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PHYSICS FOR ENGINEERS 1 (PHY 2043) Spring 2013Prerequisite course required MAC 2281 or MAC 2311

Instructor: Dr. Grigoriy Kreymerman

COURSE TEXT BOOK:PHYSICS FOR SCIENTIST AND ENGINEERS, Vol-1, Sixth EditionAuthors: Paul A. Tipler and Gene MoscaPublisher: W. H. Freeman and Company (http://whfreeman.com/tipler/)

The biggest part of this book is Mechanics fallowing by Oscillations Waves and Thermodynamics.

There will be four tests and four 15 minutes quizzes.

Test 1, 2 and 3 will grade 105 points each. The final exam will grade 120 points. The total score for tests will be 435. Quizzes each 21 points total four quizzes 84 points.Homework assignment 60 points total.MAXIMUM TOTAL COURSE POINTS POSSIBLE 579.

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The required textbook for this course is

PHYSICSFor Scientists and Engineers Sixth Edition

by Paul A. Tipler and Gene Mosca

(©2008, W.H. Freeman & Company)

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1-CHAPTER

Units

Conversion of Units

Dimensions of Physical Quantities

Vectors

General Properties of Vectors

MEASUREMENT AND VECTORS

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Physical unit is the define standard for measurement of physical quantity or value.

For example

Distance_____ meters, kilometers, feet, yards, miles…….

Time _____ seconds, minutes, hours, days, ……

Mass_______ kilograms, grams, milligrams, pounds ….

The basic standard, which use in physics is The International System of Units (or SI units)-we will use in this course base SI quantities - seconds (s), meters (m), kilograms (kg)

In 1960, an international committee established a set of standards for the scientific community called SI (for System International).

U.S. customary system inches, feet, yards, miles, pounds,….Foot originally defined as the length of the king’s foot in France.

To express measurement quantitatively we need introduce units.

?

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There are seven base quantities in the SI system. They are length, mass, time, electric current, thermodynamic temperature, amount of substance (mole), and luminous intensity.

For now we define only three base units or fundamental quantities:Time, Length, and Mass

Time ----- second (s) Historically it is (1/60)x(1/60)x(1/24) of the mean solar day

Modern etalon of the time define by frequency of E.M. radiation emittedfrom a certain level excitation in cesium (9192631770 cycles per second)

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Length-----meter (m) Historically length was define as 1/10,000,000 or of the distance between the equator and North Pole.

Today length define by speed of light (299792458 m/s)in empty space. The meter is the distance which light travel1/ 299792458 second.

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Standard 1m between two scratches on platinum –iridium alloy at constant temperature adapted 1889.

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Mass-----kilogram (kg) Historically was defined as the mass of one liter of distillated water at 4ºC.

The kilogram is now defined to be the mass of a specific platinum-iridium alloy cylinder, which store in the International Bureau of Weights and Measures in Sèvres, France.

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The classical example of importance of units is NASA fiasco with Mars probe in 1999. The Jet Propulsion Laboratory in California and Lockhead Martin in Colorado use different units of measurement.

Units Prefixes

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How many centimeters are there in one foot? How many centimeters are there in one mile?

Example:

We can use the facts that there are 2.540 centimeters in 1 inch and 12 inches in 1 foot to show that there are 30.48 cm per ft. We can then use the fact that there are 5280 feet in 1 mile to find the number of centimeters in one mile.

Multiply 2.540 cm/in by 12 in/ft to find the number of cm per ft:

cm/ft.ft

in

in

cm. 4830125402

Multiply 30.48 cm/ft by 5280 ft/mi to find the number of centimeters in one mile:

cm/mi.mi

ft

ft

cm. 510609152804830

Conversion of Units

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Dimensions of Physical Quantities

We going use next notation : for distance = [L], for time = [T], mass = [M]

We can multiply or divide physical quantities (values) in deferent units.

Example speed = [L] / [T]

When we adding or subtracting physical quantities (values) dimensions of this quantities should be same.

Example total length = [L1] + [L2]

Dimensional analysis. Falling time as function of high and ……?

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Force has dimensions of mass times acceleration. Acceleration has dimensions of speed divided by time. Pressure is defined as force divided by area. What are the dimensions of pressure? Express pressure in terms of the SI base units kilogram, meter and second.

Example:

Use the definition of pressure and the dimensions of force and area to obtain:

22

2

LT

M

LT

ML

A

FP

Express pressure in terms of the SI base units to obtain:

22

2

2 sm

kg

ms

mkg

m

N

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True or false:(a) Two quantities must have the same dimensions in order to be added.(b) Two quantities must have the same dimensions in order to be multiplied.

(a) True. You cannot add apples to oranges or a length (distance traveled) to a volume (liters of milk).

(b) False. The distance traveled is the product of speed (length/time) multiplied by the time of travel (time).

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Example:

In doing a calculation, you end up with m/s in the numerator and m/s^2 in the denominator. What are your final units? (a) m^2/s^3, (b) 1/s, (c) s^3/m^2, (d) s, (e) m/s.

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Order of Magnitude

Rounding number to the nearest power of 10 called an order of magnitude.

is approximately g4109 g510

Assume, percentage of Human Body that is Water Up to 60 percent. The mass of a water molecule is 30 10-27 kg. If the mass of a person is 60 kg, estimate the number of water molecules in that person.

Problem:

N represent the number of water molecules in a person of mass m

60.molecule water

body human m

mN

molecules .

.

moleculekg

kg

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27

1021

601030

60

N

g5109 is approximately ?

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VECTORS

Equal Vectors

Vector define by magnitude (displacement or length) and direction.

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Addition and Subtraction of Vectors

Vector sum, or resultant.

Head-to-Tail method addition.

Parallelogram method addition

Vector addition obeys the commutative law

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CBACBAVector addition is associative.

BAC it is not equal to .BAC Except when and are parallel.

A

B

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Subtraction of Vectors

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A vector points in the +x direction. Show graphically at least three choices for a vector such that points in the +y direction.

A

B

AB

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CBAE

CBAD

BACC

ACBB

ACBA

.

.

.

.

.

is

and, vectorsamong iprelationsh the

describeshat equation t vector The

CBA

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Component of Vector

Component of vector in define direction is the projection of the vector onto an axis in that direction.

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The process of finding the x,y, and z component of vector is called resolving the vector

We can find angle θ if we know Ax and Ay.

In three dimensions.

22yx AAA

222zyx AAAA

x

y

A

Atan

x

y

A

Aarctan

(or decomposition vector)

jAiAA yx

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XXX BAC YYY BAC

BAC

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A vector A 7.00 units long and a vector B 5.50 units long are added. Their sum is a vector C 10.0 units long. Determine the angle between of two vectors.

Problem:

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180

cos2222 ABBAC

ABCBA

2cos

2221

6.105

5.5720.1050.500.7

cos222

1

746.105180

Apply the law of cosines

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Unit Vectors

A Unit Vector of vector is vector which is in same direction as vector but without dimensions and with magnitude equal to 1.

kBAjBAiBA

kBjBiBkAjAiABA

kAjAiAA

AAAAwhereA

AA

zzyyxx

zyxzyx

zyx

zyx

222

A

A A

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Given the following vectors: , and (a) Find the vector , in unit vector notation, such that (b) Express your answer in Part (a) in terms of magnitude.

A 3.4ˆ i 4.7 ˆ j

B 7.7 ˆ i 3.2 ˆ j

C 5.4ˆ i 9.1 ˆ j

D

D 2A 3

C 4

B 0

(a) Solve the vector equation that gives the condition that must satisfied for D

BCAD

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Substitute for BCA

and ,

ji

ji

jijijiD

ˆ5.49ˆ2.40

ˆ8.123.274.9ˆ8.302.168.6

ˆ2.3ˆ7.74ˆ1.9ˆ4.53ˆ7.4ˆ4.32

(b) Use the Pythagorean Theorem 22yx DDD 8.635.492.40 22 D

(c) Find unit vector for D vector.

(c) jiji

D

DD ˆ78.0ˆ63.0

8.63

ˆ5.49ˆ2.40ˆ

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