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

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



Lecture 2 Slide 2


Fall 2004


Spring 2009

PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet

*Homework Handout

Date Day Lecture Chapter Homework Due Jan 5 6 7 9

M T W F*

Class Admin: Intro.Physics Phenomena Problem solving and math Units, Scalars, Vectors, Speed and Velocity

1 App. B, C 1 2

-

Jan 12 14 16

M W F*

Acceleration Free Falling Objects Projectile Motion

2 3 3

1

Jan 19 21 23

M W F*

Martin Luther King Newton’s Laws Mass and Weight

No Class 4 4

2

Jan 26 28 29 30

M W Th F

Motion with Friction Review Test 1 Circular Motion

4 1-4 1-4 5

3

Feb 2 4 6

M W F*

Planetary Motion and Gravity Energy Harmonic Motion

5 6 6

4

Feb 9 11 13

M W F*

Momentum Impulse and Collisions Rotational Motion

7 7 8

5

Feb 16 17 18 19 20

M Tu W H F*

Presidents Day Angular Momentum (Virtual Monday) Review Test 2 Static Fluids, Pressure

No Class 8 5-8 5-8 9

-

Feb 23 25 27

M W F*

Flotation Fluids in Motion Temperature and Heat

9 9 10

6

Mar 2 4 6

M W F*

First Law of Thermodynamics Heat flow and Greenhouse Effect Climate Change

10 10 -

7

Mar 9-13 M-F Spring Break No Classes Mar 16 18 20

M W F*

Heat Engines Power and Refrigeration Electric Charge

11 11 12

8

Mar 23 25 26 27

M W H F*

Electric Fields and Electric Potential Review Test 3 Electric Circuits

12 13 9-12 13

-

Mar 30 Apr 1 3

M W F

Magnetic Force Review Electromagnets Motors and Generators

14 9-12 14

9

Apr 6 8 10

M W F*

Making Waves Sound Waves E-M Waves, Light and Color

15 15 16

10

Apr 13 15 17

M W F*

Mirrors and Reflections Refraction and Lenses Telescopes and Microscopes

17 17 17

11

Apr 20 22 24

M W F

Review Seeing Atoms The really BIG & the really small

1-17 18 (not on test) 21 (not on test)

No test week 12

May 1 F Final Exam: 09:30-11:20am



Lecture 2 Slide 3


Fall 2004


Spring 2009


PHYS 1800

Introduction

to

Physics



Lecture 2 Slide 4


Fall 2004


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



Lecture 2 Slide 5


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Spring 2009

Current State of Physics cira 2009

Electricity & MagnetismMaxwell Equations (c 1880)

Weak Nuclear Force Radioactivity

Strong Nuclear ForceComposition of subatomic particles

Mechanics (Gravity)…… General RelativitySpace and time

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



Lecture 2 Slide 6


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Spring 2009


PHYS 1800

Lecture 2


Units



Lecture 2 Slide 7


Fall 2004


Spring 2009

What Do We Need To Measure?

What is the minimum about things we need to know?

Where things are—a length, LWhen things are there—a time, T

How thing interact with gravity—a mass, MHow things interact with E&M—a charge, Q

How thing inter act with weak nuclear forceHow things interact with strong nuclear force



Lecture 2 Slide 8


Fall 2004


Spring 2009

Units of MeasurementsUnits 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



Lecture 2 Slide 9


Fall 2004


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 1015 mMass (M): kilogram (kg) 1 kg = 1000g (~ 2.2 lbs)

Mass of Earth = 5.98 x 1024 kg

Volume (L3): liter (l) 1 l = 1000 ml (1 gal = 3.786 l)

Energy (ML2T-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-1T-2): Pascal (Pa) or N / m2 Atmospheric Pressure = 1 x 105 Pa (=14.78 lb/in2)

Useful values: Speed of light ~ 3.0 x 108 m/s

Acceleration due to gravity = 9.81 m/s2 (approx 10 m/s2) Electron charge = 1.6 x 10-19 C (Coulombs)



Lecture 2 Slide 10


Fall 2004


Spring 2009

Examples of Units

Consider the lowly penny:

Value Notes on units Scientific notation 0.75 in “natural unit” 7.5 · 10-1 in 2 cm “natural” unit,

metric unit (note prefix) 2 cm

0.02 m SI unit, metric unit 2 · 10-2 m

0.00002 km metric unit (note prefix) 2 · 10-5 km

0.000012 mile 1.2 · 10-5 mile

0.01 fathom “odd” unit 1 · 10-2 fathom

0.000000000000000000002 light year “odd” unit 2 · 10-20 light year

0.000000002 angstrom “odd” unit 2 · 10-8 angstrom



Lecture 2 Slide 11


Fall 2004


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.



Lecture 2 Slide 12


Fall 2004


Spring 2009



Lecture 2 Slide 13


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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 = 102 1,000 = 103 100,000 = 105 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 107 km (or D = 1.5 x 108 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)



Lecture 2 Slide 14


Fall 2004


Spring 2009


PHYS 1800

Lecture 2


Units—A “small” example for USU



Lecture 2 Slide 15


Fall 2004


Spring 2009

Here at USU, TC Shen can make wires 1 atom wide!

An atom is ~0.1 nm across.The moon is 4x108 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?



Lecture 2 Slide 16


Fall 2004


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 4x108 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?



Lecture 2 Slide 17


Fall 2004


Spring 2009


PHYS 1800

Lecture 2


Scalars and Vectors



Lecture 2 Slide 18


Fall 2004


Spring 2009

Scalars and VectorsScalar: 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.



Lecture 2 Slide 19


Fall 2004


Spring 2009

Examples of Scalars

Consider the lowly penny:

Scalar Quanity SI Unit # pennies in my pocket 15¢ (not SI unit)

# atoms in penny 1/12 mole (5 · 10+22 atoms)

mass of penny 0.003 kg

diameter of penny 0.02 m

volume of penny 3 · 10-7 m3

density of penny 9 · 10+3 kg/m3

temperature of penny 293 K



Lecture 2 Slide 20


Fall 2004


Spring 2009

Basic Trigonometry:

90or

18090

BA

BA

Hypotenuse Opposite side

A

B

Adjacent Side

y

A

Bh

x

hypotenuse

adjacentcos

adjacent

oppositetan

hypotenuse

oppositesin

A

A

A

versa viceand cossin so

cos and sin

BA

h

yB

h

yA

h

xcos

x

ytan

h

y sin

A

A

A

22yxh

Right Angle Triangle



Lecture 2 Slide 21


Fall 2004


Spring 2009

Example

Triangle components:

A=30°

B=60°y(=1)

h (=2)

)3(x 3

130tan

2

330cos

2

130sin

Ax cos.hx

Ah

cos

Ay sin.hor y

Ah

sin

yA

xtan Ay tan.x



Lecture 2 Slide 22


Fall 2004


Spring 2009

How to Represent a Vector:

N

E40°

Arrow • Represents its magnitude by its length.

• Represents its direction by its angle.

y = v . sin 40°

N

E40°

v

x = v . cos 40° We have resolved the vector motion into 2 “components”.



Lecture 2 Slide 23


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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 x 20

40tan. m20

tan. Ay x

tan y

xA



Lecture 2 Slide 24


Fall 2004


Spring 2009

river30 kmlaunch

N

E55°

ballooncourse15 km/hr

Question: How long before the balloon crosses the river?

Example: Vectors

Solution:

VE = v cos(55°)

VN= v sin(55°)

55°

v =15 km/hrVE = 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 vN to get distance traveled Northwards.



Lecture 2 Slide 25


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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.

cB

A

E

N

“Math-Lite” Method: (graphical)1. Draw 1st vector to scale and in appropriate direction,2. Start 2nd vector at head of 1st 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

1st

2nd

3rd

E

N

origin



Lecture 2 Slide 26


Fall 2004


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.

cB

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

1st

2nd

3rd

E

N

origin



Lecture 2 Slide 27


Fall 2004


Spring 2009

Vector subtraction:A

-A

BD

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.



Lecture 2 Slide 28


Fall 2004


Spring 2009

Example: Vector Velocities

Boat crossing a river…

35°

plannedcourse

actualcourseE

N

riverflow

Question: How fast is the river flowing?

Solution:

35°

vB = 7 km/hr

actualcourse

vR = vB tan(35°)

Boat speed vB = 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!



Lecture 2 Slide 29


Fall 2004


Spring 2009


Next Lab/Demo: MotionTuesday 1:30-2:45

ESLC 46 Ch 2

Next Class: Fri 10:30-11:20BUS 318 roomReview Ch 2

Documents

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