Lecture 1 Introduction of Physics and Kinematics

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Slide 1: 

Course Introduction Scope of the course Structure of the course what you have to do Chapter 1 Introductions

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물리학 및 실험 Ⅱ 강의 계획서 강의 목표: 초등학교 교과과정에서 자연교과서와 특별활동의 물리영역을 지도하는데 필요한 물리학 배경지식을 실험과 이론의 양 측면에서 심도 있게 학습한다. 수업 방법: 강의 + 과제 및 실험 평가 기준: 중간고사(30%)+기말고사(30%)+과제 및 실험(30%)+출석(10%) 교재 및 참고문헌  -교재: 수학없는 물리 (원제: Conceptual Physics by Paul G, Hewtt.)          탐구형 물리실험 ∏(출판사 북스힐), http://learn.uci.edu/oo/getOCWPage.php?course=OC0811004&lesson=6&topic=1&page=1   -참고문헌: 영재들의 물리노트 Ⅰ, Ⅱ (출판사: 이치), 청소년을 위한 물리학(출판사 북스힐)

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주별 강의 계획: 1주 (9. 1): 물체의 운동 벡터와 스칼라, 위치와 변위, 속도와 가속도, 포물선운동 2주 (9. 8): 힘과 운동 뉴턴의 운동법칙, 마찰, 종단속도, 등속원운동 3주 (9. 15): 일과 에너지 용수철에 의한 일, 역학적 에너지, 에너지 보존 4주 (9. 29): 입자계 선운동량, 충돌이란, 충격력과 충격량                 5주 (10. 6): 회전운동과 각운동량 회전운동, 회전운동에너지, 각운동량 보존                    6주 (10. 13): 중력 만류인력법칙 , 중력상수의 측정, 위성 궤도와 에너지

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7주 (11. 10): 유체 유체란, 밀도와 압력, 파스칼의 원리, 아르키메데스의 원리, 베르누이의 방정식            8주 (11. 17): 열역학 제1법칙 온도, 열, 열역학 0 법칙, 열전달 방법, 열역학 1 법칙 9주 (11. 24): 엔트로피와 열역학 2법칙 동력기관, 냉동기관, 열역학 2 법칙, 카르노 순환과정 10주 (12. 1): 상대론(1/2) 가설, 사건, 로렌츠 변환                     11주 (12. 8): 상대론(2/2)   속도변환, 상대론적 운동량, 상대론적 에너지 12주 (9. 22 보강): 저항과 온도변화 실험 13주 (10. 27 보강): CD, DVD와 레이저 포인터를 이용한 광학실험            14주 (11. 3 보강): LED를 이용한 프랑크상수 측청 15주 (6. 16): 기말고사

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Classical Mechanics: Mechanics: How and why things work. motion, balance, energy, vibrations Classical: Not too fast (v << c) Not too small (d >> atom) Most everyday situations can be described in these terms. Path of baseball Orbit of planets Vibrations of a piano wire

Mechanics : 

Mechanics Motion in One and Two Dimension Laws of Motion Energy, Momentum and Collisions Rotational Motion and the law of Gravity Rotational Equilibrium and Dynamics Solids and Fluids

Thermodynamics : 

Thermodynamics Thermal Physics Energy in Thermal Processes The Laws of Thermodynamics Vibrations and Waves Vibrations and Waves Sound

Scientific Notation : 

Scientific Notation

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Historical Development of the Atom Model

Scientific Notation : 

Scientific Notation The speed of light in vacuum c » 300 000 000 m/s c » 3.0 x 108 m/s The app. mass of a mosquito m » 0.00001 kg m » 10-5 kg http://en.wikipedia.org/wiki/Orders_of_magnitude_(mass)

Trigonometry : 

Trigonometry Pythagorean theorem: c2 = a2 + b2

Standard Quantities : 

Standard Quantities The elements of substances and motion. All things in classical mechanics can be expressed in terms of the fundamental quantities: Length L Mass M Time T Some examples of more complicated quantities: Speed has the quantity of L / T (i.e Kilometer per hour). Acceleration has the quantity of L/T2. Force has the quantity of ML / T2 (as you will learn).

Units : 

Units SI (Système International) Units: mks: L = meters (m), M = kilograms (kg), T = seconds (s) British Units: L = inches, feet, miles, M = slugs (pounds), T = seconds We will use mostly SI units, but you may run across some problems using British units. You should know how to convert back & forth.

Standards of Length : 

Standards of Length Length is measured in Meters (m) The Meter is defined as the distance traveled by light in 1/299 792 458 second The speed of light is therefore 299 792 458 meters per second. Used to be: one ten-millionth of the distance from the North Pole to equator.

Length: : 

Length: Distance Length (m) Radius of Visible Universe 1 x 1026 To Andromeda Galaxy 2 x 1022 To nearest star 4 x 1016 Earth to Sun 1.5 x 1011 Radius of Earth Sears Tower 4.5 x 102 Football Field 1.0 x 102 Tall person 2 x 100 Thickness of paper Wavelength of blue light Diameter of hydrogen atom 1 x 10-10 Diameter of proton 1 x 10-15

Order of Magnitude Calculations / Estimates Earth’s radius ? : 

Order of Magnitude Calculations / Estimates Earth’s radius ? Need to know something from your experience: Flying from NYC to SF one accumulates ~ 3,500 miles NYC to SF spans about 1/6 of the Earth’s circumference So, the Earth’s circumference L = 3,500 x 6 ~ 20,000 mi Since circumference of a circle is : L = 2  r Estimate of Earth radius :

Standards of Time : 

Standards of Time Time is measured in Seconds (s) The Second in defined as 9 192 631 700 times the period of radiation from a cesium atom. Used to be: (1/24)(1/60)(1/60) of a average length of solar day in 1900

Time: : 

Time: Interval Time (s) Age of Universe 5 x 1017 Age of Grand Canyon 3 x 1014 Average age of college student 6.3 x 108 One year One hour Light travel from Earth to Moon One cycle of guitar A string 2 x 10-3 One cycle of FM radio wave 6 x 10-8 One cycle of visible light Time for light to cross a proton 1 x 10-24

Standards of Mass : 

Standards of Mass Mass is measured in Kilograms (Kg) The international prototype of the kilogram is a cylinder 39 mm in height and 39 mm in diameter. It consists of an alloy of 90% platinum and 10% iridium (Pt-Ir) and has a density of approximately 21500 kg/m3. We are still using the “old” definition

Mass: : 

Mass: Object Mass (kg) visible universe ~ 1052 Milky Way galaxy 7 x 1041 Sun 2 x 1030 Earth 6 x 1024 Boeing 747 4 x 105 Car 1 x 103 Student 7 x 101 Dust particle 1 x 10-9 Bacterium 1 x 10-15 Proton 2 x 10-27 Electron 9 x 10-31

The Building Blocks of Matter : 

The Building Blocks of Matter Atoms and Molecules Hydrogen atom ~ 10-10 m The Atomic Nucleus Atomic nucleus ~ 10-14 m Protons and neutrons Proton ~ 10-15 m Quarks: up, down, strange, charmed, bottom, and top

Some Prefixes for Power of Ten : 

Some Prefixes for Power of Ten Power Prefix Abbreviation 103 kilo k 106 mega M 109 giga G 1012 tera T 1015 peta P 1018 exa E 10-18 atto a 10-15 femto f 10-12 pico p 10-9 nano n 10-6 micro m 10-3 milli m

Dimensional Analysis : 

Dimensional Analysis The word dimension has a special meaning in Physics. It is the physical nature of a quantity. The dimension of a distance is Length, whether we measure it in yards or meters. The dimension of Area A is [A] = L2 The dimension of velocity v is written [v] = L/T

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This is a very important tool to check your work It’s also very easy! Doing a problem you get the answer for distance Example: d = v t 2 ( velocity x time2 )? Quantity on left side = L Quantity on right side = L / T x T2 = L x T Left units and right units don’t match, so answer must be wrong !!

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The force (F) to keep an object moving in a circle can be described in terms of the velocity (v, dimension L/T) of the object, its mass (m, dimension M), and the radius of the circle (R, dimension L). Which of the following formulas for F could be correct ? Problem

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There is a famous Einstein's equation connecting energy and mass (relativistic). Using dimensional analysis find which is the correct form of this equation : Note : c is speed of light (L/T) E is energy (M L2 / T2) Problem

Converting between different systems of units : 

Converting between different systems of units Useful Conversion factors: 1 inch = 2.54 cm 1 m = 3.28 ft 1 mile = 5280 ft 1 mile = 1.61 km Example: convert miles per hour to meters per second:

Converting between different systems of units : 

Converting between different systems of units When on travel in Europe you rent a small car which consumes 6 liters of gasoline per 100 km. What is the MPG of the car ? Useful Conversion factors: 1 gallon = 4 liters 1 mile = 1.61 km

Significant Figures : 

Significant Figures 2 x 3.1 = 6 3.1 + 0.004 = 3.1 4.0 x 101  2.07 x 102 = 1.9 X 10-1 x = 123; y = 5.35 123.xxx + 5.35x 128.xxx

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Vectors and Scalars

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An airplane travels 450 km due east, then an unknown distance due north, before it returns home traveling 525 km. a = 450 km c = 525 km b = ? c2 = a2 + b2 Problem

Vectors... : 

Vectors... There are two common ways of indicating that something is a vector quantity: Boldface notation: A “Arrow” notation: A = http://www.youtube.com/watch?v=xJBGfPfE4fQ

Vectors: definition : 

Vectors: definition A vector is composed of a magnitude and a direction examples: displacement, velocity, acceleration magnitude of A is designated |A| usually carries units A vector has no particular position Two vectors are equal if their directions and magnitudes match.

Vectors and scalars: : 

Vectors and scalars: A scalar is an ordinary number. a magnitude without a direction may have units (kg) or be just a number usually indicated by a regular letter, no bold face and no arrow on top. Note: the lack of specific designation of a scalar can lead to confusion The product of a vector and a scalar is another vector in the same direction but with modified magnitude. A B A = -0.75 B

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A) my velocity (3 m/s) C) my destination (the pub - 100,000 m) B) my acceleration downhill (30 m/s2) D) my mass (150 kg) Which of the following is not a vector ? (For bonus points, which answer has a reasonable magnitude listed ?)

Vector addition: : 

Vector addition: The sum of two vectors is another vector. A = B + C B C A B C

Vector subtraction: : 

Vector subtraction: Vector subtraction can be defined in terms of addition. B - C = B + (-1)C

Unit Vectors: : 

Unit Vectors: A Unit Vector is a vector having length 1 and no units. It is used to specify a direction. Unit vector u points in the direction of U. Often denoted with a “hat”: u = û

Vector addition using components: : 

Vector addition using components: Consider C = A + B. (a) C = (Ax i + Ay j ) + (Bx i + By j ) = (Ax + Bx )i + (Ay + By )j (b) C = (Cx i + Cy j ) Comparing components of (a) and (b): Cx = Ax + Bx Cy = Ay + By C Bx A By B Ax Ay

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Kinematics deals with the concepts that are needed to describe motion. Dynamics deals with the effect that forces have on motion. Together, kinematics and dynamics form the branch of physics known as Mechanics. Chapter 2 Kinematics in One Dimension

Kinematic Variables : 

Kinematic Variables Measured with respect to a reference frame. (x-y axis) Measured using coordinates (having units). Many kinematic variables are vectors, which means they have a direction as well as a magnitude. Vectors denoted by boldface v or arrow Location and motion of objects is described using Kinematic Variables: Position: x Vector Velocity: v Vector Speed: v Scalar Acceleration: a Vector

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Position The position of an object is the point or area it occupies in space Often in basic physics problems we will be concerned with position along a one-dimensional line, or height above the ground, or position in a two-dimensional plane.

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Example The position of the University of California, Irvine, on a map of the United States  is latitude 33.64 N, longitude 117.79 W. This can be written as (33.64 N, -117.79) because, by convention, east of the Greenwich meridian is positive and west is negative. It is implied that the origin of these longitude and latitude values is (0,0). Therefore the position of UCI is a vector that points from the point at (0,0) to the point at (33.64 N, -117.79).

Slide 48: 

How many kilometres is mumbai from calcutta?

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Distance and displacement Distance  “how much ground covered” along the path from start to finish has a magnitude, but no direction. (temperature, energy, and voltage) Displacement. difference between an object’s final and initial positions independent of the path taken to get from one to the other  change in position.

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The symbol Δ is a shorthand way of writing “change of.” Position s or (s arrow) and displacement d

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Example An x-axis is marked out on the floor. A toy car sits parked at x = 3.5. Later it is found at x = 14.2.

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Example A bus travels 1 mile due north, then turns left and goes 1 mile due west. It then does a U-turn and retraces its path, going 1 mile due east and 1 mile due south. What is the distance traveled, and what is the displacement?

Slide 54: 

Example A vector pointing from the start point to the finish point would have a y component of:

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Speed Average speed distance traveled / time taken for this distance The instantaneous speed speed at any given moment or instant in time shown on the speedometer of a bus or car.

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Example The World’s Fastest Jet-Engine Car Andy Green in the car Thrust SSC set a world record of 341.1 m/s in 1997. To establish such a record, the driver makes two runs through the course, one in each direction, to nullify wind effects. From the data, determine the average velocity for each run.

Slide 57: 

Velocity In conversation, velocity and speed may be used interchangeably, and indeed velocity and speed have the same units (meters per second, say, or miles per hour). But in physics, velocity is a vector quantity that has a direction, while speed is a scalar. The symbol for velocity is v, or (v→). Speed is “how fast something is moving” Velocity is “the rate of change in position The instantaneous velocity indicates how fast the car moves and the direction of motion at each instant of time.

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Example A motorcycle travels northeast from Victorville to Barstow, a distance of 30 miles, in 30 minutes. What is its average speed and what is its velocity? The average speed is 30miles 0.5hour or 60 miles per hour. The velocity is 60 miles per hour, northeast.

Slide 59: 

Velocity can be a negative number. Consider a car traveling right and left on a number line, as shown in this diagram. In one second, it goes from the position at 5 on the number line to position 11 on the number line. Then it reverses direction, and in two seconds goes from 11 on the number line to 3 on the number line. When it was traveling to the right, its velocity was 6 units per second to the right or +6/second. When it was traveling to the left, its velocity was 8 units in two seconds, or 4 units per second, to the left, or -4/second. The negative sign indicates the direction of travel on the number line: right to left.

Slide 60: 

The notion of acceleration emerges when a change in velocity is combined with the time during which the change occurs.

Slide 61: 

DEFINITION OF AVERAGE ACCELERATION http://learn.uci.edu/oo/getOCWPage.php?course=OC0811004&lesson=007&topic=3&page=1

1-D kinematics... : 

1-D kinematics... Acceleration a is the “rate of change of velocity” If a = aav is constant, and set t1=0, v1= v0 , and then v2= v

Slide 63: 

So for constant acceleration we find:

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A car is traveling with an initial velocity vo. At t = 0, the driver puts on the brakes, which slows the car at a rate of ab

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A car traveling with an initial velocity vo. At t = 0, the driver puts on the brakes, which slows the car at a rate of ab. At what time tf does the car stop, and how much farther xf does it travel ?? x = xf , t = tf v = 0 x = 0, t = 0 ab v0

Free Fall : 

Free Fall When any object is let go it falls toward the ground !! The force that causes the objects to fall is called gravity. The acceleration caused by gravity is typically written as g Any object, be it a baseball or an elephant, experiences the same acceleration (g) when it is dropped, thrown, spit, or hurled, i.e. g is a constant. http://www.youtube.com/watch?v=z_sJ15feNGw

Gravity facts: : 

Gravity facts: g does not depend on the nature of the material! Galileo (1564-1642) figured this out without fancy clocks & rulers! demo - feather & penny in vacuum Nominally, g = 9.81 m/s2 At the equator g = 9.78 m/s2 At the North pole g = 9.83 m/s2

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When throwing a ball straight up, which of the following is true about its velocity v and its acceleration a at the highest point in its path? (a) Both v = 0 and a = 0. (b) v  0, but a = 0. (c) v = 0, but a  0. y Motion in One Dimension

2-D Kinematics : 

2-D Kinematics So for constant acceleration we get: (where , are all vectors)

“x” and “y” components of motion are independent. A man on a train tosses a ball straight up in the air. View this from two reference frames:

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Alice and Bill are playing air hockey on a table with no bumpers at the ends. Alice scores a goal and the puck goes flying off the end of the table. Which diagram best describes the path of the puck ? Alice Bill A) B) C)

Shooting the Monkey : 

Shooting the Monkey Where does the zookeeper aim if he wants to hit the monkey? ( He knows the monkey willlet go as soon as he shoots ! )

Shooting the Monkey... : 

Shooting the Monkey... If there were no gravity, simply aim at the monkey r = r0 r =v0t

Slide 76: 

r = v0 t - 1/2 g t2 With gravity, still aim at the monkey! r = r0 - 1/2 g t2

Projectile motion : 

Projectile motion What is the maximum height the ball reaches (h) ? How long does it take to reach maximum height ? = 0 at P y :

Typical questions :(projectile motion; for given v0 and q) : 

Typical questions :(projectile motion; for given v0 and q) What is the range of the ball (L) ? How long does it take for ball to reach final point (P) ? y = (v0 sin q) t - 1/2 g t2 = 0 ! when at P [ (v0 sin q) - 1/2 g t] t = 0 t = 0 ; t = 2 (v0 sin q) / g L = vx0 t = (v0 cos q) t x : y :

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 x v0x = v0 cos q v0y = v0 sin q vx = v0x = v0 cos q : const. , x = v0x t = v0cos q t vy = v0y - g·t = v0 sin q - g·t , y = v0 sin q t - g·t2 at Top : vy = 0 

Projectile Motion : 

Projectile Motion Typical Questions 1. Dx: How far will it go ? 4. q: At what angle should I start ? 2. Dy: How high will it be? 5. v0: How fast must I start ? 3. t: How long until it hits ? v0 q g Key Equations x-displacement: v0x = v0 cosq Dx = voxt y-displacement: v0y = v0 sinq Dy = v0yt - gt2 /2

Problem 1 : 

Problem 1 v0 Q g UConn football team wants to complete a 45m pass (about 50 yards). Our qb can throw the ball at 30 m/s. At what angle must he throw the ball to get it there ?

Problem 2 : 

Problem 2 Suppose a projectile is aimed at a target at rest placed at the same height. At the time that the projectile leaves the cannon the target is released from rest and starts falling toward ground. Would the projectile miss or hit the target ? t = t1 ( A ) MISS ( B ) HIT ( C ) CAN’T TELL

Slide 83: 

x = x0 y = -1/2 g t2 This may be easier to think about. It’s exactly the same idea!! They both have the same Vy(t) in this case x = v0 t y = -1/2 g t2