Physics 121, Sections: 1, 2, 3 And 4

Physics 121, Sections: 1, 2, 3 and 4

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Instructor: Kyungseon Joo, Assistant Professor of Physics [email protected], http://www.phys.uconn.edu/~kjoo

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Office Hours: Fridays 10:00am – 12:00 pm (or by appointment)

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Research Interest: Experimental Particle and Nuclear physics

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Course Info z

All information about the course is on the website: http://www.phys.uconn.edu/~kjoo/p121.html

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Course has several components: ÍReading Assignments: from our text. ÍLecture: (me talking, Active learning). ÍHomework Sets: One problem set every week. ÍExams: three midterms (drop one with the lowest score) plus a final. » Questions on exams will look like those we do in class and in homework. » No surprises ÍLabs: (group exploration of physical phenomena).

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Become familiar with the Physics Learning Resource Center for help in problem sets. Room P-207C.

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Announcements z

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Homeworks posted on WileyPlus Í You need to register at http://edugen.wiley.com/edugen/class/cls29750 ÍHomework will be posted on Tuesday during the lecture starting next week. ÍHomework will be due by 8:00 AM the following Tuesday. ÍHomework will be graded automatically. ÍYou try up to 5 attempts per problem.

Labs Í Begin in two week (01/29/2007)

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Course Evaluation z

Homework

20%

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Lab

20%

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Three Midterm Exams (drop the lowest score one) 30%

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Final Exam

30%

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07

Background Needed for Course z

High school algebra Ímanipulation of formulas Ísolution of simultaneous and multivariable equations Ísolution of quadratic equation

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Trigonometry Ísines, cosines, tangents ÍPythagorean theorem

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Geometry Ígeometric shape Íangular meausre

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Lecture Organization z

Three main components: ÍLecturer discusses class material » Topics from text

ÍYou and I will interact with conceptual “Active Learning” problems. » Usually two or three per lecture

Act

ÍActive Figures » To illustrate concepts

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Interactive lecture in a large class?!

Question: Why am I studying Physics? Answer: 1. It is a degree requirement 2. I will gain analytical abilities 3. I can apply basic physics concepts to figure out answers to a large body of day-to-day problems correct 4. All of the above

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Scope of Physics 121 z

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Classical Mechanics: ÍClassical: » Not too fast (v << c) » Not too small (d >> atom)

Most everyday situations can be described in these terms. Í Path of baseball Í Orbit of planets Í Vibrations of a piano wire

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Mechanics z z z z z z

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

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Thermodynamics z z z

Thermal Physics Energy in Thermal Processes The Laws of Thermodynamics

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Vibrations and Waves z z

Vibrations and Waves Sound

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Mathematical Notation z

Mathematical symbols Í∝ : proportionality i.e. y ∝ x2 Í< : is less than Í > : is greater than Í<< : is much less than Í >> : is much greater than Í≈ : is approximately equal to Í≡ : is defined as

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Scientific Notation z

Large number: Í100 = 1 Í101 = 10 Í102 = 100 Í … etc

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Small numbers: Í10-1 = 0.1 Í10-2 = 0.01 Í10-3 = 0.001 … etc

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Scientific Notation z

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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

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Algebra z

Basic Rules 8 x Y=32 8 x Y / 8 = 32 / 8 Y=4 X+2=8 X+2-2=8–2 X=6

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Basic Rules z z z z

Multiplying: (a/b)(c/d) Dividing: (a/b)/(c/d) Adding: a/b ± c/d Factoring: ax + ay + az = a(x + y +z) a2 + 2ab + b2 = (a + b)2 a2 - b2 = (a + b)(a –b)

= (ac)/(bd) = (ad)/(bc) = (ad ± bc)/(bd)

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1.2 Units Physics experiments involve the measurement of a variety of quantities. These measurements should be accurate and reproducible. The first step in ensuring accuracy and reproducibility is defining the units in which the measurements are made.

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SI units meter (m): unit of length kilogram (kg): unit of mass second (s): unit of time

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The units for length, mass, and time (as well as a few others), are regarded as base SI units. These units are used in combination to define additional units for other important physical quantities such as force and energy.

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Units z

SI (Système International) Units: Ímks: L = meters (m), M = kilograms (kg), T = seconds (s)

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British Units: ÍL = inches, feet, miles, M = slugs (pounds), T = seconds

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We will use mostly SI units, but you may run across some problems using British units. You should know how to convert back & forth.

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Standards of Length z z z z

Length is measured in Meters (m) The Meter is defined as the distance traveled by light in vacuum in 1/299 792 458 second The speed of light is therefore 299 792 458 meters per second. Used to be: ÍOne ten-millionth of the distance from the North Pole to equator ÍDistance between two marks on a bar of a platinumiridium alloy kept at a temperature of 0 C degree.

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Standards of Time z z z

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.

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Standards of Mass z z

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Mass is measured in Kilograms (Kg) The Kilogram is defined as the mass of a specific platinumiridium alloy cylinder kept at the International Bureau of Weights and Measures at Sevres, France We are still using the “old” definition

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Length: Distance Radius of Visible Universe To Andromeda Galaxy To nearest star Earth to Sun Radius of Earth Sears Tower Football Field Tall person Thickness of paper Wavelength of blue light Diameter of hydrogen atom Diameter of proton

Length (m) 1 x 1026 2 x 1022 4 x 1016 1.5 x 1011 6.4 x 106

4.5 x 102 1.0 x 102 2 x 100 1 x 10-4 4 x 10-7 1 x 10-10

1 x 10-15

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

Need to know something from your experience: ÍFlying from NYC to SF one accumulates ~ 3,500 miles ÍNYC to SF spans about 1/6 of the Earth’s circumference ÍSo, the Earth’s circumference L = 3,500 x 6 ~ 20,000 mi ÍSince circumference of a circle is : L = 2 π r ÍEstimate of Earth radius :

L 20,000mi r= ≈ ≈ 3,000mi 2π 6

3x103 mi = 3x103 x 1.61 km ~ 5x103 km = 5x106 m

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Time: Interval Age of Universe Age of Grand Canyon Avg age of college student One year One hour Light travel from Earth to Moon One cycle of guitar A string One cycle of FM radio wave One cycle of visible light Time for light to cross a proton

Time (s) 5 x 1017 3 x 1014 6.3 x 108 3.2 x 107 3.6 x 103 1.3 x 100 2 x 10-3 6 x 10-8 1 x 10-15 1 x 10-24

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Mass: Object

visible universe Milky Way galaxy Sun Earth Boeing 747 Car Student Dust particle Bacterium Proton Electron

Mass (kg)

~ 1052 7 x 1041 2 x 1030 6 x 1024 4 x 105 1 x 103 7 x 101 1 x 10-9 1 x 10-15 2 x 10-27 9 x 10-31

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1.3 The Role of Units in Problem Solving

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1.3 The Role of Units in Problem Solving THE CONVERSION OF UNITS 1 ft = 0.3048 m 1 mi = 1.609 km 1 hp = 746 W 1 liter = 10-3 m3

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Example 1 The World’s Highest Waterfall The highest waterfall in the world is Angel Falls in Venezuela, with a total drop of 979.0 m. Express this drop in feet.

Since 3.281 feet = 1 meter, it follows that (3.281 feet)/(1 meter) = 1

⎛ 3.281 feet ⎞ Length = (979.0 meters)⎜ ⎟ = 3212 feet ⎝ 1 meter ⎠ Physics 121: Lecture 1, Pg 33

Reasoning Strategy: Converting Between Units 1. In all calculations, write down the units explicitly. 2. Treat all units as algebraic quantities. When identical units are divided, they are eliminated algebraically. 3. Use the conversion factors located on the page facing the inside cover. Be guided by the fact that multiplying or dividing an equation by a factor of 1 does not alter the equation.

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Example 2 Interstate Speed Limit Express the speed limit of 65 miles/hour in terms of meters/second. Use 5280 feet = 1 mile and 3600 seconds = 1 hour and 3.281 feet = 1 meter.

feet ⎛ miles ⎞ ⎛ miles ⎞⎛ 5280 feet ⎞⎛ 1 hour ⎞ Speed = ⎜ 65 ⎟(1)(1) = ⎜ 65 ⎟⎜ ⎟⎜ ⎟= 95 second ⎝ hour ⎠⎝ mile ⎠⎝ 3600 s ⎠ ⎝ hour ⎠

feet ⎞ feet ⎞⎛ 1 meter ⎞ meters ⎛ ⎛ ( ) 29 Speed = ⎜ 95 1 95 = = ⎜ ⎟⎜ ⎟ ⎟ second ⎝ second ⎠⎝ 3.281 feet ⎠ ⎝ second ⎠

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Dimensional Analysis z z z z z z

The word dimension has a special meaning in Physics. It is the physical nature of a quantity. The dimension of a length is [L], whether we measure it in yards or meters. The dimension of time is [T] The dimension of mass is [M] The dimension of Area A is [A] = [L]2 The dimension of velocity v is written [v] = [L]/[T]

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DIMENSIONAL ANALYSIS [L] = length

[M] = mass

[T] = time

Is the following equation dimensionally correct?

x = vt 1 2

2

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See text : 1-4

Dimensional Analysis z

This is a very important tool to check your work ÍIt’s also very easy!

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Example: ( distance = velocity x time2 )

x = vt

2 1 2 Dimension on left side = [L] Dimension on right side = [L] / [T] x [T]2 = [L] x [T] z

Left units and right units don’t match, so answer must be wrong !!

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Dimensional Analysis z z z z

Dimensions can be treated as algebraic quantities They can be added or subtracted only if they have the same dimensions. Both sides of equation must have the same dimensions. Dimensional analysis helps to determine whether or not an expression has the correct form.

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ACT 1 z

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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 :

E = mc

(b)

E = mc

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(c)

E = mc 3

Note : Í c is speed of light ([L]/[T]) ÍE is energy ([M][L]2/[T]2)

Solution ->

(b) Physics 121: Lecture 1, Pg 40