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University Physics Volume 1 SENIOR CONTRIBUTING A UTHORS SAMUEL J. LING, TRUMAN STATE UNIVERSITY JEFF SANNY, LOYOLA MARYMOUNT UNIVERSITY WILLIAM MOEBS, PHD |
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Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Unit 1. Mechanics Chapter 1: Units and Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1. 1 The Scope and Scale of Physics . . . . . . . . . . . . . . . . . . ... |
9. 5 Collisions in Multiple Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 9. 6 Center of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 9. 7 Rocket Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 Chapter 10: Fixed-... |
17. 6 Beats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 880 17. 7 The Doppler Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 882 17. 8 Shock Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 889 Appendix A: Units .... |
This Open Stax book is available for free at http://cnx. org/content/col12031/1. 10 |
PREFACE Welcome to University Physics, an Open Stax resource. This textbook was written to increase student access to high-quality learning materials, maintaining highest standards of academic rigor at little to no cost. About Open Stax Open Stax is a nonprofit based at Rice University, and it's our mission to improve ... |
VOLUME I Unit 1: Mechanics Chapter 1: Units and Measurement Chapter 2: Vectors Chapter 3: Motion Along a Straight Line Chapter 4: Motion in Two and Three Dimensions Chapter 5: Newton's Laws of Motion Chapter 6: Applications of Newton's Laws Chapter 7: Work and Kinetic Energy Chapter 8: Potential Energy and Conservation... |
Chapter 2: Geometric Optics and Image Formation Chapter 3: Interference Chapter 4: Diffraction Unit 2: Modern Physics Chapter 5: Relativity Chapter 6: Photons and Matter Waves Chapter 7: Quantum Mechanics Chapter 8: Atomic Structure Chapter 9: Condensed Matter Physics Chapter 10: Nuclear Physics Chapter 11: Particle Ph... |
encourage instructors to join the hubs for the subjects most relevant to your teaching and research as an opportunity both to enrich your courses and to engage with other faculty. To reach the Community Hubs, visit www. oercommons. org/hubs/Open Stax (https://www. oercommons. org/ hubs/Open Stax). Partner resources Ope... |
Gavin Buxton, Robert Morris University Erik Christensen, South Florida State College Clifton Clark, Fort Hays State University Nelson Coates, California Maritime Academy Herve Collin, Kapi'olani Community College Carl Covatto, Arizona State University Alejandro Cozzani, Imperial Valley College Danielle Dalafave, The Co... |
Preface This Open Stax book is available for free at http://cnx. org/content/col12031/1. 10 |
1|UNITS AND MEASUREMENT Figure 1. 1 This image might be showing any number of things. It might be a whirlpool in a tank of water or perhaps a collage of paint and shiny beads done for art class. Without knowing the size of the object in units we all recognize, such as meters or inches, it is difficult to know what we'r... |
realize that physics plays a much larger role in your life than you first thought, no matter your life goals or career choice. 1. 1|The Scope and Scale of Physics Learning Objectives By the end of this section, you will be able to: Describe the scope of physics. Calculate the order of magnitude of a quantity. Compare m... |
of the physics underlying these devices is required to shrink their size or increase their processing speed. Or, think about a GPS. Physics describes the relationship between the speed of an object, the distance over which it travels, and the time it takes to travel that distance. When you use a GPS in a vehicle, it re... |
The Scale of Physics From the discussion so far, it should be clear that to accomplish your goals in any of the various fields within the natural sciences and engineering, a thorough grounding in the laws of physics is necessary. The reason for this is simply that the laws of physics govern everything in the observable... |
diameter of the Sun. This is much easier to do in your head than using the more precise values of 1. 06× 10-10mfor a hydrogen atom diameter and 1. 39× 109mfor the Sun's diameter, to find that it would take 1. 31× 1019hydrogen atoms to stretch across the Sun's diameter. In addition to being easier, the rough estimate is... |
Figure 1. 4 This table shows the orders of magnitude of length, mass, and time. Visit this site (https://openstaxcollege. org/l/21scaleuniv) to explore interactively the vast range of length scales in our universe. Scroll down and up the scale to view hundreds of organisms and objects, and click on the individual objec... |
Figure 1. 5 (a) Enrico Fermi (1901-1954) was born in Italy. On accepting the Nobel Prize in Stockholm in 1938 for his work on artificial radioactivity produced by neutrons, he took his family to America rather than return home to the government in power at the time. He became an American citizen and was a leading parti... |
The word theory means something different to scientists than what is often meant when the word is used in everyday conversation. In particular, to a scientist a theory is not the same as a “guess” or an “idea” or even a “hypothesis. ” The phrase “it's just a theory” seems meaningless and silly to scientists because sci... |
We define a physical quantity either by specifying how it is measured or by stating how it is calculated from other measurements. For example, we might define distance and time by specifying methods for measuring them, such as using a meter stick and a stopwatch. Then, we could define average speed by stating that it i... |
ISQ Base Quantity SI Base Unit Electrical current ampere (A) Thermodynamic temperature kelvin (K) Amount of substance mole (mol) Luminous intensity candela (cd) Table 1. 1 ISQ Base Quantities and Their SI Units You are probably already familiar with some derived quantities that can be formed from the base quantities in... |
Figure 1. 8 An atomic clock such as this one uses the vibrations of cesium atoms to keep time to a precision of better than a microsecond per year. The fundamental unit of time, the second, is based on such clocks. This image looks down from the top of an atomic fountain nearly 30 feet tall. (credit: Steve Jurvetson) T... |
Figure 1. 10 Redefining the SI unit of mass. Complementary methods are being investigated for use in an upcoming redefinition of the SI unit of mass. (a) The U. S. National Institute of Standards and Technology's watt balance is a machine that balances the weight of a test mass against the current and voltage (the “wat... |
1. 1only time this becomes a bit confusing is when discussing masses. As we have seen, the base SI unit of mass is the kilogram (kg), but metric prefixes need to be applied to the gram (g), because we are not allowed to “double-up” prefixes. Thus, a thousand kilograms (103kg) is written as a megagram (1 Mg) since 103kg... |
1. 3|Unit Conversion Learning Objectives By the end of this section, you will be able to: Use conversion factors to express the value of a given quantity in different units. It is often necessary to convert from one unit to another. For example, if you are reading a European cookbook, some quantities may be expressed i... |
1. 2 1. 30. 50mile min×1609m 1 mile×1 min 60s=(0. 50)(1609) 60m/s = 13m/s. Significance Check the answer in the following ways: 1. Be sure the units in the unit conversion cancel correctly. If the unit conversion factor was written upside down, the units do not cancel correctly in the equation. We see the “miles” in th... |
1. 4seen with the Mars Climate Orbiter. This probe was launched by NASA on December 11, 1998. On September 23, 1999, while attempting to guide the probe into its planned orbit around Mars, NASA lost contact with it. Subsequent investigations showed a piece of software called SM_FORCES (or “small forces”) was recording ... |
for the density of the material from which the cylinder is made, then [m] = M and[ρ] = ML-3. The importance of the concept of dimension arises from the fact that any mathematical equation relating physical quantities must be dimensionally consistent, which means the equation must obey the following rules: Every term in... |
1. 5 Check Your Understanding Suppose we want the formula for the volume of a sphere. The two expressions commonly mentioned in elementary discussions of spheres are 4πr2and4πr3/3. One is the volume of a sphere of radius rand the other is its surface area. Which one is the volume? Example 1. 5 Checking Equations for Di... |
1. 6textbook on a quantitative subject such as physics (including this one) almost certainly contains some equations with typos. Checking equations routinely by dimensional analysis save us the embarrassment of using an incorrect equation. Also, checking the dimensions of an equation we obtain through algebraic manipul... |
shoulders to reach the ceiling. Last, estimate the height of a person. The product of these three estimates is your estimate of the height of the building. It helps to have memorized a few length scales relevant to the sorts of problems you find yourself solving. For example, knowing some of the length scales in Figure... |
1. 7following the advice to “get areas and volumes from lengths” again, we can approximate Earth as a sphere and use the formula for the surface area of a sphere of diameter d—that is, A=πd2,to estimate the surface area of the oceans. Now we just need to estimate the average depth of the oceans. For this, we use the ad... |
1. 6|Significant Figures Learning Objectives By the end of this section, you will be able to: Determine the correct number of significant figures for the result of a computation. Describe the relationship between the concepts of accuracy, precision, uncertainty, and discrepancy. Calculate the percent uncertainty of a m... |
variation from one measurement to another. Notice that the concept of precision depends only on the actual measurements acquired and does not depend on an accepted reference value. The measurements in the paper example are both accurate and precise, but in some cases, measurements are accurate but not precise, or they ... |
1. 8At any rate, the uncertainty in a measurement must be calculated to quantify its precision. If a reference value is known, it makes sense to calculate the discrepancy as well to quantify its accuracy. Percent uncertainty Another method of expressing uncertainty is as a percent of the measured value. If a measuremen... |
uncertainties in the items used to make the calculation. For example, if a floor has a length of 4. 00 m and a width of 3. 00 m, with uncertainties of 2% and 1%, respectively, then the area of the floor is 12. 0 m2and has an uncertainty of 3%. (Expressed as an area, this is 0. 36 m2[12. 0m2× 0. 03 ], which we round to ... |
7. 56kg-6. 052kg +13. 7kg 15. 208kg= 15. 2kg. Next, we identify the least-precise measurement: 13. 7 kg. This measurement is expressed to the 0. 1 decimal place, 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... |
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 made long enough t... |
Check the answer to see whether it is reasonable. Does it make sense? This step is extremely important:-the goal of physics is to describe nature accurately. To determine whether the answer is reasonable, check both its magnitude and its sign, in addition to its units. The magnitude should be consistent with a rough es... |
accuracy base quantity base unit conversion factor derived quantity derived units dimension dimensionally consistent dimensionless discrepancy English units estimation kilogram law meter method of adding percents metric system model order of magnitude percent uncertainty physical quantity physics precision second SI un... |
theory uncertainty unitstestable explanation for patterns in nature supported by scientific evidence and verified multiple times by various groups of researchers a quantitative measure of how much measured values deviate from one another standards used for expressing and comparing measurements KEY EQUATIONS Percent unc... |
°One “sig. fig. ” is fine. °Ask yourself: Does this make any sense? 1. 6 Significant Figures Accuracy of a measured value refers to how close a measurement is to an accepted reference value. The discrepancy in a measurement is the amount by which the measurement result differs from this value. Precision of measured val... |
1. 6 Significant Figures 11. (a) What is the relationship between the precision and the uncertainty of a measurement? (b) What is the relationship between the accuracy and the discrepancy of a measurement?1. 7 Solving Problems in Physics 12. What information do you need to choose which equation or equations to use to s... |
than one but less than 1000. For example, 7. 9× 10-2m could be written either as 7. 9 cm or 79 mm. (a) 7. 59× 107m; (b) 0. 0074 m; (c) 8. 8× 10-11m; (d) 1. 63× 1013m. 28. The following masses are written using metric prefixes on the gram. Rewrite them in scientific notation in terms of the SI base unit of mass: the kil... |
1. 4 Dimensional Analysis 50. A student is trying to remember some formulas from geometry. In what follows, assume Ais area, Vis volume, and all other variables are lengths. Determine which formulas are dimensionally consistent. (a) V=πr2h;(b)A= 2πr2+2πrh; (c)V= 0. 5bh; (d) V=πd2;(e)V=πd3/6. 51. Consider the physical q... |
⎛ ⎝1. 60× 10-19⎞ ⎠(3712) 73. (a) How many significant figures are in the numbers 99 and 100. ? (b) If the uncertainty in each number is 1, what is the percent uncertainty in each? (c) Which is a more meaningful way to express the accuracy of these two numbers: significant figures or percent uncertainties? 74. (a) If yo... |
was able to determine the rate at which the radius of the fireball from the blast grew. Using dimensional analysis, he was then able to deduce the amount of energy released in the explosion, which was a closely guarded secret at the time. Because of this, Taylor did not publish his results until 1950. This problem chal... |
2|VECTORS Figure 2. 1 A signpost gives information about distances and directions to towns or to other locations relative to the location of the signpost. Distance is a scalar quantity. Knowing the distance alone is not enough to get to the town; we must also know the direction from the signpost to the town. The direct... |
2. 1|Scalars and Vectors Learning Objectives By the end of this section, you will be able to: Describe the difference between vector and scalar quantities. Identify the magnitude and direction of a vector. Explain the effect of multiplying a vector quantity by a scalar. Describe how one-dimensional vector quantities ar... |
type with an arrow above it denotes a vector, and a letter without an arrow denotes a scalar. For example, a distance of 2. 0 km, which is a scalar quantity, is denoted by d= 2. 0 km, whereas a displacement of 2. 0 km in some direction, which is a vector quantity, is denoted by d. Suppose you tell a friend on a camping... |
Figure 2. 4 A displacement Dof magnitude 6 km is drawn to scale as a vector of length 12 cm when the length of 2 cm represents 1 unit of displacement (which in this case is 1 km). Suppose your friend walks from the campsite at Ato the fishing pond at Band then walks back: from the fishing pond at Bto the campsite at A.... |
2. 1 Figure 2. 5 Various relations between two vectors Aand B. (a) A≠Bbecause A≠B. (b)A≠Bbecause they are not parallel and A≠B. (c)A≠-Abecause they have different directions (even though|A|=|-A|=A). (d)A=B because they are parallel andhave identical magnitudes A=B. (e) A≠Bbecause they have different directions (are not... |
Figure 2. 6 Displacement vectors for a fishing trip. (a) Stopping to rest at point Cwhile walking from camp (point A) to the pond (point B). (b) Going back for the dropped tackle box (point D). (c) Finishing up at the fishing pond. Suppose your friend departs from point A(the campsite) and walks in the direction to poi... |
antiparallel to the direction of A. These principles are illustrated in Figure 2. 7 (a) by two examples where the length of vector Ais 1. 5 units. When α= 2, the new vector B= 2Ahas length B= 2A= 3. 0units (twice as long as the original vector) and is parallel to the original vector. When α=-2, the new vector C=-2Ahas ... |
displacement vector D ADfrom point Ato point Dand his displacement vector D DBfrom point Dto the fishing hole: D AB=D AD+D DB(see Figure 2. 6 (c)). This means his displacement vector D DBis the difference of two vectors : (2. 5)D DB=D AB-D AD=D AB+(-D AD). Notice that a difference of two vectors is nothing more than a ... |
magnitude of 6. 0 km and a direction of northeast, we can introduce a unit vector u^that points to the northeast and say succinctly that D AB= (6. 0km) u^. Then the southwesterly direction is simply given by the unit vector-u^. In this way, the displacement of 6. 0 km in the southwesterly direction is expressed by the ... |
2. 2Solution The resultant of all the displacement vectors is D=D 1+D 2+D 3+D 4+D 5 = (15cm)(+ u^)+(56cm)(-u^)+(3cm)(+ u^)+(25cm)(+ u^)+(19cm)(-u^) = (15-56+3+25-19)cm u^ =-32cm u^. In this calculation, we use the distributive law given by Equation 2. 9. The result reads that the total displacement vector points away f... |
For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors Aand Bare at the arbitrary positions shown in Figure 2. 10. Translate either one of them in parallel to the beginning of the other vector, so that after the translation, both vectors have their origi... |
Figure 2. 11 When we use the parallelogram rule four times, we obtain the resultant vector R=A+B+C+D+E, which is the green vector connecting Tallahassee with Gainesville. Drawing the resultant vector of many vectors can be generalized by using the following tail-to-head geometric construction. Suppose we want to draw t... |
Figure 2. 12 Tail-to-head method for drawing the resultant vector R=A+B+C+D. (a) Four vectors of different magnitudes and directions. (b) Vectors in (a) are translated to new positions where the origin (“tail”) of one vector is at the end (“head”) of another vector. The resultant vector is drawn from the origin (“tail”... |
the diagonals is the difference A-B. We use a ruler to measure the lengths of the diagonals, and a protractor to measure the angles with the horizontal. For the resultant R, we obtain R= 5. 8 cm and θR≈ 0°. For the difference D, we obtain D= 16. 2 cm and θD= 49. 3°, which are shown in Figure 2. 14. Figure 2. 14 Using t... |
2. 3Check Your Understanding Using the three displacement vectors A,B, and Fin Figure 2. 13, choose a convenient scale, and use a ruler and a protractor to find vector Ggiven by the vector equation G=A+2B-F. Observe the addition of vectors in a plane by visiting this vector calculator (https://openstaxcollege. org/l/ 2... |
Figure 2. 16 Vector Ain a plane in the Cartesian coordinate system is the vector sum of its vector x-and y-components. The x-vector component A xis the orthogonal projection of vector Aonto the x-axis. The y-vector component A yis the orthogonal projection of vector Aonto the y-axis. The numbers Axand Aythat multiply t... |
Example 2. 3 Displacement of a Mouse Pointer A mouse pointer on the display monitor of a computer at its initial position is at point (6. 0 cm, 1. 6 cm) with respect to the lower left-side corner. If you move the pointer to an icon located at point (2. 0 cm, 4. 5 cm), what is the displacement vector of the pointer? Str... |
2. 4The vector x-component D x=-4. 0i^= 4. 0(-i^)of the displacement vector has the magnitude |D x|=|-4. 0||i^ |= 4. 0 because the magnitude of the unit vector is|i^ |= 1. Notice, too, that the direction of the x-component is-i^, which is antiparallel to the direction of the + x-axis; hence, the x-component vector D xp... |
Figure 2. 18 When the vector lies either in the first quadrant or in the fourth quadrant, where component Axis positive (Figure 2. 19), the direction angle θAin Equation 2. 16) is identical to the angle θ. When the vector lies either in the first quadrant or in the fourth quadrant, where component Axis positive (Figure... |
2. 5Example 2. 4 Magnitude and Direction of the Displacement Vector You move a mouse pointer on the display monitor from its initial position at point (6. 0 cm, 1. 6 cm) to an icon located at point (2. 0 cm, 4. 5 cm). What are the magnitude and direction of the displacement vector of the pointer? Strategy In Example 2.... |
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