chapter i quantities editing

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Using Your Brain for a Change 1Created by Rozie

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CHAPTER 1

BESARAN dan SATUAN

3. Pengukuran

1. Besaran

2. Dimensi

4. Ketidakpastian Pengukuran

5. Angka Penting dan Notasi Ilmiah


Measurement or to measure is an activity to compare a quantity with another quantity that is assigned as a unit

1.Measurement

A. The Unit Of Length: metre

1 metre

“The distance between two marks on a bar of platinum - iridium alloy that was stored in IBWM in Sevres, France “

Before 1967

From 1967- 1983

“1,650,763.73 times the wavelength of a certain orange spectral line of atomic krypton-86”

Afte

r 19

83

“the path traveled by light in vacuum during a time interval of 1/299,792,458 s”


B. The Unit of time: second

“1 second is defined as the time required for exactly 9,192,631,770 oscillations of an isotope cesium -133 atom particle “

C. The Unit of Mass: kilogram

“ 1 kg is the mass of a platinum – iridium cylinder kept in the IBWM, France

D. The Unit of Electric Current: ampere

“ 1 A is the electric current flowing in two long parallel wires and have distance of 1 m in vacuum space and it gives force of 2 x 10 -7N/m”


E. The Unit of Temperature: kelvin

“1 K is 1/273.16 times temperature of triple point of water “

F. The Unit of Luminous Intensity: candela

“1 cd is 1/16 of luminous intensity resulted from 1 cm2 of the blackbody radiation glowing at temperature of frozen platinum, that is 2046 K “

G. The Unit of Amount of Substance: mole

“1 mole is the amount of substances that contains 6.02 x 1023 particles “


Awalan Satuan


2. Quantities (Besaran)“Something that’s measurable and

expressible by number”

Quantities

Basic (pokok)

Derived (turunan)

“the physical quantities the units of which are predetermined”

“the physical quantities the units of which are derived from basic quantity units”

Berdasarkan satuan

Berdasarkan kepemilikan arah Skalar

Vector“described by both a magnitude and a direction”

“described by a magnitude (or numerical value) alone “


Basic Quantities

BASIC QUANTITIES BASIC UNITSName Symbol

Length (l) metre mMass (m) kilogram kgTime (t) second sTemperature (T) kelvin KLuminous Intensity (I) candela CdAmount of Substance (n) mole mol

electr ic current ( i) ampere A

In 1960, scientist at the General Conference of Weight and Measures adopted the international usage of a metric system of measurement called International System of Units (abbreviated as SI)


Derived Quantities

Formula Derived from Basic quantities

Units

Area A= p . l Length m2

Velocity Length and Time m/s

Acceleration Length and Time m/s2

Force F = m . a Mass, Length and Time kg m/s2 = N

Density Mass and Length kg/m3

Work W = F . s Mass, Length and Time kg m2/s2 = J

Derived Quantitiest

sv =

t

sv =

t

va =

For Example:

V

m=ρ


Vector and Scalar Quantities

Examples of scalars and vectors

Scalar quantity Vector quantity

distancespeedtemperatureenergypowermassdensityvolume time

displacementvelocityaccelerationforceweightmomentumtorqueelectric fieldmagnetic flux density


3. DimensionUsed to describe the method of arrangement of derived quantities from basic quantities

BASIC QUANTITIES DIMENSIONS

Length [L]Mass [M]Time [T]Temperature [θ]Luminous Intensity [J]Amount of Substance [N]electr ic current [I]

ghv ρ=


Benefit of Dimension:1. Dimension can be used to check that 2 quantities are homogeneity or

equality. For example: Proof that “Work (W = F . S)” and “kinetic energy (EK = ½ mv2) ” are equal!

2. To find that a equation is true or false (however, does not guarantee that the equation is physically correct).

For example:

Which of these equations could be correct!

a. b. c.

d.

3. To find dimension or units of unknown quantities in a equation.

For example:

What is dimension of h in the equation E = h f (E = energy, f = frequency, and h = Planck constant)

ghv ρ= λgv =T

v=λ

asvv 220

2 +=


Question 11. Find the dimension of the derived quantities follow!

a. weight, w (w= m . g) b. Pressure, P ( P= F/A)

c. Electric charge, q (q= I . t) d. Power, P (P= E/t)

2. Find the units (in term of the basic units) and the dimension of k in the equation

(F= electrostatic force, q= electric charge, and r= distance)

3. Find the units (in term of the basic units) and the dimension of R in the equation (P= pressure, V= volume, n= amount of substance, and T= temperature)

221

r

qqkF =

nRTPV =


The instrument to measure length1. Ruler

3. Micrometer screw gauge

2. Vernier Caliper

Smallest scale value: 1mm

Smallest scale value: 0.1mm

Smallest scale value: 0.01mm


HOW TO READ A MEASUREMENT FROM THE SCALES ON THE VERNIER CALIPER and THE MICROMETER

1. Vernier Calipera. Type 1

•Main Scale : 2.3 cm

•Vernier Scale : (2 x 0.01) = 0.02 cm

The Reading is 2.32 cm = 23.2 mm


b. Type 2

•Main Scale : 1.9 cm

•Vernier Scale : (6.4 x 0.01) = 0.064 cm

The Reading is 1.964 cm = 19.64 mm


2. Micrometer Screw Gauge

•Main Scale : 14.5 mm

•Vernier Scale : (11 x 0.01) = 0.11 mm

The Reading is 14.61 mm = 1.461 cm


4. Measurement Uncertainly (MU)

MU Caused by

- General error/ Human error: skill to use instrument, mistake in read scale

- Systematic error: mistake of instrument calibration, mistake of zero point, mistake of parallax, mistake of instrument component, and mistake of environmental condition (temperature, atmospheric pressure, air humanity)

- Random error: electric voltage fluctuation, Brown movement of air molecules


For single measurement

For Recurrent Measurement

Absolute Uncertainly

MU

Relative Uncertainly

nstX ×=∆ 21

1

)( 221

−Σ−Σ=∆

n

XXnX ii

n

RU = Relative Uncertainly

X0 = result of the single measurement

n = the sum of recurrent measurementXi = the result of quantity measurement of i - th

For single measurement

For Recurrent Measurement

%1000

×∆=X

XRU

%100×∆=X

XRU

∆X = Absolute Uncertainly

nst = smallest scale value

n

XX iΣ=

=X The mean of quantity measurement


Reporting the Result of Measurement

• For single measurement:

XXX ∆±= 0

• For recurrent measurement:

XXX ∆±=X = physical quantity measured

X0 = result of single measurement

= The mean of quantity measurement

∆X = absolute uncertainly

X


Sample Problem:

1.The result of a coin diameter measurement use a vernier caliper is 1.24 cm. Write the report of result measurement!Solution:D0 = 1.24 cm

½ nst = ½ x 0.01 cm = 0.005 cm

Thus, the diameter of the coin is

or

DDD ∆±= 0

cmD )005.024.1( ±=

%4.0%10024.1

005.0 == xRUcmD %)4.024.1( ±=


2. A six times measurement of electric current finds the reading of 12.8 mA, 12.2 mA, 12.5 mA, 13.1 mA, 12.9 mA, dan 12.4 mA. Write the report of result measurement aforesaid!

Solution:

163.84 mA

148.84 mA

156.25 mA

171.61 mA

166.41 mA

153.76 mA

12.8 mA

12.2 mA

12.5 mA

13.1 mA

12.9 mA

12.4 mA

1

2

3

4

5

6

Ii2Iii

mAI i 9.75=Σ mAI i 71.9602 =Σ


mAn

II i 65.12

6

9.75 ==Σ=

Thus, the electric current is

14.016

)9.75()71.960(6

6

1

1

)( 2221 =

−−=

−Σ−Σ=∆

n

IInI ii

n

mAI )14.065.12( ±=


5. Significant Digits

Significant Numbers (SN)

SN“all numbers that are gained from measurement”

Consist of

Exact numbers

Estimation number

(“the latest number”)

EX: “The result of a coin diameter measurement use a vernier caliper is 1.25 cm”. Numbers of 1.25 has 3 SN, numbers of 1 and 2 are exact number, while number 0f 5 is estimation number

Exact Numbers

NUMBERS

“all numbers that are gained from counting”

EX: “A book has 75 pages”. Number of 75 is exact number


1. All number other than zero are SN (Significant Number) 6.234 has 4 SN 5.3 has 2 SN

The Significant Numbers Rules

B. The zeroes number on the left hand of numbers other than zeroes, is not significant number

• 0.008 has 1 SN• 0.0123 has 3 SN• 0.00460 has 3 SN

2. Rules for zeroes number

A. The zeroes number between two numbers other than zero is SN

• 406 has 3 SN• 20,0408 has 6 SN


C. The zeroes number on the right hand of numbers other than zero and behind the decimal point is significant number.

• 0.4600 has 4 SN

D. The zeroes number on the right hand of numbers other than zero but not behind the decimal point is not significant number, except if there is a sign like an underline.

• 25000 has 2 SN

• 25000 has 4 SNIf the number of 25000 is written by scientific notation, so number of significant digits depend of its written.

• 2.5 x 104 has 2 SN

• 2.50 x 104 has 3 SN

• 2.500 x 104 has 4 SN


Rules of Significant numbers calculation1. For Addition or Subtraction

“the result can only one estimation numbers” • Sample Problem:

a. 273.219 9 is estimation number (EN)

15.5 5 is estimation number

8.43 3 is estimation number ------------- +

297.149 (has 3 EN) 297.1 (the end result has one EN)

2. For Multiplication or Division

“the result can only have SN as many as the smallest SN between the numbers multiplied”

0.6283 has 4 significant numbers (SN)

2.2 has 2 SN---------- x1.8226 has 5 SN, so the end result is 1.8 (has 2 SN)


However, for multiplication between significant numeral and exact number “the result can only have SN similar be possessed by significant numeral”EX: Thick of a book is 1.25 cm. how many thick of book heap of 20 piece?Solution: 1.25 x 20 = 25,0

has 3 SN has 3 SN

3. For Power and Root

“the result can only have SN as many as SN of the numbers that powered or rooted”

5.125.2 =

5.125.2 = 1.50 has 3 SN

( ) 25.65.2 2 = 6.2 has 2 SN


6. SCIENTIFIC NOTATION

Written of numbers in form: a x 10n with 1 < a <10 and n= integer

• 120000 1,2 x 105

• 10000 104

• 0.000253 2.53 x 104

• 125 x 10-5 1.25 x 10-3

• 0.00228 x 108 2.28 x 105

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