Precalculus Honors 3.4 Newton s Law of Cooling November 8, 2005 Mr. DeSalvo


 Muriel Holmes
 1 years ago
 Views:
Transcription
1 Precalculus Honors 3.4 Newton s Law of Cooling November 8, 2005 Mr. DeSalvo Isaac Newton ( ) proposed that the temperature of a hot object decreases at a rate proportional to the difference between its temperature and the temperature of its surroundings. Similarly, a cold object heats up at a rate proportional to the temperature difference between the object and the temperature of its surroundings. In this section, we will explore this concept known as Newton s Law of Cooling. EXAMPLE Imagine that on a cold autumn day you pour yourself a hot cup of coffee and place it on a table. Originally, the temperature of the coffee was 200 F and the temperature of the room was 70 F. Let t n be the temperature of the coffee n minutes after you place it on the table. 1. Make a careful sketch of what you think the temperature (in F) would look like as a function of the time (in minutes). Label the vertical axes temperature ( F) and the horizontal axis time (minutes). Solution: 350 Temperature of a Cup of Coffee ( F) Time (minutes) What is the value of t 0? Solution: t 0 = 200 F. 3. Over the long run, what will happen to the temperature of the coffee? Solution: Over the long run, the temperature of the coffee will level off at 70 F.
2 Newton s Law of Cooling states: the temperature of a hot object decreases at a rate proportional to the difference between its temperature and the temperature of its surroundings. In other words, for your cup of coffee, t n+1 t n = k(t n 70) for some unknown constant k. 4. Suppose that one minute after you place the cup of coffee on the table, its temperature is 180 F. Use this information to determine the value of k. Solution: We know, by Newton s Law of Cooling, that, t n+1 t n = k(t n 70). We also know that t 0 = 200 and t 1 = 180, thus we have = k(200 70). Solving for k, we obtain k = ( )/(200 70) = 20/130 = 2/ Based on your answer to question 4, you now have enough information to completely determine the recursive formula for a sequence T that will generate the successive terms that give the temperature of the coffee, n minutes after it is placed in a room whose temperature is 70 F. Solution: t 0 = 200;, t n+1 t n = (2/13)(t n 70). 6. Rewrite the recursive equation from part (5) so that it expresses t n+1 in terms of t n. (this will put the equation in standard form like the drug concentration model.) Solution: All we need to do here is add t n to both sides and simplify. Doing so, we obtain : t 0 = 200;, t n+1 = (11/13)t n + 140/13. EXERCISE 1. Use your TI (or make a spreadsheet) to generate successive terms of the sequence T. (If using the TI, remember that you first type 200 and hit ENTER. Next, type (11/13)Ans + 140/13 and hit ENTER again. From here on, each time you hit ENTER you will get a successive term of the sequence. To see the long run behavior, you need to hit ENTER about 40 times.) 2. According to question 1, what is the equilibrium point of this model? Why does this make sense given the physical conditions of this problem situation? 3. Find the equilibrium point of this model algebraically. 4. Use the method of iteration to find an explicit formula for t n. Check your answer by generating the first five terms of sequence T both recursively and explicitly. 5. Use your TI (or make a spreadsheet) to find when the temperature of the coffee will reach 85 F. 6. Repeat question 5 using your explicit formula.
3 HOMEWORK QUESTIONS 1. You bake a yam for Mr. DeSalvo at 350, and when you remove it from the oven, you let the yam cool in your dorm room, which has a temperature of 68 F. After 10 minutes, the yam has cooled to 240 F. Let t n be the temperature of the yam n 10minute periods after you take it out of the oven. (a) Write a complete recursive formula for sequence T using Newton s Law of Cooling. (b) Make a spreadsheet that generates and graphs sequence T. Use enough terms to show the longterm behavior. Save your work as yam SS and print it out. (c) Find an explicit formula for t n using the method of iteration. (d) What is the temperature of the yam 1 hour after you take it out of the oven? (e) When will the temperature of the yam be 75 F. 2. Newton s Law of Heating uses the same mathematical model as the law of cooling. Suppose you take some soup from the dining room and place it in your refrigerator. Later that evening you take the soup, which is now cooled to 36 F, and place it in an oven that has been preheated to 400 F. Five minutes later, the temperature of the soup is 120 F. (a) Let T be a sequence that gives the temperature of the soup over time. Write a recursive formula for the sequence T using Newton s Law of Cooling, which has now become Newton s Law of Heating. (b) Find the equilibrium point of this model. How do you know this? (c) Make a spreadsheet that generates and graphs sequence T. Use enough terms to show the longterm behavior. Save your work as heating soup SS and print it out. (d) Find an explicit formula for t n using the method of iteration. (e) Using your model, when will the temperature of the soup reach 350 F. 3. CSI St. Andrew s. When a murder is committed, the body, usually at 98.6 F, cools according to Newton s Law of Cooling. Suppose that two hours after a murder is committed, the temperature of the body is 95 F, and the temperature of the surrounding air is a constant 68 F.
4 (a) Let H be a sequence that gives the temperature of the body over time. Write a recursive formula for the sequence H using Newton s Law of Cooling. (b) Find the equilibrium point of this model. How do you know this? (c) Make a spreadsheet that generates and graphs sequence H. Use enough terms to show the longterm behavior. Save your work as time of death SS and print it out. (d) Find an explicit formula for h n using the method of iteration. (e) Suppose a body is found at 4 pm at a temperature of 86 F. Using your model, determine the time the time of death. Newton, Sir Isaac ( ), mathematician and physicist, one of the foremost scientific intellects of all time. Born at Woolsthorpe, near Grantham in Lincolnshire, where he attended school, he entered Cambridge University in 1661; he was elected a Fellow of Trinity College in 1667, and Lucasian Professor of Mathematics in He remained at the university, lecturing in most years, until Of these Cambridge years, in which Newton was at the height of his creative power, he singled out (spent largely in Lincolnshire because of plague in Cambridge) as "the prime of my age for invention". During two to three years of intense mental effort he prepared Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) commonly known as the Principia, although this was not published until As a firm opponent of the attempt by King James II to make the universities into Catholic institutions, Newton was elected Member of Parliament for the University of Cambridge to the Convention Parliament of 1689, and sat again in Meanwhile, in 1696 he had moved to London as Warden of the Royal Mint. He became Master of the Mint in 1699, an office he retained to his death. He was elected a Fellow of the Royal Society of London in 1671, and in 1703 he became President, being annually reelected for the rest of his life. His major work, Opticks, appeared the next year; he was knighted in Cambridge in 1705.
5 As Newtonian science became increasingly accepted on the Continent, and especially after a general peace was restored in 1714, following the War of the Spanish Succession, Newton became the most highly esteemed natural philosopher in Europe. His last decades were passed in revising his major works, polishing his studies of ancient history, and defending himself against critics, as well as carrying out his official duties. Newton was modest, diffident, and a man of simple tastes. He was angered by criticism or opposition, and harboured resentment; he was harsh towards enemies but generous to friends. In government, and at the Royal Society, he proved an able administrator. He never married and lived modestly, but was buried with great pomp in Westminster Abbey. Newton has been regarded for almost 300 years as the founding exemplar of modern physical science, his achievements in experimental investigation being as innovative as those in mathematical research. With equal, if not greater, energy and originality he also plunged into chemistry, the early history of Western civilization, and theology; among his special studies was an investigation of the form and dimensions, as described in the Bible, of Solomon's Temple in Jerusalem. (The above information was taken from and Microsoft Encarta.)
Isaac Newton. History Of Scientist An Article. Powered By Laaxmi Software  Tiruchengode. Laaxmi Software Tiruchengode I INTRODUCTION
Isaac Newton I INTRODUCTION Newton, Sir Isaac (16421727), mathematician and physicist, one of the foremost scientific intellects of all time. Born at Woolsthorpe, near Grantham in Lincolnshire, where
More informationChapter 19 Classwork Famous Scientist Biography Isaac...
Chapter 19 Classwork Famous Scientist Biography Isaac... Score: 1. is perhaps the greatest physicist who has ever lived. 1@1 2. He and are almost equally matched contenders for this title. 1@1 3. Each
More informationThe History and Philosophy of Astronomy
Astronomy 350L (Spring 2005) The History and Philosophy of Astronomy (Lecture 13: Newton I) Instructor: Volker Bromm TA: Amanda Bauer The University of Texas at Austin Isaac Newton: Founding Father of
More informationUsing Recursion in Models and Decision Making: Recursion Using Rate of Change IV.C Student Activity Sheet 5: Newton s Law of Cooling
Have you ever noticed that a container of cold liquid, such as a glass of iced tea, creates condensation on the outside of the container? Or that a cup of hot coffee does not always stay hot? What happened
More informationThe History and Philosophy of Astronomy
Astronomy 350L (Fall 2006) The History and Philosophy of Astronomy (Lecture 14: Newton) Instructor: Volker Bromm TA: Jarrett Johnson The University of Texas at Austin Isaac Newton: Founding Father of Physics
More informationNewton. Inderpreet Singh
Newton Inderpreet Singh May 9, 2015 In the past few eras, there have been many philosophers who introduced many new things and changed our view of thinking.. In the fields of physics, chemistry and mathematics,
More informationIsaac Newton: Development of the Calculus and a Recalculation of π
Isaac Newton: Development of the Calculus and a Recalculation of π Waseda University, SILS, History of Mathematics Outline Introduction Early modern Britain The early modern period in Britain The early
More informationTopic Page: Newton, Isaac,
Topic Page: Newton, Isaac, 16421727 Definition: Newton, Isaac 16421727, from Dictionary of Energy English mathematician and natural philosopher considered by many to be the most influential scientist
More informationVenus Phases & Newton s Laws
Venus Phases & Newton s Laws Homework: Questions? Seasons: Count the number of days! Winter is shortest (in northern hemisphere) Copernicus did away with major but not minor epicycles Thanks a lot for
More informationMathematics Foundation for College. Lesson Number 8a. Lesson Number 8a Page 1
Mathematics Foundation for College Lesson Number 8a Lesson Number 8a Page 1 Lesson Number 8 Topics to be Covered in this Lesson Coordinate graphing, linear equations, conic sections. Lesson Number 8a Page
More informationO1 History of Mathematics Lecture V Newton s Principia. Monday 24th October 2016 (Week 3)
O1 History of Mathematics Lecture V Newton s Principia Monday 24th October 2016 (Week 3) Summary Isaac Newton (1642 1727) Kepler s laws, Descartes theory, Hooke s conjecture The Principia Editions and
More informationCritical Thinking: Sir Isaac Newton
Critical Thinking: Sir Isaac Name: Date: Watch this NOVA program on while finding the answers for the following questions: https://www.youtube.com/watch?v=yprv1h3cgqk 1.In 19 a British Economist named
More informationInventors and Scientists: Sir Isaac Newton
Inventors and Scientists: Sir Isaac Newton By Cynthia Stokes Brown, Big History Project on 07.30.16 Word Count 909 Portrait of Sir Isaac Newton circa 17151720 Bonhams Synopsis: Sir Isaac Newton developed
More informationInventors and Scientists: Sir Isaac Newton
Inventors and Scientists: Sir Isaac Newton By Big History Project, adapted by Newsela staff on 07.30.16 Word Count 751 Portrait of Sir Isaac Newton circa 17151720 Bonhams Synopsis: Sir Isaac Newton developed
More informationFluxions and Fluents. by Jenia Tevelev
Fluxions and Fluents by Jenia Tevelev 1 2 Mathematics in the late 16th  early 17th century Simon Stevin (1548 1620) wrote a short pamphlet La Disme, where he introduced decimal fractions to a wide audience.
More informationTHE SCIENTIFIC REVOLUTION
THE SCIENTIFIC REVOLUTION REVOLUTION: a sudden, extreme, or complete change in the way people live, work, etc. (MerriamWebster) THE SCIENTIFIC REVOLUTION Time of advancements in math and science during
More informationThe History and Philosophy of Astronomy
Astronomy 350L (Spring 2005) The History and Philosophy of Astronomy (Lecture 14: Newton II) Instructor: Volker Bromm TA: Amanda Bauer The University of Texas at Austin En Route to the Principia Newton
More informationCritical Thinking: Sir Isaac Newton
Critical Thinking: Sir Isaac Name: Date: Watch this NOVA program on while finding the answers for the following questions: https://www.youtube.com/watch?v=yprv1h3cgqk 1.In 1936 a British Economist name
More informationSIR ISAAC NEWTON ( )
SIR ISAAC NEWTON (16421727) PCES 2.39 Born in the small village of Woolsthorpe, Newton quickly made an impression as a student at Cambridge he was appointed full Prof. there The young Newton in 1669,
More informationMT410 EXAM 1 SAMPLE 1 İLKER S. YÜCE DECEMBER 13, 2010 QUESTION 1. SOLUTIONS OF SOME DIFFERENTIAL EQUATIONS. dy dt = 4y 5, y(0) = y 0 (1) dy 4y 5 =
MT EXAM SAMPLE İLKER S. YÜCE DECEMBER, SURNAME, NAME: QUESTION. SOLUTIONS OF SOME DIFFERENTIAL EQUATIONS where t. (A) Classify the given equation in (). = y, y() = y () (B) Solve the initial value problem.
More informationSTATION #1: NICOLAUS COPERNICUS
STATION #1: NICOLAUS COPERNICUS Nicolaus Copernicus was a Polish astronomer who is best known for the astronomical theory that the Sun was near the center of the universe and that the Earth and other planets
More information9.2 Taylor Polynomials
9.2 Taylor Polynomials Taylor Polynomials and Approimations Polynomial functions can be used to approimate other elementary functions such as sin, Eample 1: f at 0 Find the equation of the tangent line
More informationINTRO TO LIMITS & CALCULUS MR. VELAZQUEZ AP CALCULUS
INTRO TO LIMITS & CALCULUS MR. VELAZQUEZ AP CALCULUS WHAT IS CALCULUS? Simply put, Calculus is the mathematics of change. Since all things change often and in many ways, we can expect to understand a wide
More informationWinward 1. Sir Isaac Newton. By Robert Winward. Physics Howard Demars
Winward 1 Sir Isaac Newton By Robert Winward Physics 1010 Howard Demars Winward 2 Introduction He was overly sensitive to criticism. His hair turned gray at thirty. He never married (Hewitt, 2011, p. 66).
More informationExam 3 MATH Calculus I
Trinity College December 03, 2015 MATH 13101 Calculus I By signing below, you attest that you have neither given nor received help of any kind on this exam. Signature: Printed Name: Instructions: Show
More informationOne common method of shaping
L A B 7 NEWTON S LAW OF COOLING Exponential Decay One common method of shaping plastic products is to pour hot plastic resin into a mold. The resin, which was poured at a temperature of 300 F, is then
More informationMechanics and the Foundations of Modern Physics. T. Helliwell V. Sahakian
Mechanics and the Foundations of Modern Physics T. Helliwell V. Sahakian Contents 1 Newtonian particle mechanics 3 1.1 Inertial frames and the Galilean transformation........ 3 1.2 Newton s laws of motion.....................
More informationExercise Set 2.1. Notes: is equivalent to AND ; both statements must be true for the statement to be true.
Exercise Set 2.1 10) Let p be the statement DATAENDFLAG is off, q the statement ERROR equals 0, and r the statement SUM is less than 1,000. Express the following sentences in symbolic notation. Notes:
More informationThe History of Motion. Ms. Thibodeau
The History of Motion Ms. Thibodeau Aristotle Aristotle aka the Philosopher was a Greek philosopher more than 2500 years ago. He wrote on many subjects including physics, poetry, music, theater, logic,
More informationLECTURE 10: Newton's laws of motion
LECTURE 10: Newton's laws of motion Select LEARNING OBJECTIVES: i. ii. iii. iv. v. vi. vii. viii. Understand that an object can only change its speed or direction if there is a net external force. Understand
More informationLecture 7: Sections 2.3 and 2.4 Rational and Exponential Functions. Recall that a power function has the form f(x) = x r where r is a real number.
L71 Lecture 7: Sections 2.3 and 2.4 Rational and Exponential Functions Recall that a power function has the form f(x) = x r where r is a real number. f(x) = x 1/2 f(x) = x 1/3 ex. Sketch the graph of
More informationIsaac Newton and the Laws of Motion and Gravitation 1
Isaac Newton and the Laws of Motion and Gravitation 1 ASTR 101 10/16/2017 Newton s laws of motion Newton s law of universal gravitation Orbits, Newton s cannonball experiment Mass and weight Weightlessness
More informationExponential Growth (Doubling Time)
Exponential Growth (Doubling Time) 4 Exponential Growth (Doubling Time) Suppose we start with a single bacterium, which divides every hour. After one hour we have 2 bacteria, after two hours we have 2
More information1. Under certain conditions the number of bacteria in a particular culture doubles every 10 seconds as shown by the graph below.
Exponential Functions Review Packet (from November Questions) 1. Under certain conditions the number of bacteria in a particular culture doubles every 10 seconds as shown by the graph below. 8 7 6 Number
More informationNEWTON S LAWS OF MOTION. Review
NEWTON S LAWS OF MOTION Review BACKGROUND Sir Isaac Newton (16431727) an English scientist and mathematician famous for his discovery of the law of gravity also discovered the three laws of motion. He
More informationChapter 5 Newton s Universe
Chapter 5 Newton s Universe Lecture notes about gravitation Dr. Armen Kocharian Units of Chapter 5 The Idea of Gravity: The Apple and the Moon The Law of Gravity: Moving the Farthest Star Gravitational
More informationMath 1120, Section 6 Calculus Test 3
November 15, 2012 Name The total number of points available is 158 Throughout this test, show your work Using a calculator to circumvent ideas discussed in class will generally result in no credit In general
More informationIsaac Newton. Isaac Newton, Woolsthorpe Manor
Isaac Newton Nature, and Nature s Laws lay hid in Night. God said, Let Newton be! and All was Light. SC/STS 3760, XIV 1 Isaac Newton, 16421727 Born December 25, 1642 by the Julian Calendar or January
More informationSequence. A list of numbers written in a definite order.
Sequence A list of numbers written in a definite order. Terms of a Sequence a n = 2 n 2 1, 2 2, 2 3, 2 4, 2 n, 2, 4, 8, 16, 2 n We are going to be mainly concerned with infinite sequences. This means we
More information7.1 Indefinite Integrals Calculus
7.1 Indefinite Integrals Calculus Learning Objectives A student will be able to: Find antiderivatives of functions. Represent antiderivatives. Interpret the constant of integration graphically. Solve differential
More informationRedhound Day 2 Assignment (continued)
Redhound Day 2 Assignment (continued) Directions: Watch the power point and answer the questions on the last slide Which Law is It? on your own paper. You will turn this in for a grade. Background Sir
More informationLesson 2  The Copernican Revolution
Lesson 2  The Copernican Revolution READING ASSIGNMENT Chapter 2.1: Ancient Astronomy Chapter 2.2: The Geocentric Universe Chapter 2.3: The Heliocentric Model of the Solar System Discovery 21: The Foundations
More informationNewton s Laws of Motion. Steve Case NMGK8 University of Mississippi October 2005
Newton s Laws of Motion Steve Case NMGK8 University of Mississippi October 2005 Background Sir Isaac Newton (16431727) an English scientist and mathematician famous for his discovery of the law of gravity
More informationNewton s Cooling Model in Matlab and the Cooling Project!
Newton s Cooling Model in Matlab and the Cooling Project! James K. Peterson Department of Biological Sciences and Department of Mathematical Sciences Clemson University March 10, 2014 Outline Your Newton
More informationExercise 4) Newton's law of cooling is a model for how objects are heated or cooled by the temperature of an ambient medium surrounding them.
Exercise 4) Newton's law of cooling is a model for how objects are heated or cooled by the temperature of an ambient medium surrounding them. In this model, the bo temperature T = T t changes at a rate
More informationThe Isaac Newton School Of Driving: Physics And Your Car By Barry Parker READ ONLINE
The Isaac Newton School Of Driving: Physics And Your Car By Barry Parker READ ONLINE If you are searched for a book by Barry Parker The Isaac Newton School of Driving: Physics and Your Car in pdf format,
More informationEngineering Systems & Investigation. Dynamic Systems Fundamentals
Engineering Systems & Investigation Dynamic Systems Fundamentals Dynamics: Linear Motion Linear Motion Equations s.u.v.a.t s = Displacement. u = Initial Velocity. v = Final Velocity. a = Acceleration.
More informationDifferential Equations
Chapter 7 Differential Equations 7. An Introduction to Differential Equations Motivating Questions In this section, we strive to understand the ideas generated by the following important questions: What
More informationRobert Hooke ( ) Arguably the greatest experimental natural philosopher of the 17 th century
? Robert Hooke (16351703) Arguably the greatest experimental natural philosopher of the 17 th century His most famous work is Micrographia, in which he coined the term "cell" for a basic biological structure.
More informationBe on time Switch off mobile phones. Put away laptops. Being present = Participating actively
A couple of house rules Be on time Switch off mobile phones Put away laptops Being present = Participating actively Het basisvak Toegepaste Natuurwetenschappen http://www.phys.tue.nl/nfcmr/natuur/collegenatuur.html
More informationModels of the Solar System. The Development of Understanding from Ancient Greece to Isaac Newton
Models of the Solar System The Development of Understanding from Ancient Greece to Isaac Newton Aristotle (384 BC 322 BC) Third in line of Greek thinkers: Socrates was the teacher of Plato, Plato was the
More informationMath 2930 Worksheet Equilibria and Stability
Math 2930 Worksheet Equilibria and Stabilit Week 3 September 7, 2017 Question 1. (a) Let C be the temperature (in Fahrenheit) of a cup of coffee that is cooling off to room temperature. Which of the following
More informationPreCalculus Honors Summer Assignment
PreCalculus Honors Summer Assignment Dear Future PreCalculus Honors Student, Congratulations on your successful completion of Algebra! Below you will find the summer assignment questions. It is assumed
More informationLecture 4: Newton s Laws
Lecture 4: Newton s Laws! Galileo (cont)! Newton! Laws of motion Sidney Harris This week: read Chapter 3 of text 9/6/18 1 Impact of Galileo s observations! Chipping away at Aristotelian point of view:!
More informationASTR 1010 Spring 2016 Study Notes Dr. Magnani
The Copernican Revolution ASTR 1010 Spring 2016 Study Notes Dr. Magnani The Copernican Revolution is basically how the West intellectually transitioned from the Ptolemaic geocentric model of the Universe
More informationLecture 16 Newton on Space, Time, and Motion
Lecture 16 Newton on Space, Time, and Motion Patrick Maher Philosophy 270 Spring 2010 Isaac Newton 1642: Born in a rural area 100 miles north of London, England. 1669: Professor of mathematics at Cambridge
More informationc4 d 4 + c 3 d 3 + c 2 d 2 + c 1 d + c 0
2.3 Newton s Proportional Method 125 Exercise 2.31. (a) By expanding with the binomial theorem and gathering together common powers of y, show that with the substitution x = d + y, the polynomial, p (x)
More informationIsaac Newton Benjamin Franklin Michael Faraday
Isaac Newton (4 January 1643 31 March 1727) was born and raised in England. He was a greater thinker and made many discoveries in physics, mathematics, and astronomy. Newton was the first to describe the
More informationDate: Tuesday, 21 October :00PM. Location: Museum of London
Newton's Laws Transcript Date: Tuesday, 21 October 20141:00PM Location: Museum of London 21 October 2014 Newton s Laws Professor Raymond Flood Slide: Title of talk Thank you for coming along. This is
More informationDifferential Equations
Differential Equations Collège AndréChavanne Genève richard.odonovan@edu.ge.ch 2012 2 1 INITIAL PROBLEMS 1 Initial problems Exercise 1 Radioactivity is due to the decay of nuclei in the atoms. The following
More informationSpring 2015, Math 111 Lab 8: Newton s Method
Spring 2015, Math 111 Lab 8: William and Mary April 7, 2015 Spring 2015, Math 111 Lab 8: Historical Outline Intuition Learning Objectives Today, we will be looking at applications of. Learning Objectives:
More informationMA 180 Lecture. Chapter 0. College Algebra and Calculus by Larson/Hodgkins. Fundamental Concepts of Algebra
0.) Real Numbers: Order and Absolute Value Definitions: Set: is a collection of objections in mathematics Real Numbers: set of numbers used in arithmetic MA 80 Lecture Chapter 0 College Algebra and Calculus
More informationTypes of Curves. From `A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball.
Calculus CURVES Types of Curves In the second book Descartes divides curves into two classes, namely, geometrical and mechanical curves. He defines geometrical curves as those which can be generated by
More informationPrincipia : Vol. 1 The Motion Of Bodies By Florian Cajori, Isaac Newton
Principia : Vol. 1 The Motion Of Bodies By Florian Cajori, Isaac Newton If searching for a book Principia : Vol. 1 The Motion of Bodies by Florian Cajori, Isaac Newton in pdf form, then you've come to
More informationMeasuring Newton's Constant of Universal Gravitation using a Gravitational Torsion Balance
Journal of the Advanced Undergraduate Physics Laboratory Investigation Volume 1 Issue 1 Article 5 2013 Measuring Newton's Constant of Universal Gravitation using a Gravitational Torsion Balance Zachary
More informationName Class Date. Ptolemy alchemy Scientific Revolution
Name Class Date The Scientific Revolution Vocabulary Builder Section 1 DIRECTIONS Look up the vocabulary terms in the word bank in a dictionary. Write the dictionary definition of the word that is closest
More informationAlan Mortimer PhD. Ideas of Modern Physics
Alan Mortimer PhD Ideas of Modern Physics Introductory Remarks Lecture Series Outline 1. Foundations of Modern Physics 2. A Window on the Modern World Electromagnetism & Relativity 3. Quantum Physics and
More information2. (12 points) Find an equation for the line tangent to the graph of f(x) =
November 23, 2010 Name The total number of points available is 153 Throughout this test, show your work Throughout this test, you are expected to use calculus to solve problems Graphing calculator solutions
More informationFundamental Algorithms
Fundamental Algorithms Chapter 1: Introduction Jan Křetínský Winter 2016/17 Chapter 1: Introduction, Winter 2016/17 1 Part I Overview Chapter 1: Introduction, Winter 2016/17 2 Organization Extent: 2 SWS
More information102: Exponential Function Introduction
Math 95 102: Exponential Function Introduction Quadratic functions, like y = x B, are made of a sum of powers of the independent variable. In a quadratic function, the variables are in the base of the
More informationMathematics for Computer Scientists
Mathematics for Computer Scientists Lecture notes for the module G51MCS Venanzio Capretta University of Nottingham School of Computer Science Chapter 6 Modular Arithmetic 6.1 Pascal s Triangle One easy
More informationPaper read at History of Science Society 2014 Annual Meeting, Chicago, Nov. 9,
Euler s Mechanics as Opposition to Leibnizian Dynamics 1 Nobumichi ARIGA 2 1. Introduction Leonhard Euler, the notable mathematician in the eighteenth century, is also famous for his contributions to mechanics.
More informationNewton s Law of Motion
Newton s Law of Motion Physics 211 Syracuse University, Physics 211 Spring 2019 Walter Freeman February 11, 2019 W. Freeman Newton s Law of Motion February 11, 2019 1 / 1 Announcements Homework 3 due Friday
More informationPreAP Algebra 2 Lesson 15 Linear Functions
Lesson 15 Linear Functions Objectives: Students will be able to graph linear functions, recognize different forms of linear functions, and translate linear functions. Students will be able to recognize
More informationActivity Title: It s Either Very Hot or Very Cold Up There!
Grades 35 Teacher Pages Activity Title: It s Either Very Hot or Very Cold Up There! Activity Objective(s): In this activity, and the followup activity next week, teams will design and conduct experiments
More informationMay the mass times acceleration be with you. Sir Isaac Newton
May the mass times acceleration be with you Sir Isaac Newton OBE 1 Newton? Alexander Pope s Epitaph Nature and Nature s laws lay hid in night: God said, "Let Newton be!" and all was light. c.f. Genesis
More informationWho invented Calculus Newton or Leibniz? Join me in this discussion on Sept. 4, 2018.
Who invented Calculus Newton or Leibniz? Join me in this discussion on Sept. 4, 208. Sir Isaac Newton idology.wordpress.com Gottfried Wilhelm Leibniz et.fhkoeln.de Welcome to BC Calculus. I hope that
More informationChapter 11 Logarithms
Chapter 11 Logarithms Lesson 1: Introduction to Logs Lesson 2: Graphs of Logs Lesson 3: The Natural Log Lesson 4: Log Laws Lesson 5: Equations of Logs using Log Laws Lesson 6: Exponential Equations using
More informationActivity 6. Exploring the Exponential Function. Objectives. Introduction
Objectives Activity 6 Exploring the Exponential Function Differentiate between exponential growth or decay from an equation Identify the coefficient in an equation that represents the rate of growth/decay
More informationSpeed/Velocity in a Circle
Speed/Velocity in a Circle Speed is the MAGNITUDE of the velocity. And while the speed may be constant, the VELOCITY is NOT. Since velocity is a vector with BOTH magnitude AND direction, we see that the
More information3.5 Equation Solving and Modeling
3.5 Equation Solving and Modeling Objective SWBAT apply the properties of logarithms to solve exponential and logarithmic equation algebraically and solve application problems using these equations. A
More informationPart 1: You are given the following system of two equations: x + 2y = 16 3x 4y = 2
Solving Systems of Equations Algebraically Teacher Notes Comment: As students solve equations throughout this task, have them continue to explain each step using properties of operations or properties
More information11/2/10. Physics. May the Force be With you Obe Wan Konabe. Video. A Typical Physics Problem. A gun mounted on a moving traincar.
Physics May the Force be With you Obe Wan Konabe Video A Typical Physics Problem A gun mounted on a moving traincar. 1 COURSE MODULE INFORMATION Dr Rick Goulding C3004 rgoulding@mun.ca 864 6111 Course
More informationMATH 1101 Chapter 5 Review
MATH 1101 Chapter 5 Review Section 5.1 Exponential Growth Functions Section 5.2 Exponential Decay Functions Topics Covered Section 5.3 Fitting Exponential Functions to Data Section 5.4 Logarithmic Functions
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS TSOKOS LSN 22A THE CONCEPT OF FORCE Introductory Video Introducing Sir Isaac Newton Essential Idea: Classical physics requires a force to change a
More informationIsaac Newton Biographyç
Isaac Newton Biographyç Isaac Newton. [Internet]. 2015. The Biography.com website. Available from: http://www.biography.com/people/isaacnewton9422656 [Accessed 05 Jan 2015]. English physicist and mathematician
More informationMath3 Lesson 87. b) ph problems c) Sound Intensity Problems d) Money Problems e) Radioactive Decay Problems. a) Cooling problems
Math Lesson 87 Unit 5 (Part) Notes 1) Solve Radical Equations ) Solve Eponential and Logarithmic Equations ) Check for Etraneous solutions 4) Find equations for graphs of eponential equations 5) Solve
More informationIntroduction to Calculus
Introduction to Calculus Contents 1 Introduction to Calculus 3 11 Introduction 3 111 Origin of Calculus 3 112 The Two Branches of Calculus 4 12 Secant and Tangent Lines 5 13 Limits 10 14 The Derivative
More informationDay 4: Scientific Ideas Change the World
Day 4: Scientific Ideas Change the World Learning Goal 4: Describe how the ideas of Copernicus, Galileo, Newton and Boyle and the invention of the printing press contributed to the Scientific Revolution
More informationOn the Shoulders of Giants: Isaac Newton and Modern Science
22 May 2012 MP3 at voaspecialenglish.com On the Shoulders of Giants: Isaac Newton and Modern Science SHIRLEY GRIFFITH: This is Shirley Griffith. STEVE EMBER: And this is Steve Ember with the VOA Special
More information2. (10 points) Find an equation for the line tangent to the graph of y = e 2x 3 at the point (3/2, 1). Solution: y = 2(e 2x 3 so m = 2e 2 3
November 24, 2009 Name The total number of points available is 145 work Throughout this test, show your 1 (10 points) Find an equation for the line tangent to the graph of y = ln(x 2 +1) at the point (1,
More informationForces as Interactions
Forces as Interactions 1.1 Observe and Describe a) Pick up a tennis ball and hold it in your hand. Now pick up a bowling ball and hold it. Do you feel the difference? Describe what you feel in simple words.
More informationSir Isaac Newton. Born: 4 Jan 1643 in Woolsthorpe, Lincolnshire, England Died: 31 March 1727 in London, England
Sir Isaac Newton Born: 4 Jan 1643 in Woolsthorpe, Lincolnshire, England Died: 31 March 1727 in London, England Isaac Newton's life can be divided into three quite distinct periods. The first is his boyhood
More informationProject Two. James K. Peterson. March 26, Department of Biological Sciences and Department of Mathematical Sciences Clemson University
Project Two James K. Peterson Department of Biological Sciences and Department of Mathematical Sciences Clemson University March 26, 2019 Outline 1 Cooling Models 2 Estimating the Cooling Rate k 3 Typical
More informationForces as Interactions
Forces as Interactions 1.1 Observe and Describe a) Pick up a tennis ball and hold it in your hand. Now pick up a medicine ball and hold it. Do you feel the difference? Describe what you feel in simple
More informationNew Theory About Light and Colors Philosophiae Naturalis Principia Mathematica Opticks
Newton s Principia Isaac Newton 4 I 1643 Born in Woolsthorpe (25 XII 1642) 1661 Began studies in Cambridge 16651667 Woolsthorpe 1669 Professor of mathematics in Cambridge 1672 New Theory About Light and
More informationProject Two. Outline. James K. Peterson. March 27, Cooling Models. Estimating the Cooling Rate k. Typical Cooling Project Matlab Session
Project Two James K. Peterson Department of Biological Sciences and Department of Mathematical Sciences Clemson University March 27, 2018 Outline Cooling Models Estimating the Cooling Rate k Typical Cooling
More informationAnother enormous superfamily of functions are exponential functions.
Hartfield College Algebra (Version 2018  Thomas Hartfield) Unit FIVE Page  1  of 39 Topic 37: Exponential Functions In previous topics we ve discussed power functions, n functions of the form f x x,
More informationSection 5.3 (Solving Systems of Two Linear Equations in Two Unknowns Algebraically)
Systems of equations can be solved in a variety of ways and without a graphing calculator, I typically do not turn to graphical means of solution. This is because in real world problems the answers don
More information