The problem said to use the numbers given and determine g. We did that. By shortening the pendulum's length, the period is also reduced, speeding up the pendulum's motion. Homogeneous first-order linear partial differential equation: if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[336,280],'physexams_com-leader-1','ezslot_11',112,'0','0'])};__ez_fad_position('div-gpt-ad-physexams_com-leader-1-0'); Therefore, with increasing the altitude, $g$ becomes smaller and consequently the period of the pendulum becomes larger. >> /Name/F7 The rope of the simple pendulum made from nylon. endobj /FThHh!nmoF;TSooevBFN""(+7IcQX.0:Pl@Hs (@Kqd(9)\ (jX 1000 1000 1055.6 1055.6 1055.6 777.8 666.7 666.7 450 450 450 450 777.8 777.8 0 0 Websimple-pendulum.txt. endobj An engineer builds two simple pendula. Find the period and oscillation of this setup. :)kE_CHL16@N99!w>/Acy rr{pk^{?; INh' To Find: Potential energy at extreme point = E P =? The two blocks have different capacity of absorption of heat energy. %PDF-1.5 481.5 675.9 643.5 870.4 643.5 643.5 546.3 611.1 1222.2 611.1 611.1 611.1 0 0 0 0 A "seconds pendulum" has a half period of one second. l(&+k:H uxu {fH@H1X("Esg/)uLsU. 9.742m/s2, 9.865m/s2, 9.678m/s2, 9.722m/s2. 10 0 obj (Take $g=10 m/s^2$), Solution: the frequency of a pendulum is found by the following formula \begin{align*} f&=\frac{1}{2\pi}\sqrt{\frac{g}{\ell}}\\\\ 0.5 &=\frac{1}{2\pi}\sqrt{\frac{10}{\ell}} \\\\ (2\pi\times 0.5)^2 &=\left(\sqrt{\frac{10}{\ell}}\right)^2\\\\ \Rightarrow \ell&=\frac{10}{4\pi^2\times 0.25}\\\\&=1\quad {\rm m}\end{align*}. WebIn the case of the simple pendulum or ideal spring, the force does not depend on angular velocity; but on the angular frequency. Representative solution behavior and phase line for y = y y2. Adding pennies to the pendulum of the Great Clock changes its effective length. /Name/F9 14 0 obj ))NzX2F 298.4 878 600.2 484.7 503.1 446.4 451.2 468.8 361.1 572.5 484.7 715.9 571.5 490.3 277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 >> 525 768.9 627.2 896.7 743.3 766.7 678.3 766.7 729.4 562.2 715.6 743.3 743.3 998.9 Two simple pendulums are in two different places. 18 0 obj By the end of this section, you will be able to: Pendulums are in common usage. << endobj endobj >> 5. endobj When the pendulum is elsewhere, its vertical displacement from the = 0 point is h = L - L cos() (see diagram) Begin by calculating the period of a simple pendulum whose length is 4.4m. The period you just calculated would not be appropriate for a clock of this stature. Let's calculate the number of seconds in 30days. Websector-area-and-arc-length-answer-key 1/6 Downloaded from accreditation. 495.7 376.2 612.3 619.8 639.2 522.3 467 610.1 544.1 607.2 471.5 576.4 631.6 659.7 To compare the frequency of the two pendulums, we have \begin{align*} \frac{f_A}{f_B}&=\frac{\sqrt{\ell_B}}{\sqrt{\ell_A}}\\\\&=\frac{\sqrt{6}}{\sqrt{2}}\\\\&=\sqrt{3}\end{align*} Therefore, the frequency of pendulum $A$ is $\sqrt{3}$ times the frequency of pendulum $B$. Simplify the numerator, then divide. In this problem has been said that the pendulum clock moves too slowly so its time period is too large. But the median is also appropriate for this problem (gtilde). <> 2015 All rights reserved. 1 0 obj The <> /Type/Font (The weight mgmg has components mgcosmgcos along the string and mgsinmgsin tangent to the arc.) A simple pendulum is defined to have an object that has a small mass, also known as the pendulum bob, which is suspended from a light wire or string, such as shown in Figure 16.13. WebSo lets start with our Simple Pendulum problems for class 9. 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 The answers we just computed are what they are supposed to be. Arc length and sector area worksheet (with answer key) Find the arc length. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 458.3 458.3 416.7 416.7 /Subtype/Type1 For small displacements, a pendulum is a simple harmonic oscillator. endobj Solution: The period of a simple pendulum is related to its length $\ell$ by the following formula \[T=2\pi\sqrt{\frac{\ell}{g}}\] Here, we wish $T_2=3T_1$, after some manipulations we get \begin{align*} T_2&=3T_1\\\\ 2\pi\sqrt{\frac{\ell_2}{g}} &=3\times 2\pi\sqrt{\frac{\ell_1}{g}}\\\\ \sqrt{\ell_2}&=3\sqrt{\ell_1}\\\\\Rightarrow \ell_2&=9\ell_1 \end{align*} In the last equality, we squared both sides. Energy of the Pendulum The pendulum only has gravitational potential energy, as gravity is the only force that does any work. Pendulum 1 has a bob with a mass of 10kg10kg. Webpractice problem 4. simple-pendulum.txt. The length of the second pendulum is 0.4 times the length of the first pendulum, and the, second pendulum is 0.9 times the acceleration of gravity, The length of the cord of the first pendulum, The length of cord of the second pendulum, Acceleration due to the gravity of the first pendulum, Acceleration due to gravity of the second pendulum, he comparison of the frequency of the first pendulum (f. Hertz. The motion of the particles is constrained: the lengths are l1 and l2; pendulum 1 is attached to a xed point in space and pendulum 2 is attached to the end of pendulum 1. /FontDescriptor 11 0 R /Subtype/Type1 /BaseFont/LQOJHA+CMR7 /FirstChar 33 24 0 obj endobj /Subtype/Type1 Consider a geologist that uses a pendulum of length $35\,{\rm cm}$ and frequency of 0.841 Hz at a specific place on the Earth. Or at high altitudes, the pendulum clock loses some time. /Type/Font 3.5 Pendulum period 72 2009-02-10 19:40:05 UTC / rev 4d4a39156f1e Even if the analysis of the conical pendulum is simple, how is it relevant to the motion of a one-dimensional pendulum? 799.2 642.3 942 770.7 799.4 699.4 799.4 756.5 571 742.3 770.7 770.7 1056.2 770.7 We know that the farther we go from the Earth's surface, the gravity is less at that altitude. /BaseFont/EUKAKP+CMR8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 642.3 856.5 799.4 713.6 685.2 770.7 742.3 799.4 687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.8 562.5 625 312.5 A simple pendulum is defined to have a point mass, also known as the pendulum bob, which is suspended from a string of length L with negligible mass (Figure 15.5.1 ). /Name/F8 stream 8.1 Pendulum experiments Activity 1 Your intuitive ideas To begin your investigation you will need to set up a simple pendulum as shown in the diagram. 680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 706.4 938.5 877 781.8 754 843.3 815.5 877 815.5 endobj Solution: The frequency of a simple pendulum is related to its length and the gravity at that place according to the following formula \[f=\frac {1}{2\pi}\sqrt{\frac{g}{\ell}}\] Solving this equation for $g$, we have \begin{align*} g&=(2\pi f)^2\ell\\&=(2\pi\times 0.601)^2(0.69)\\&=9.84\quad {\rm m/s^2}\end{align*}, Author: Ali Nemati Some simple nonlinear problems in mechanics, for instance, the falling of a ball in fluid, the motion of a simple pendulum, 2D nonlinear water waves and so on, are used to introduce and examine the both methods. 343.8 593.8 312.5 937.5 625 562.5 625 593.8 459.5 443.8 437.5 625 593.8 812.5 593.8 The digital stopwatch was started at a time t 0 = 0 and then was used to measure ten swings of a /FirstChar 33 525 768.9 627.2 896.7 743.3 766.7 678.3 766.7 729.4 562.2 715.6 743.3 743.3 998.9 Web1 Hamiltonian formalism for the double pendulum (10 points) Consider a double pendulum that consists of two massless rods of length l1 and l2 with masses m1 and m2 attached to their ends. g = 9.8 m/s2. /FirstChar 33 /Name/F5 The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo 742.3 799.4 0 0 742.3 599.5 571 571 856.5 856.5 285.5 314 513.9 513.9 513.9 513.9 Based on the equation above, can conclude that mass does not affect the frequency of the simple pendulum. Period is the goal. /FirstChar 33 692.5 323.4 569.4 323.4 569.4 323.4 323.4 569.4 631 507.9 631 507.9 354.2 569.4 631 /Name/F1 /FontDescriptor 23 0 R endobj /Length 2736 << 935.2 351.8 611.1] Resonance of sound wave problems and solutions, Simple harmonic motion problems and solutions, Electric current electric charge magnetic field magnetic force, Quantities of physics in the linear motion. Solution: As stated in the earlier problems, the frequency of a simple pendulum is proportional to the inverse of the square root of its length namely $f \propto 1/\sqrt{\ell}$. 935.2 351.8 611.1] Set up a graph of period vs. length and fit the data to a square root curve. << 826.4 295.1 531.3] Webconsider the modelling done to study the motion of a simple pendulum. /LastChar 196 3.2. What is the period of oscillations? 'z.msV=eS!6\f=QE|>9lqqQ/h%80 t v{"m4T>8|m@pqXAep'|@Dq;q>mr)G?P-| +*"!b|b"YI!kZfIZNh!|!Dwug5c #6h>qp:9j(s%s*}BWuz(g}} ]7N.k=l 537|?IsV endstream >> How might it be improved? << /Pages 45 0 R /Type /Catalog >> Creative Commons Attribution License The period of a simple pendulum is described by this equation. \begin{gather*} T=2\pi\sqrt{\frac{2}{9.8}}=2.85\quad {\rm s} \\ \\ f=\frac{1}{2.85\,{\rm s}}=0.35\quad {\rm Hz}\end{gather*}. >> Which answer is the best answer? /LastChar 196 24/7 Live Expert. Describe how the motion of the pendula will differ if the bobs are both displaced by 1212. 5 0 obj /Type/Font 762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 The equation of period of the simple pendulum : T = period, g = acceleration due to gravity, l = length of cord. 61) Two simple pendulums A and B have equal length, but their bobs weigh 50 gf and l00 gf respectively. Which has the highest frequency? You may not have seen this method before. This shortens the effective length of the pendulum. Dividing this time into the number of seconds in 30days gives us the number of seconds counted by our pendulum in its new location. We will present our new method by rst stating its rules (without any justication) and showing that they somehow end up magically giving the correct answer. 36 0 obj endobj This book uses the by /Contents 21 0 R 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 /Type/Font sin If this doesn't solve the problem, visit our Support Center . In part a i we assumed the pendulum was a simple pendulum one with all the mass concentrated at a point connected to its pivot by a massless, inextensible string. endobj WebThe simple pendulum system has a single particle with position vector r = (x,y,z). How does adding pennies to the pendulum in the Great Clock help to keep it accurate? Exams will be effectively half of an AP exam - 17 multiple choice questions (scaled to 22. Exams: Midterm (July 17, 2017) and . when the pendulum is again travelling in the same direction as the initial motion. 896.3 896.3 740.7 351.8 611.1 351.8 611.1 351.8 351.8 611.1 675.9 546.3 675.9 546.3 This method for determining /BaseFont/UTOXGI+CMTI10 2.8.The motion occurs in a vertical plane and is driven by a gravitational force. For angles less than about 1515, the restoring force is directly proportional to the displacement, and the simple pendulum is a simple harmonic oscillator. 24/7 Live Expert. >> 542.4 542.4 456.8 513.9 1027.8 513.9 513.9 513.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24 0 obj This leaves a net restoring force back toward the equilibrium position at =0=0. Except where otherwise noted, textbooks on this site What is the value of g at a location where a 2.2 m long pendulum has a period of 2.5 seconds? endobj endobj 770.7 628.1 285.5 513.9 285.5 513.9 285.5 285.5 513.9 571 456.8 571 457.2 314 513.9 285.5 799.4 485.3 485.3 799.4 770.7 727.9 742.3 785 699.4 670.8 806.5 770.7 371 528.1 820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 In this case, the period $T$ and frequency $f$ are found by the following formula \[T=2\pi\sqrt{\frac{\ell}{g}}\ , \ f=\frac{1}{T}\] As you can see, the period and frequency of a pendulum are independent of the mass hanged from it. /Type/Font Half of this is what determines the amount of time lost when this pendulum is used as a time keeping device in its new location. What is the period of the Great Clock's pendulum? Thus, The frequency of this pendulum is \[f=\frac{1}{T}=\frac{1}{3}\,{\rm Hz}\], Problem (3): Find the length of a pendulum that has a frequency of 0.5 Hz. /Type/Font /Subtype/Type1 384.3 611.1 675.9 351.8 384.3 643.5 351.8 1000 675.9 611.1 675.9 643.5 481.5 488 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 753.7 1000 935.2 831.5 Mathematically we have x2 1 + y 2 1 = l 2 1; (x2 x1) 2 + (y2 y1)2 = l22: 0 0 0 0 0 0 0 615.3 833.3 762.8 694.4 742.4 831.3 779.9 583.3 666.7 612.2 0 0 772.4 /FontDescriptor 32 0 R /LastChar 196 Compare it to the equation for a straight line. /Name/F3 Want to cite, share, or modify this book? Solution: The period and length of a pendulum are related as below \begin{align*} T&=2\pi\sqrt{\frac{\ell}{g}} \\\\3&=2\pi\sqrt{\frac{\ell}{9.8}}\\\\\frac{3}{2\pi}&=\sqrt{\frac{\ell}{9.8}} \\\\\frac{9}{4\pi^2}&=\frac{\ell}{9.8}\\\\\Rightarrow \ell&=9.8\times\left(\frac{9}{4\pi^2}\right)\\\\&=2.23\quad{\rm m}\end{align*} The frequency and periods of oscillations in a simple pendulum are related as $f=1/T$. /LastChar 196 Solution; Find the maximum and minimum values of \(f\left( {x,y} \right) = 8{x^2} - 2y\) subject to the constraint \({x^2} + {y^2} = 1\). The period of a pendulum on Earth is 1 minute. 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 295.1 <> stream 323.4 354.2 600.2 323.4 938.5 631 569.4 631 600.2 446.4 452.6 446.4 631 600.2 815.5 /Widths[306.7 514.4 817.8 769.1 817.8 766.7 306.7 408.9 408.9 511.1 766.7 306.7 357.8 That's a loss of 3524s every 30days nearly an hour (58:44). What is its frequency on Mars, where the acceleration of gravity is about 0.37 that on Earth? supplemental-problems-thermal-energy-answer-key 1/1 Downloaded from engineering2. x DO2(EZxIiTt |"r>^p-8y:>C&%QSSV]aq,GVmgt4A7tpJ8 C |2Z4dpGuK.DqCVpHMUN j)VP(!8#n 1. 285.5 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 285.5 285.5 endobj 0 0 0 0 0 0 0 615.3 833.3 762.8 694.4 742.4 831.3 779.9 583.3 666.7 612.2 0 0 772.4 [894 m] 3. 570 517 571.4 437.2 540.3 595.8 625.7 651.4 277.8] 460.7 580.4 896 722.6 1020.4 843.3 806.2 673.6 835.7 800.2 646.2 618.6 718.8 618.8 777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 /LastChar 196 to be better than the precision of the pendulum length and period, the maximum displacement angle should be kept below about <> 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 312.5 312.5 342.6 WebSimple Harmonic Motion and Pendulums SP211: Physics I Fall 2018 Name: 1 Introduction When an object is oscillating, the displacement of that object varies sinusoidally with time. All of the methods used were appropriate to the problem and all of the calculations done were error free, so all of them. A classroom full of students performed a simple pendulum experiment. 460 511.1 306.7 306.7 460 255.6 817.8 562.2 511.1 511.1 460 421.7 408.9 332.2 536.7 /BaseFont/WLBOPZ+CMSY10 Each pendulum hovers 2 cm above the floor. 833.3 1444.4 1277.8 555.6 1111.1 1111.1 1111.1 1111.1 1111.1 944.4 1277.8 555.6 1000 42 0 obj WebThe section contains questions and answers on undetermined coefficients method, harmonic motion and mass, linear independence and dependence, second order with variable and constant coefficients, non-homogeneous equations, parameters variation methods, order reduction method, differential equations with variable coefficients, rlc not harmonic or non-sinusoidal) response of a simple pendulum undergoing moderate- to large-amplitude oscillations. This part of the question doesn't require it, but we'll need it as a reference for the next two parts. Notice how length is one of the symbols. Adding one penny causes the clock to gain two-fifths of a second in 24hours. /FirstChar 33 @ @y ss~P_4qu+a" ' 9y c&Ls34f?q3[G)> `zQGOxis4t&0tC: pO+UP=ebLYl*'zte[m04743C 3d@C8"P)Dp|Y /Name/F5 WebSimple pendulum definition, a hypothetical apparatus consisting of a point mass suspended from a weightless, frictionless thread whose length is constant, the motion of the body about the string being periodic and, if the angle of deviation from the original equilibrium position is small, representing simple harmonic motion (distinguished from physical pendulum). /Subtype/Type1 /FirstChar 33 570 517 571.4 437.2 540.3 595.8 625.7 651.4 277.8] /Widths[1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 Examples of Projectile Motion 1. g 384.3 611.1 675.9 351.8 384.3 643.5 351.8 1000 675.9 611.1 675.9 643.5 481.5 488 WebA simple pendulum is defined to have an object that has a small mass, also known as the pendulum bob, which is suspended from a light wire or string, such as shown in Figure 16.13. /Name/F7 Simple Harmonic Motion describes this oscillatory motion where the displacement, velocity and acceleration are sinusoidal. 30 0 obj WebThe simple pendulum system has a single particle with position vector r = (x,y,z). <>/ExtGState<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> 0 0 0 0 0 0 0 0 0 0 777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 0 0 777.8 endobj << Second method: Square the equation for the period of a simple pendulum. /FirstChar 33 324.7 531.3 531.3 531.3 531.3 531.3 795.8 472.2 531.3 767.4 826.4 531.3 958.7 1076.8 If the length of the cord is increased by four times the initial length, then determine the period of the harmonic motion. (7) describes simple harmonic motion, where x(t) is a simple sinusoidal function of time. 8 0 obj WebView Potential_and_Kinetic_Energy_Brainpop. /Name/F4 29. WebThe essence of solving nonlinear problems and the differences and relations of linear and nonlinear problems are also simply discussed. endobj Given: Length of pendulum = l = 1 m, mass of bob = m = 10 g = 0.010 kg, amplitude = a = 2 cm = 0.02 m, g = 9.8m/s 2. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 642.9 885.4 806.2 736.8 WebSimple Pendulum Calculator is a free online tool that displays the time period of a given simple. endobj Websome mistakes made by physics teachers who retake models texts to solve the pendulum problem, and finally, we propose the right solution for the problem fashioned as on Tipler-Mosca text (2010). << /Type /XRef /Length 85 /Filter /FlateDecode /DecodeParms << /Columns 5 /Predictor 12 >> /W [ 1 3 1 ] /Index [ 18 54 ] /Info 16 0 R /Root 20 0 R /Size 72 /Prev 140934 /ID [<8a3b51e8e1dcde48ea7c2079c7f2691d>] >> Restart your browser. 639.7 565.6 517.7 444.4 405.9 437.5 496.5 469.4 353.9 576.2 583.3 602.5 494 437.5 295.1 826.4 501.7 501.7 826.4 795.8 752.1 767.4 811.1 722.6 693.1 833.5 795.8 382.6 /BaseFont/JFGNAF+CMMI10 |l*HA /Type/Font 500 500 611.1 500 277.8 833.3 750 833.3 416.7 666.7 666.7 777.8 777.8 444.4 444.4 /FirstChar 33 877 0 0 815.5 677.6 646.8 646.8 970.2 970.2 323.4 354.2 569.4 569.4 569.4 569.4 569.4 /FirstChar 33 are licensed under a, Introduction: The Nature of Science and Physics, Introduction to Science and the Realm of Physics, Physical Quantities, and Units, Accuracy, Precision, and Significant Figures, Introduction to One-Dimensional Kinematics, Motion Equations for Constant Acceleration in One Dimension, Problem-Solving Basics for One-Dimensional Kinematics, Graphical Analysis of One-Dimensional Motion, Introduction to Two-Dimensional Kinematics, Kinematics in Two Dimensions: An Introduction, Vector Addition and Subtraction: Graphical Methods, Vector Addition and Subtraction: Analytical Methods, Dynamics: Force and Newton's Laws of Motion, Introduction to Dynamics: Newtons Laws of Motion, Newtons Second Law of Motion: Concept of a System, Newtons Third Law of Motion: Symmetry in Forces, Normal, Tension, and Other Examples of Forces, Further Applications of Newtons Laws of Motion, Extended Topic: The Four Basic ForcesAn Introduction, Further Applications of Newton's Laws: Friction, Drag, and Elasticity, Introduction: Further Applications of Newtons Laws, Introduction to Uniform Circular Motion and Gravitation, Fictitious Forces and Non-inertial Frames: The Coriolis Force, Satellites and Keplers Laws: An Argument for Simplicity, Introduction to Work, Energy, and Energy Resources, Kinetic Energy and the Work-Energy Theorem, Introduction to Linear Momentum and Collisions, Collisions of Point Masses in Two Dimensions, Applications of Statics, Including Problem-Solving Strategies, Introduction to Rotational Motion and Angular Momentum, Dynamics of Rotational Motion: Rotational Inertia, Rotational Kinetic Energy: Work and Energy Revisited, Collisions of Extended Bodies in Two Dimensions, Gyroscopic Effects: Vector Aspects of Angular Momentum, Variation of Pressure with Depth in a Fluid, Gauge Pressure, Absolute Pressure, and Pressure Measurement, Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action, Fluid Dynamics and Its Biological and Medical Applications, Introduction to Fluid Dynamics and Its Biological and Medical Applications, The Most General Applications of Bernoullis Equation, Viscosity and Laminar Flow; Poiseuilles Law, Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes, Temperature, Kinetic Theory, and the Gas Laws, Introduction to Temperature, Kinetic Theory, and the Gas Laws, Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature, Introduction to Heat and Heat Transfer Methods, The First Law of Thermodynamics and Some Simple Processes, Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency, Carnots Perfect Heat Engine: The Second Law of Thermodynamics Restated, Applications of Thermodynamics: Heat Pumps and Refrigerators, Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy, Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation, Introduction to Oscillatory Motion and Waves, Hookes Law: Stress and Strain Revisited, Simple Harmonic Motion: A Special Periodic Motion, Energy and the Simple Harmonic Oscillator, Uniform Circular Motion and Simple Harmonic Motion, Speed of Sound, Frequency, and Wavelength, Sound Interference and Resonance: Standing Waves in Air Columns, Introduction to Electric Charge and Electric Field, Static Electricity and Charge: Conservation of Charge, Electric Field: Concept of a Field Revisited, Conductors and Electric Fields in Static Equilibrium, Introduction to Electric Potential and Electric Energy, Electric Potential Energy: Potential Difference, Electric Potential in a Uniform Electric Field, Electrical Potential Due to a Point Charge, Electric Current, Resistance, and Ohm's Law, Introduction to Electric Current, Resistance, and Ohm's Law, Ohms Law: Resistance and Simple Circuits, Alternating Current versus Direct Current, Introduction to Circuits and DC Instruments, DC Circuits Containing Resistors and Capacitors, Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field, Force on a Moving Charge in a Magnetic Field: Examples and Applications, Magnetic Force on a Current-Carrying Conductor, Torque on a Current Loop: Motors and Meters, Magnetic Fields Produced by Currents: Amperes Law, Magnetic Force between Two Parallel Conductors, Electromagnetic Induction, AC Circuits, and Electrical Technologies, Introduction to Electromagnetic Induction, AC Circuits and Electrical Technologies, Faradays Law of Induction: Lenzs Law, Maxwells Equations: Electromagnetic Waves Predicted and Observed, Introduction to Vision and Optical Instruments, Limits of Resolution: The Rayleigh Criterion, *Extended Topic* Microscopy Enhanced by the Wave Characteristics of Light, Photon Energies and the Electromagnetic Spectrum, Probability: The Heisenberg Uncertainty Principle, Discovery of the Parts of the Atom: Electrons and Nuclei, Applications of Atomic Excitations and De-Excitations, The Wave Nature of Matter Causes Quantization, Patterns in Spectra Reveal More Quantization, Introduction to Radioactivity and Nuclear Physics, Introduction to Applications of Nuclear Physics, The Yukawa Particle and the Heisenberg Uncertainty Principle Revisited, Particles, Patterns, and Conservation Laws, A simple pendulum has a small-diameter bob and a string that has a very small mass but is strong enough not to stretch appreciably.

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