Physics of Technology PHYS 1800 Recitation 1 Introduction

Physics of Technology PHYS 1800 Recitation 1 Introduction Section 0 Lecture 1 Slide 1 Math Background INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 1

Physics of Technology PHYS 1800 Basic Algebra Introduction Section 0 Lecture 1 Slide 2 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 2

Basic Algebra (Appendix A) Introduction Section 0 Lecture 1 Slide 3 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 3

Adding Fractions Introduction Section 0 Lecture 1 Slide 4 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 4

Scientific Notation (Appendix B) Physics deals with a vast range of scale sizes from atoms and molecules (billionth of a meter) to every day phenomena (m, km) to stellar and galactic dimensions (trillions of km). Scientific notation (power of 10) allows us to represent these numbers in a simple and concise way. eg. 100 = 10 x 10 = 102 1/1, 000 = 10 -3 1, 000 = 103 100, 000 = 105 etc. 1/100, 000 = 10 -5 etc. Examples: – 1. Distance from the Earth to the Sun … – D = 150, 000 km – or D = 15 x 107 km (or D = 1. 5 x 108 km) Introduction – 2. Red color in. Section 0 Lecture a wavelength… rainbow has 1 Slide 5 – λ = 0. 0000007 m – or λ = 0. 7 x 10 -6 m (or λ = 7. 0 x 10 -7 m) INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 5

Introduction Section 0 Lecture 1 Slide 6 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 6

Multiplying Powers of 10: Rule: Add together powers of 10 Example: Jet flying at speed of sound for one hour… D = speed x time = (300 m/s) x (3, 600 s) 2+3=5 D = (3 x 102) x (3. 6 x 103) = 10. 8 x 105 m Dividing Powers of 10: Rule: Subtract denominator power from numerator power. Example: Car travelling 60 km in 30 min… Distance 60, 000 m 6 x 104 m = = Speed = Time. Lecture 1 30 x 60 s 18 x 102 s Introduction Section 0 Slide 7 4 -2=2 1 2 2 x 10 m/s = 0. 33 x 10 m/s = 33 m/s Speed = 3 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 7

Physics of Technology PHYS 1800 Units Introduction Section 0 Lecture 1 Slide 8 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 8

Units of Measurements Units are an essential part of any measurement. – eg. Gas in the USA is sold by the gallon but in Europe it is sold by the liter (1 gal ≈ 4 l). Types of units: – English / US (inch, foot, yard, mile, pound, pint, quart, gallon) – Metric (meter, kilogram, liter) – * The metric system uses standard prefixes representing multiples of 10 and is much simpler to use. – eg. kilo = 1000, mega = 1, 000, giga = 1, 000, 000 – milli = 1/1, 000, micro = 1/1, 000, nano = 1/ 1, 000, 000 – Example: 1 Section 0 Lecture 1000 meters, kilogram = 1000 grams Introduction kilometer = 1 Slide 9 1 milliliter = 1/1, 000 liter = 0. 001 liters – Compare with: 1 mile = 5, 280 feet = 63, 360 inches INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 9

Examples of Metric Units Length: meter (m) 1 km = 1000 m (~ 0. 6 miles) 1 light- year = 9. 46 x 1015 m Mass: kilogram (kg) 1 kg = 1000 g (~ 2. 2 lbs) Mass of Earth = 5. 98 x 1024 kg Volume: liter (l) 1 l = 1000 ml (1 gal = 3. 786 l) Energy: Joules (J) or N. m (1 calorie = 4. 2 J) Temperature: Kelvin (K) “Absolute zero” 0 K = -273°C Force: Newtons (N) (1 lb = 4. 448 N) Pressure: Pascal (Pa) or N / m 2 Atmospheric Pressure = 1 x 105 Pa (=14. 78 lb/in 2) Useful values: Introduction Section 0 Lecture 1 Slide 10 Speed of light ~ 3. 0 x 108 m/s Acceleration due to gravity = 9. 81 m/s 2 (approx 10 m/s 2) Electron charge = 1. 6 x 10 -19 C (Coulombs) INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 10

Adding Units Introduction Section 0 Lecture 1 Slide 11 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 11

Dimensional Analysis Introduction Section 0 Lecture 1 Slide 12 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 12

Physics of Technology PHYS 1800 Trigonometry Introduction Section 0 Lecture 1 Slide 13 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 13

Basic Trigonometry: Right Angle Triangle sin A = B Hypotenuse Opposite side tan A = cos A = A Adjacent Side sin A = tan A = B h Introduction A Section 0 y Lecture 1 INTRODUCTION TO Modern Physics PHYX 2710 x Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 h = x 2 hypotenuse opposite adjacent hypotenuse y h y x Slidex 14 cos A = opposite sin A = y h cos B = and so sin A = cos B y h and vice versa h + y 2 Math Background Recitation 1 Slide 14

Example sin 30° = B=60° h (=2) y(=1) A=30° x (= 3) 1 2 3 2 1 tan 30° = 3 cos 30° = Triangle components: sin A = Introduction cos A = Lecture Section 0 tan A = INTRODUCTION TO Modern Physics PHYX 2710 y h x 1 h y Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 or Slide 15 y = h. sin A x = h. cos A y = x. tan A x Math Background Recitation 1 Slide 15

Components of a Triangle Resolving a right angle triangle into its horizontal (x) and vertical (y) components can be very helpful in solving problems of motion as well as static trigonometry. Example: Calculate the height of your house… x y x = y. tan A = 20 m. tan 40° tan A = Introduction Section 0 Lecture 1 INTRODUCTION TO Modern Physics PHYX 2710 Slide 16 = 20 x 0. 84 = 16. 8 m high Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 16

Physics of Technology Next Recitation: Math and Problem Solving Review Tuesday 1: 30 -2: 45 ESLC 53 Review Appendices A, B, C Next Class: Introduction Section 0 Lecture 1 Wed 10: 30 -11: 20 Slide 17 BUS 318 room. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Math Background Recitation 1 Slide 17