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
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
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
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
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
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
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
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
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, 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
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 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
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 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)
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:
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
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.
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
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 = 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)
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
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 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?
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 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?
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
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 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.
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:
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
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:
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
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
130tan
2
330cos
2
130sin
Ax cos.hx
Ah
cos
Ay sin.hor y
Ah
sin
yA
xtan Ay tan.x
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
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”.
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 x 20
40tan. m20
tan. Ay x
tan y
xA
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
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.
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.
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
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.
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
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
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.
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°
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!
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: MotionTuesday 1:30-2:45
ESLC 46 Ch 2
Next Class: Fri 10:30-11:20BUS 318 roomReview Ch 2
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