FisDas - Week 01 - Unit, Dimension & Vector

8/11/2019 FisDas - Week 01 - Unit, Dimension & Vector

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Unit, Dimension & Vector

Physics I

Setyawan P Sakti


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What is Physics

Physics

(from Greek

(

), i.e. "knowledge of nature", from

,

physis

, i.e. "nature

")

is the natural science that involves the study of

matter

and its motion through space and time, along with related concepts

such as energy and

force. More

broadly, it is the general analysis of nature,

conducted in order to understand how the universe behaves

.

Physics involves the

study of energy and matter that is scientific in nature.

Included in such study is the observation and comprehension of the

interaction of said energy and matter. The energy involved here usually

takes a lot of forms. Said forms include gravity, radiation, electricity, light,

motion, etc. On the other hand, the matters that are dealt with by Physics

are those ranging from particles to galaxies.

Physics

is a natural science based on experiments, measurements and

mathematical analysis with the purpose of finding quantitative physical laws

for everything from the

nanoworld

of the

microcosmos

to the planets, solar

systems and galaxies that occupy the

macrocosmos

.


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Nano material


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Galaxy


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10-15


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10-14


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10-10


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10-9


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10-8


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10-7


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10-6


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10-4


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10-3


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10-2


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10-1


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1


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10


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10+2


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10+3


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10+4


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10+6


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10+7


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10+8


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10+9


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10+10


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10+12


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10+13


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10+15


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10+21


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10+26


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Review

Berapakah berat saudara ?

Berapakah jarak dari rumah anda ke

kampus ?

Berapa lama perjalanan dari rumah kekampus dengan berjalan kaki ?


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Systems of Measurements

cgs -- Gaussian system named for the first letters of the units it uses

for fundamental quantities

US Customary everyday units (ft, etc.)

often uses weight, in pounds, instead of mass

as a fundamental quantity


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Basic Quantities and Their Dimension

Length [L]

Mass [M]

Time [T]

Why do we need standards?


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Length

Units SI -- meter, m

cgs -- centimeter, cm

US Customary -- foot, ft

Defined in terms of a meter -- the distance

traveled by light in a vacuum during a

given time (1/299 792 458 s)


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Mass

Units SI -- kilogram, kg

cgs -- gram, g

USC -- slug, slug

Defined in terms of kilogram, based on a

specific Pt-Ir cylinder kept at the

International Bureau of Standards


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Standard Kilogram

Why is it hidden under two glass domes?


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Time

Units seconds, s in all three systems

Defined in terms of the oscillation of

radiation from a cesium atom(9 192 631 700 times frequency of light emitted)


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Time Measurements


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US Official Atomic Clock


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Dimensional Analysis

Dimension denotes the physical nature of aquantity

Technique to check the correctness of an

equation Dimensions (length, mass, time,

combinations) can be treated as algebraicquantities add, subtract, multiply, divide

quantities added/subtracted only if have sameunits

Both sides of equation must have the same

dimensions


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Dimensional Analysis

Dimensions for commonly used quantities

Length L m (SI)

Area L2 m2 (SI)

Volume L3 m3 (SI)

Velocity (speed) L/T m/s (SI)

Acceleration L/T2 m/s2 (SI)

Example of dimensional analysis

distance = velocity time

L = (L/T) T


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Units

Phys ical quan ti ty Unit Dim en tion

Length m L

Mass kg M

Time s T

Current A ITemperature K

Number of molecules/atom mol N

Light intensity cd J

What about taste ? Smell ?


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Conversions

When units are not consistent, you may

need to convert to appropriate ones

Units can be treated like algebraicquantities that can cancel each other out

1 mile = 1609 m = 1.609 km 1 ft = 0.3048 m = 30.48 cm

1m = 39.37 in = 3.281 ft 1 in = 0.0254 m = 2.54 cm

Example 1

Scotch tape:


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Example 1. Scotch tape:

Example 2. Trip to Surabaya:Legal freeway speed limit in Indonesia is 100 km/h.

What is it in miles/h?

h

miles

km

mile

h

km

h

km62

609.1

1100100


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Prefixes

Prefixes correspond to powers of 10

Each prefix has a specific name/abbreviation

Power Prefix Abbrev.

1015 peta P

109 giga G

106 mega M

103

kilo k10-2 centi c

10-3 milli m

10-6 micro m

10-9 nano n

Distance from Earth to nearest star 40 Pm

Mean radius of Earth 6 Mm

Length of a housefly 5 mmSize of living cells 10 mm

Size of an atom 0.1 nm


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Enormous Dynamic Range

cm33

10

cm28

10

0,000000000000000000000000000000001 cm 10000000000000000000000000000 cm

m35

10

m26

10


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Uncertainty in Measurements

There is uncertainty in everymeasurement, this uncertainty carries over

through the calculations

need a technique to account for thisuncertainty

We will use rules for significant figures to

approximate the uncertainty in results ofcalculations

Si ifi t Fi


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Significant Figures

A significant figure is one that is reliably known

All non-zero digits are significant

Zeros are significant when

between other non-zero digits after the decimal point and another significant figure

can be clarified by using scientific notation

4

4

4

1074000.10.17400

107400.1.17400

1074.117400

3 significant figures




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Operations with Significant Figures

Accuracy -- number of significant figures

When multiplying or dividing, round the result

to the same accuracy as the least accuratemeasurement

When adding or subtracting, round the resultto the smallest numberof decimal places ofany term in the sum

Example: 135 m + 6.213 m = 141 m

meter stick: cm1.0

rectangular plate: 4.5 cmby 7.3 cm

area: 32.85 cm2 33 cm2


Example:

Example:

Order of Magnitude


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Order of Magnitude

Approximation based on a number of assumptions

may need to modify assumptions if more precise results

are needed

Order of magnitude is the power of 10 that applies

Example: Jono has 3 apples, Joni has 5 apples.

Their numbers of apples are of the same order of magnitude

Question: McDonalds sells about 250 million packages of fries

every year. Placed back-to-back, how far would the fries reach?

Solution: There are approximately 30 fries/package, thus:

(30 fries/package)(250 . 106packages)(3 in./fry) ~ 2 . 1010 in ~ 5 . 108 m,

which is greater then Earth-Moon distance (4 . 108 m)!


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Coordinate Systems

Used to describe the position of a point inspace

Coordinate system (frame) consists of

a fixed reference point called the origin

specific axes with scales and labels

instructions on how to label a point relative to

the origin and the axes

T f C di t S t


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Types of Coordinate Systems

Cartesian Plane polar

C t i di t t


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Cartesian coordinate system

also called rectangular coordinate system x- and y- axes

points are labeled (x,y)

Pl l di t t


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Plane polar coordinate system

origin and reference line are noted point is distance r from the origin in the

direction of angle , ccw from reference line

points are labeled (r,)


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VECTOR

Physics deals with a great many quantities that have both size anddirection, and it needs a special mathematical languagethelanguage of vectorsto describe those quantities. (Halliday-Resnick, Chapter 3)


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Scalar and Vector Quantities

Scalarquantities are completely described bymagnitude only (temperature, length,)

Vectorquantities need both magnitude (size)

and direction to completely describe them

(force, displacement, velocity,)

Represented by an arrow, the length of the arrow is

proportional to the magnitude of the vector Head of the arrow represents the direction

Vector Notation


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Vector Notation

When handwritten, use an arrow: When printed, will be in bold print: A

When dealing with just the magnitude of a

vector in print, an italic letter will be used:A

A

Properties of Vectors


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Properties of Vectors

Equality of Two Vectors Two vectors are equal if they have the same

magnitude and the same direction

Movement of vectors in a diagramAny vector can be moved parallel to itself

without being affected

More Properties of Vectors


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More Properties of Vectors

Negative Vectors Two vectors are negative if they have the

same magnitude but are 180 apart (opposite

directions) A = -B

Resultant Vector

The resultant vector is the sum of a given set

of vectors

Adding Vectors


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Adding Vectors

When adding vectors, their directions mustbe taken into account

Units must be the same

Graphical Methods Use scale drawings

Algebraic Methods

More convenient

Adding Vectors Graphically


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Adding Vectors Graphically(Triangle or Polygon Method)

Choose a scale Draw the first vector with the appropriate length

and in the direction specified, with respect to a

coordinate system

Draw the next vector with the appropriate length

and in the direction specified, with respect to a

coordinate system whose origin is the end of

vector A and parallel to the coordinate systemused for A

Graphically Adding Vectors


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Continue drawing the vectors tip-to-tail The resultant is drawn from the origin of A to the end

of the last vector

Measure the length of R and its angle Use the scale factor to convert length to actual magnitude



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When you have manyvectors, just keeprepeating the process untilall are included

The resultant is still drawnfrom the origin of the firstvector to the end of thelast vector

Alternative Graphical Method


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Alternative Graphical Method

When you have only twovectors, you may use the

Parallelogram Method

All vectors, including the

resultant, are drawn froma common origin

The remaining sides of the

parallelogram are sketched

to determine the diagonal,

R

Notes about Vector Addition


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Notes about Vector Addition

Vectors obey theCommutative Law of

Addition

The order in which the

vectors are addeddoesnt affect theresult

Vector Subtraction


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Vector Subtraction

Special case of vectoraddition

If A B, then useA+(-B)

Continue with

standard vector

addition procedure

Multiplying or Dividing a Vector


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p y g gby a Scalar

The result of the multiplication or division is a vector

The magnitude of the vector is multiplied or divided by the

scalar

If the scalar is positive, the direction of the result is the

same as of the original vector

If the scalar is negative, the direction of the result is

opposite that of the original vector

C t f V t


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Components of a Vector

A component is a part

It is useful to use rectangular

components These are the projections of the

vector along the x- and y-axes

Vector A is now a sum of its

components:

yx AA

A What are and ?xA

yA

Components of a Vector


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Components of a Vector The components are the legs of the right triangle

whose hypotenuse is A

The x-component of a vector

is the projection along the x-axis

The y-component of a vector

is the projection along the y-axis

Then,

cosAAx

sinAAy

yx

AA

A

x

y12

y

2

xA

AtanandAAA

yA

N t Ab t C t


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Notes About Components

The previous equations are valid only i f is

measured w i th respect to the x-axis

The components can be positive or negative

and will have the same units as the original

vector

Example 1


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A golfer takes two putts to get his ball into the hole once he is on the green. Thefirst putt displaces the ball 6.00 m east, and the second, 5.40 m south. Whatdisplacement would have been needed to get the ball into the hole on the first putt?

Given:

Dx1= 6.00 m (east)

Dx2= 5.40 m (south)

Find:

R = ?

Solution:

2 2

6.00 m 5.40 m 8.07 mR

1 15.40 m

tan tan 0.900 42.06.00 m

6.00 m

5.40 m1. Note right triangle, usePythagorean theorem

2. Find angle:

What Components Are Good For:


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What Components Are Good For:

Adding Vectors Algebraically

Choose a coordinate system and sketch the

vectors v1, v2,

Find the x- and y-components of all the vectors

Add all the x-components

This gives Rx:

Add all the y-components

This gives Ry:

xx vR

yy vR

Magnitudes of vectors

pointing in the same

direction can be addedto find the resultant!

Adding Vectors Algebraically (cont )


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Adding Vectors Algebraically (cont.)

Use the Pythagorean Theorem to find themagnitude of the Resultant:

Use the inverse tangent function to find

the direction of R:

2y2x RRR

x

y1

R

Rtan

More About Components of a


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pVector

The previous equations are valid on ly i f ismeasu red w i th respect to the x-axis

The components can be positive or negative andwill have the same units as the original vector

The components are the legs of the right trianglewhose hypotenuse is A

May still have to find with respect to the positive x-axis

x

y12

y

2

x

A

AtanandAAA


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Area


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Area

Length times length

Q. Which one is correct for area. It is

vector or scalar? Jawaban

Volume
http://localhost/var/www/apps/conversion/tmp/scratch_3/Luas%20sebagai%20vektor.swfhttp://localhost/var/www/apps/conversion/tmp/scratch_3/Luas%20sebagai%20vektor.swf


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Volume

Q. Which one is correct for volume. It is

vector or scalar?

Unit Vector Notation in


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Cartesian Coordinate


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Example:

Vector Addition


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Example: Vector Addition

III. Problem Solving Strategy


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g gy

Slide 13

Fig. 1.7, p.14

Known: angle and one side

Find: another sideKey: tangent is defined via two sides!

mmdistheight

dist

buildingofheight

3.37)0.46)(0.39(tantan.

,.

tan

Problem Solving Strategy


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Problem Solving Strategy

Read the problem identify type of problem, principle involved

Draw a diagram

include appropriate values and coordinatesystem

some types of problems require very specific

types of diagrams

Problem Solving cont


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Problem Solving cont.

Visualize the problem Identify information

identify the principle involved

list the data (given information) indicate the unknown (what you are looking

for)

Problem Solving, cont.


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Problem Solving, cont.

Choose equation(s) based on the principle, choose an equation or

set of equations to apply to the problem

solve for the unknown Solve the equation(s)

substitute the data into the equation

include units

Problem Solving, final


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Problem Solving, final

Evaluate the answer find the numerical result

determine the units of the result

Check the answer

are the units correct for the quantity being found?

does the answer seem reasonable?

check order of magnitude

are signs appropriate and meaningful?

Tugas

dan

Latihan


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Tugas dan Latihan

The fastest growing plant on record is a Hesperoyucca whippleithatgrew 3.7 m in 14 days.What was its growth rate in micrometers per

second?

You are to make four straight-line moves over a flat desert floor,

starting at the origin of anxycoordinate system and ending at thexy

coordinates (140 m, 30 m).Thex component and y component of

your moves are the following, respectively, in meters: (20 and 60),

then (bxand 70), then (20 and cy), then (60 and 70). What are (a)

component bxand (b) component cy? What are (c) the magnitude

and (d) the angle (relative to the positive direction of thex axis) of

the overall displacement?

FisDas - Week 01 - Unit, Dimension & Vector

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