1. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 1 Lecture 2 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 2 Units, Scalars and Vectors

2. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 2 Lecture 2 Slide 2 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet *Homework Handout

3. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 3 Lecture 2 Slide 3 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Introduction to Physics

4. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 4 Lecture 2 Slide 4 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 What is Physics? “Study of the basic nature of matter and the interactions that govern its behavior.” “Common Sense Approach to How Things Work” (with units!) Common Sense—A minimal set of simple, straightforward guides. Units—Predictions on a quantitative level

5. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 5 Lecture 2 Slide 5 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Current State of Physics cira 2009 Standard Model QCD Unites E&M, Strong NF, Weak NF Conservation Laws Energy Linear & Angular Momentum Charge, Spin Lepton and Baryon Number Quantum Mechanics Schrodinger/Dirac Equation Probabilistic approach Statistical Mechanics Physics of many particles Fermions and Bosons Partitioning of Energy Thermodynamics Time and Entropy Weinburg-Salom Model QED Unites E&M, Weak NF

6. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 6 Lecture 2 Slide 6 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 2 Units, Scalars and Vectors Units

7. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 7 Lecture 2 Slide 7 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 What Do We Need To Measure? What is the minimum about things we need to know? Where things are—a length, L When things are there—a time, T How thing interact with gravity—a mass, M How things interact with E&M—a charge, Q How thing inter act with weak nuclear force How things interact with strong nuclear force

8. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 8 Lecture 2 Slide 8 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Units of Measurements Units are an essential part of any measurement. –Gas at $1.50 sounds good…but if its $1.50 per liter you loose! –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 = 1,000,000, giga = 1,000,000,000 –milli = 1/1,000, micro = 1/1,000,000, nano = 1/ 1,000,000,000 –Example: 1 kilometer = 1000 meters, kilogram = 1000 grams 1 milliliter = 1/1,000 liter = 0.001 liters –Compare with: 1 mile = 5,280 feet = 63,360 inches

9. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 9 Lecture 2 Slide 9 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Examples of Metric Units Time (T): second (s or sec) Length (L): meter (m) 1 km = 1000 m (~ 0.6 miles) 1 light- year = 9.46 x 10 15 m Mass (M): kilogram (kg)1 kg = 1000g (~ 2.2 lbs) Mass of Earth = 5.98 x 10 24 kg Volume (L3): liter (l)1 l = 1000 ml (1 gal = 3.786 l) Energy (ML 2 T -2 ): Joules (J) or N.m (1 calorie = 4.2 J) Temperature: Kelvin (K) “ Absolute zero ” 0K = -273°C Force (MLT -2 ): Newtons (N)(1 lb = 4.448 N) Pressure (ML -1 T -2 ): Pascal (Pa) or N / m 2 Atmospheric Pressure = 1 x 10 5 Pa (=14.78 lb/in 2 ) Useful values: Speed of light ~ 3.0 x 10 8 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)

10. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 10 Lecture 2 Slide 10 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Examples of Units Consider the lowly penny:

11. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 11 Lecture 2 Slide 11 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Metric Prefixes Add Griffith Table 1.3 Refer to the front inside cover and Table 1.2 for listings of units and prefixes.

12. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 12 Lecture 2 Slide 12 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009

13. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 13 Lecture 2 Slide 13 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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 = 10 2 1,000 = 10 3 100,000 = 10 5 etc. 1/1,000 = 10 -3 1/100,000 = 10 -5 etc. Examples: –1. Distance from the Earth to the Sun … –D = 150,000,000 km –or D = 15 x 10 7 km (or D = 1.5 x 10 8 km) –2. Red color in rainbow has a wavelength… –λ = 0.0000007 m –or λ = 0.7 x 10 -6 m (or λ = 7.0 x 10 -7 m)

14. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 14 Lecture 2 Slide 14 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 2 Units, Scalars and Vectors Units—A “small” example for USU

15. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 15 Lecture 2 Slide 15 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Here at USU, TC Shen can make wires 1 atom wide! An atom is ~0.1 nm across. The moon is 4x10 8 m from the Earth (see front cover). How many atoms, in a 1 atom wide wire, would it take to reach the Moon? How much would this amount of Cu weigh?

16. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 16 Lecture 2 Slide 16 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 TC Shen can make wires 1 atom wide. An atom is ~0.1 nm across. (1 nm = 10 -9 m) The moon is 4x10 8 m from the Earth (see front cover). How many atoms, in a 1 atom wide wire, would it take to reach the Moon? How much would this amount of Cu weigh?

17. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 17 Lecture 2 Slide 17 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 2 Units, Scalars and Vectors Scalars and Vectors

18. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 18 Lecture 2 Slide 18 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Scalars and Vectors Scalar: Measure of quantity or size Sometimes called “magnitude”. Examples: Length, volume, mass, temperature, speed… Vectors: Many measurements in physics require a knowledge of the magnitude and direction of quantity. These are termed vector quantities. Examples: Velocity, acceleration, force, electric field… Direction is an essential feature of a vector quantity. Example: Flying at 1000 km/hr due North is quite different to the same speed due East! Vectors require 2 pieces of information MAGNITUDE and DIRECTION.

19. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 19 Lecture 2 Slide 19 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Examples of Scalars Consider the lowly penny:

20. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 20 Lecture 2 Slide 20 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Basic Trigonometry: HypotenuseOpposite side A B Adjacent Side y A B h x hypotenuse adjacent cos adjacent opposite tan hypotenuse opposite sin    A A A versa viceand cos sin so cos and sin BA h y B h y A   h x cos x y tan h y sin    A A A 22 yxh  Right Angle Triangle

21. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 21 Lecture 2 Slide 21 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Example Triangle components: A=30° B=60° y(=1) h (=2) )3(  x 3 1 30tan 2 3 30cos 2 1 30sin    Axcos.h  x A h  Aysin.hor  y A h sin  y A x tan  Ay.x 

22. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 22 Lecture 2 Slide 22 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 How to Represent a Vector: N E 40° Arrow Represents its magnitude by its length. Represents its direction by its angle. y = v. sin 40° N E 40° v x = v. cos 40° We have resolved the vector motion into 2 “components”.

23. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 23 Lecture 2 Slide 23 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Resolving a Right Triangle into Components 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… high m 8.1684.0 x20 40tan. m20   tan.  Ayx  y x A

24. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 24 Lecture 2 Slide 24 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 river 30 km launch N E55° balloon course 15 km/hr Question: How long before the balloon crosses the river? Example: Vectors Solution: V E = v cos(55°) V N = v sin(55°) 55° v =15 km/hr V E = v cos(55°) = 15 x 0.5736 = 8.6 km/hr As river is 30 km due E; the balloon will reach it in: (30 km)/(8.6 km/hr) = 3.49 hrs. Note: Can also use v N to get distance traveled Northwards.

25. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 25 Lecture 2 Slide 25 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 How to add vectors: We are often interested in combining 2 (or more) vectors to solve a problem. e.g. Flying in strong winds. c B A E N “Math-Lite” Method: (graphical) 1. Draw 1 st vector to scale and in appropriate direction, 2. Start 2 nd vector at head of 1 st vector and in appropriate direction. 3. Repeat for other vectors. 4. Resultant (sum) vector is found by drawing vector from origin to head of last vector. C = A + B Resultant vector 1 st 2 nd 3 rd E N origin

26. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 26 Lecture 2 Slide 26 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 How to add vectors: We are often interested in combining 2 (or more) vectors to solve a problem. e.g. Flying in strong winds. c B A E N “Full-on Math” Method: (components) 1. Break each vector into components. 2. Add all the “X” components separately. 3. Add all the “Y” components separately. 4. Plot a point at the sum coordinates, (X,Y). 4. Resultant (sum) vector is found by drawing vector from origin to (X,Y). C = A + B Resultant vector 1 st 2 nd 3 rd E N origin

27. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 27 Lecture 2 Slide 27 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Vector subtraction: A -A B D origin D = B - A Method: 1. Draw B vector to scale and in positive direction. 2. Draw A vector from tip of B but in opposite direction to yield (-A). 3. Resultant difference vector D is found by joining the origin to the tip of (-A) vector. Note: Alternate solution is given by finding the horizontal and vertical vector components and adding/subtracting as appropriate.

28. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 28 Lecture 2 Slide 28 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Example: Vector Velocities Boat crossing a river… 35° planned course actual course E N river flow Question: How fast is the river flowing? Solution: 35° v B = 7 km/hr actual course v R = v B tan(35°) Boat speed v B = 7 km/hr. = (7 km/hr) x 0.7002 = 4.9 km/hr Answer: The river is flowing at 4.9 km/hr Northwards. Note: To cross the river on planned course, the boat needs to aim upriver at an angle of 35°. Aircraft always need to take account of wind to get to the right place!

29. Units, Scalars, Vectors Introduction Section 0 Lecture 1 Slide 29 Lecture 2 Slide 29 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology Next Lab/Demo: Motion Tuesday 1:30-2:45 ESLC 46 Ch 2 Next Class:Fri 10:30-11:20 BUS 318 room Review Ch 2