km 5.00 min - = Δ′ Δ = −1.50 km 5.00 min 60 min 1 h = −18.0 km/h Discussion The negative velocity indicates motion to the left. Example 2.7 Calculating Deceleration: The S... |
obvious for acceleration. Most people interpret negative acceleration as the slowing of an object. This was not the case in Example 2.7, where a positive acceleration slowed a negative velocity. The crucial distinction was that the acceleration was in the opposite direction from the velocity. In fact, a negative accel... |
the results of the analysis using narrative, mathematical, and graphical representations. (S.P. 5.1) We might know that the greater the acceleration of, say, a car moving away from a stop sign, the greater the displacement in a given time. But we have not developed a specific equation that relates acceleration and dis... |
( ) from Average Velocity when Acceleration ( ) is Constant To get our first two new equations, we start with the definition of average velocity: - = Δ Δ. Substituting the simplified notation for Δ and Δ yields - = − 0. Solving for yields where the average velocity is = 0 +, - = 0 + 2 (constant ). This content is avai... |
for example, we will get twice as far in a given time if we average 90 km/h than if we average 45 km/h. 58 Chapter 2 | Kinematics Figure 2.39 There is a linear relationship between displacement and average velocity. For a given time, an object moving twice as fast as another object will move twice as far as the other ... |
the relationships among velocity, acceleration, and time. From it we can see, for example, that • • • final velocity depends on how large the acceleration is and how long it lasts if the acceleration is zero, then the final velocity equals the initial velocity ( = 0), as expected (i.e., velocity is constant) if is neg... |
(Think about it like the starting line of a race. It can be anywhere, but we call it 0 and measure all other positions relative to it.) We can use the equation = 0 + 0 + 1 2 2 once we identify 0,, and from the statement of the problem. Solution 1. Identify the knowns. Starting from rest means that 0 = 0, is given as 2... |
required. 2 + 2( − 0) is ideally suited to this task because it relates velocities, acceleration, and Solution 1. Identify the known values. We know that 0 = 0, since the dragster starts from rest. Then we note that − 0 = 402 m (this was the answer in Example 2.10). Finally, the average acceleration was given to be = ... |
stop a car moving at 30.0 m/s (about 110 km/h) (a) on dry concrete and (b) on wet concrete. (c) Repeat both calculations, finding the displacement from the point where the driver sees a traffic light turn red, taking into account his reaction time of 0.500 s to get his foot on the brake. Strategy Draw a sketch. Figure... |
stopping time. It is reasonable to assume that the velocity remains constant during the driver's reaction time. 1. Identify the knowns and what we want to solve for. We know that We take 0 − reaction to be 0. We are looking for reaction. - = 30.0 m/s ; reaction = 0.500 s ; reaction = 0. 2. Identify the best equation t... |
? (Such information might be useful to a traffic engineer.) Strategy Draw a sketch. Figure 2.48 We are asked to solve for the time. As before, we identify the known quantities in order to choose a convenient physical relationship (that is, an equation with one unknown, ). Solution 1. Identify the knowns and what we wan... |
In some problems both solutions are meaningful, but in others, such as the above, only one solution is reasonable. The 10.0 s answer seems reasonable for a typical freeway on-ramp. With the basics of kinematics established, we can go on to many other interesting examples and applications. In the process of developing ... |
the ability to apply broad physical principles, usually represented by equations, to specific situations is a very powerful form of knowledge. It is much more powerful than memorizing a list of facts. Analytical skills and problem-solving abilities can be applied to new situations, whereas a list of facts cannot be ma... |
of equations. You may have to use two (or more) different equations to get the final answer. Step 5 Substitute the knowns along with their units into the appropriate equation, and obtain numerical solutions complete with units. This step produces the numerical answer; it also provides a check on units that can help yo... |
sense, but there is more to describing nature than just manipulating equations correctly. Checking the result of a problem to see if it is reasonable does more than help uncover errors in problem solving—it also builds intuition in judging whether nature is being accurately described. Use the following strategies to d... |
2.2) • 3.A.1.2 The student is able to design an experimental investigation of the motion of an object. (S.P. 4.2) • 3.A.1.3 The student is able to analyze experimental data describing the motion of an object and is able to express the results of the analysis using narrative, mathematical, and graphical representations... |
important that its magnitude is given its own symbol,. It is constant at any given location on Earth and has the average value = 9.80 m/s2. (2.74) Although varies from 9.78 m/s2 to 9.83 m/s2, depending on latitude, altitude, underlying geological formations, and local topography, the average value of 9.80 m/s2 will be... |
times. It is reasonable to take the initial position 0 to be zero. This problem involves one-dimensional motion in the vertical direction. We use plus and minus signs to indicate direction, with up being positive and down negative. Since up is positive, and the rock is thrown upward, the initial velocity must be posit... |
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