chapter i quantities

CHAPTER 1

QUANTITIES and MEASUREMENTSand1. Measurement

2. Quantities

• Basic and Derived Quantities

• Scalar and Vector Quantities

Using Your Brain for a Change 1Created by Rozie

3. Dimension

4. Measurement Uncertainly

5. Significant Numbers and Scientific Notation

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: metreA. 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

Afte

r 19

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


1 metre

From 1967- 1983

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

Afte

r 19

83

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 “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


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: candelaF. 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 “

The Prefixes of SI Units


2. Quantities“Something that’s measurable and expressible by number” Basic Quantities

“the physical quantities the units of which are predetermined”

Quantities

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

Base of Units

Vector


Base of have or haven’t direction Scalar

Vector“described by both a magnitude and a direction”

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

Basic Quantities

BASIC QUANTITIES BASIC UNITS

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)

BASIC QUANTITIES BASIC UNITSName Symbol

Length metre m

Mass kilogram kg

Time second s

Temperature kelvin K


Temperature kelvin K

Luminous Intensity candela cd

Amount of Substance mole mol

electric current ampere A

Derived Quantities

Formula Derived from Basic quantities

Units

Derived Quantitiest

sv

For Example:

Area A= p . l Length m2

Velocity Length and Time m/s

Acceleration Length and Time m/s2

t

sv

t

va


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

V

m

Vector and Scalar Quantities

Examples of scalars and vectors

Scalar quantity Vector quantity

distance displacementdistance

speed

temperature

energy

power

displacement

velocity

acceleration

force

weight


mass

density

volume

time

momentum

torque

electric field

magnetic flux density

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

BASIC QUANTITIES DIMENSIONS

ghv

BASIC QUANTITIES DIMENSIONS

Length [L]

Mass [M]

Time [T]

Temperature [θ]

Luminous Intensity [J]


Luminous Intensity [J]

Amount of Substance [N]

electric current [I]

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).that the equation is physically correct).

For example:

Which of these equations could be correct!

a. b. c.

d.

ghv gvT

v

asvv 220

2


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)

asvv 20

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)2

21

r

qqkF


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)

nRTPV

The instrument to measure length1. Ruler

2. Vernier Caliper

Smallest scale value: 1mm

3. Micrometer screw gauge

2. Vernier Caliper

Smallest scale value: 0.1mm


3. Micrometer screw gauge

Smallest scale value: 0.01mm

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

1. Vernier Calipera. Type 1a. 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)

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

MU Caused By

- 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)


atmospheric pressure, air humanity)

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

For single measurement

Absolute Uncertainly

nstX 21

)( 221

XXn

X ii

For Recurrent Measurement

∆X = Absolute Uncertainly

nst = smallest scale value

MU

1

)(1

n

XXnX ii

n

RU = Relative Uncertainly

X0 = result of the single

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

For single measurement

%100

X

XRU


For Recurrent MeasurementRelative Uncertainly

X0 = result of the single measurement

%1000

X

RU

%100

X

XRU n

XX i

X The mean of quantity measurement

Reporting the Result of Measurement

• For single measurement:

XXX 0

• For recurrent measurement:• For recurrent measurement:

XXX X = physical quantity measured

X0 = result of single measurement

= The mean of quantity measurementX


= 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:Solution:D0 = 1.24 cm

½ nst = ½ x 0.01 cm = 0.005 cm

Thus, the diameter of the coin is

DDD 0


orcmD )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:I 2Ii

Solution:

163.84 mA

148.84 mA

156.25 mA

171.61 mA

166.41 mA

12.8 mA

12.2 mA

12.5 mA

13.1 mA

12.9 mA

1

2

3

4

5

Ii2Iii


166.41 mA

153.76 mA

12.9 mA

12.4 mA

5

6

mAIi 9.75 mAIi 71.9602

mAn

II i 65.12

6

9.75

14.0)9.75()71.960(61)( 222

1

IIn

I ii

Thus, the electric current is

14.016

)9.75()71.960(6

6

1

1

)(1

n

IInI ii

n

mAI )14.065.12(


5. Significant Numbers

Exact Numbers “all numbers that are gained from counting”

EX: “A book has 75 pages”.

Significant Numbers (SN)

SN “all numbers that are gained from Consist of

Exact numbers

Estimation number

NUMBERSEX: “A book has 75 pages”.

Number of 75 is exact number


are gained from measurement”

Consist ofEstimation 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

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

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


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

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 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


If 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 number15.5 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


“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)

But 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?

5.125.2

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


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

5.125.2 1.50 has 3 SN

25.65.2 2 6.2 has 2 SN

6. SIGNIFICANT NOTATION

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

• 120000 1,2 x 105• 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


• 0.00228 x 108 2.28 x 105

chapter i quantities

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