Section 1.1: The Nature of Science

Section 1.1: The Nature of Science

Section 1.2: The Scientific Method

Section 1.3: Measurement

Section 1.4: Scientific Notation

Section 1.5: Measurement Calculations

Section 1.6: Significant Digits

Section 1.7: Mathematical Techniques

Ever gaze at a hawk in wonder? Most folks take note of the hawk only momentarily – turning their attention to something else.

If you found yourself curious as to how it flies, how accurate is its vision, then you may have the makings of a scientist.

Science is a mode of inquiry.

Section 1.1

The discipline of science seeks to:

• Describe nature, matter, and energy

• Ascertain the cause behind every observed change in nature, matter, and energy

Branch Emphasis

Astronomy Galaxies, star systems, dark matter/ energy, planets, physical properties of outer space, celestial bodies

Biology Living organisms, how they interact with their environment, exchange energy

Chemistry Composition and changes in matter

Geology Earth’s origin, geological formations of the past, and structure

Physics Matter and energy

Physics is a discipline

of extremes…

Physics studies range from

examining the composition

and behavior of matter as tiny as quarks to that of a giant red star.

The domain extends from examining the

impact of a raindrop, to the explosion of a

hydrogen bomb.

Or, investigate the solidification of air particles at super cold temperatures to the ionization of matter into plasma

at temperatures comparable to our

star, the sun.

The quest for scientific knowledge

is a God-given behavior.

The desire to fashion scientific knowledge

into practical knowledge, giving

way to trades is also God-given.

From the brilliant, philosophical mind of Paul,

comes:

“For the invisible things of him from the creation of the world are clearly seen, being understood by the things that

are made, even his eternal power and Godhead; so that they are without excuse.”

Romans 1:20

“For the invisible things of him from the creation of the world are clearly seen, being understood by the things that

are made, even his eternal power and Godhead; so that they are without excuse.”

Romans 1:20

General Revelation vs. Special Revelation

They are in perfect harmony with one another.

The Branches of Physics

Classical physics – handles subjects dating back to Galileo, such as

1. Newtonian mechanics

2. Thermodynamics

3. Sound

4. Light

5. Electromagnetism

The Branches of Physics

Modern physics – handles subjects dating back to Galileo, such as

1. Quantum mechanics

2. Relativity

3. Solid-state physics

4. Particle physics

Section 1.2

Ways of inquiring about natural phenomena:

The Reformers who brought us the Scientific Method refuted the

ability of sinful man to merely pontificate or cogitate,

recognizing that the Fall of Adam impacted the descendants who followed not only morally,

but cognitively, as well.

Peter Harrison, PhD, 2007 The Fall of Man and the Foundations of Science

With the founding of The Royal Society, November 28, 1660,

experimentation became the gold standard for acquiring knowledge.

Papers were then drafted and submitted to the Society and

followed by rigorous peer review.

After peer review, papers were then published.

What are the steps in the scientific method?

1. Make observations of an area that interests you and formulate a testable question

2. Conduct a literature search – gather information concerning the question

3. Consider all the facts/ data available 4. Develop a testable hypothesis 5. Design an experiment that can refute or confirm

your hypothesis 6. Perform the controlled experiment 7. Analyze your results 8. Publish your results

Section 1.3

Lord Kelvin (1824 – 1907) aka William Thompson, one of the founders of

thermodynamics wrote:

“I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it;

but when you cannot express it in numbers, your knowledge is of a meagre and

unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of Science,

whatever the matter may be.”

In physics, physical quantities are measured, using an accepted unit of measurement.

Fundamental units – are the result of direct measurement, such as meter, liter, gram.

Derived units - are the arithmetic

combination of fundamental units,

like cubic meter, Newton, or joules.

Table 1.1 – Fundamental Physical Quantities in SI Units

Quantity Unit Symbol

length meter m

mass kilogram kg

time second s

electric current ampere A

temperature Kelvin K

amount of substance mole mol

luminous intensity candela cd

Most common system of units used by scientists is the International System (SI) aka metric system

What are the seven fundamental SI units?

a. meter b. kilogram c. second d. ampere e. kelvin f. mole g. candela

Table 1.2 – Commonly Used Metric Prefixes

Symbol Prefix Factor Example Relation to Unit

*M mega x 106 2.5 Ms = 2.5 x 106 s

*k kilo- x 103 8.0 km = 8.0 x 103 m

da deca- x 101 4.21 daL = 42.1 L

d deci- x 10-1 5.68 ds = 0.568 s

*c centi- x 10-2 861 cm = 8.61 m

*m milli- x 10-3 556 mL = 0.556 L

*μ micro- x 10-6 3.7 μg = 3.7 x 10-6 g

*n nano- x 10-9 437 ns 4.37 x 10-7 s *Denotes most commonly used prefixes

Why is it important to include the units when

reporting measurements?

A measurement reported without units is meaningless, since many different units may be in use for the same numerical quantity.

• Meter – SI unit of length, is defined as the distance light travels in 1/299,792,458 seconds

• Kilogram – SI unit of mass, defined by a cylinder of platinum-iridium alloy kept at the International Bureau in France

• Second – SI unit of time, defined as 9,192,631,770 vibrations of the cesium-133 atom

Section 1.4

Since in the world of physics very large and very small numbers are

used, scientists use scientific notation to save time and space to write down

all the zeros in these numbers.

Example of a very large number: The sun is 93,000,000 miles from the earth; in scientific notation we can report it as 9.3 x 107 miles

Example of a very small one: The charge on an electron is 0.000 000 000 000 000 000 16 coulomb; we can write it as 1.6 x 10-19 coulomb

Write the following numbers in scientific notation:

(a) 86,400

8.64 x 104

(b) 299,790,000

2.9979 x 108

(c) 0.000004161

4.161 x 10-6

(d) 0.0821

8.21 x 10-2

Write the following numbers in decimal notation:

(a) 7.03 x 105

703,000

(b) 3.41 x 10-3

0.00341

(c) 2.385 x 103

2,385

(d) 4.53 x 10-3

0.00453

Perform the following additions and subtractions:

(a) 3.174 x 10-4 + 1.21 x 10-4

4.384 x 10-4

(b) 2.87 x 105 -3.41 x 106

-3.123 x 106

(c) 9.84 x 103 + 2.77 x 103

3.754 x 103

Perform the following multiplications and divisions:

(a) (3.2 x 104) (6.81 x 107)

2.1792 x 1012

(b) (6.29 x 10-2) (1.87 x 103)

1.176223 x 102

(c) (8.54 x 106) ∕ (3.20 x 103)

2.66875 x 103

(d) (4.38 x 10-2) ∕ (6.4 x 104)

6.84375 x 10-7

Section 1.5

Metric to metric conversations

These are easy if you understand the power of ten corresponding to each unit.

Example 1.3: change 0.14 mg to kg

Milli- correspond to the -3 power of ten, kilo- to the +3 power, resulting in a difference of 6.

Decimal point is moved 6 places to the left for a solution of 0.000 000 14 kg or 1.4 x 10-7 kg.

Convert:

(a) 1,560,000 s to Ms

(b) 0.0054 m to mm

(c) 0.0000078 s to μs

(d) 0.0285 μg to mg

(e) 5200 ms to s

(f) 11.300 km to nm

Measured quantities having unlike units:

4.00 kg, 1.61 s

cannot be added or subtracted,

but they can be multiplied or divided.

Perform, if possible, the following calculations

(a) add 45.0 s and 150 m

(b) subtract 153 m from 1.625 km

(c) multiply 0.00654 g by 14.2 m

(d) divide 4.64 kg by 800 g

When converting from English units (pounds, feet, quarts) to metric units (kg,

meters, liters), it is helpful to use dimensional analysis.

This uses conversion factors equal to or approximately equal to 1 as a series of

multiplied fractions to cancel out unwanted units, leaving only the desired

units.

Use dimensional analysis to perform the following

conversions:

(a) 15 weeks to min

(b) 14 yr to s

(c) 45 mi/hr to m/s

(d) 92 ft/min to m/s

(e) 75 m/s to km/hr

Section 1.6

Due to the limitations of our instrumentation, all measured quantities

have some degree of “error.”

Whether you are using an inexpensive piece of equipment with a low resolution,

or a state-of-the-art piece, the limitations of your equipment must be reflected in the

answers you report when making measurements.

This, it is impossible to make a measurement of the exact true value of anything, except

when counting.

Significant digits are the meaningful digits in a measured quantity.

Answers expressed mathematically involving measured quantities should have no more

significant digits than the starting measurement with the least number of

significant digits.

Calculation Rules 1. When adding or subtracting, the answer must be

rounded to the place which has the greatest uncertainty.

2. When multiplying or dividing, the answer must be rounded to the same number of significant figures as the factor having the smallest number of significant figures.

What does that mean? Huh?

Adding/ Subtracting Calculation Rules

When adding or subtracting, the answer must be rounded to the place which has the greatest uncertainty.

These calculated values represent the limitations of our measuring devices (ruler, graduated cylinder, mass scale).

169.0237 582.818 2,026.8378

Adding/ Subtracting Calculation Rules

When adding or subtracting, the answer must be rounded to the place which has the greatest uncertainty.

These calculated values represent the limitations of our measuring devices (ruler, graduated cylinder, mass scale).

169.0 582.8 2,026.8

Multiplication/ Division Calculation Rules

When multiplying or dividing, the answer must be rounded to the same number of significant figures as the factor having smallest number of significant figures.

23.7 x 3.8 = ________ 43.678 x 64.1 = ________

28.367/ 3.74 = ________ 4278/ 1.006 = _________

90.06 2,779.7598

7.584759 4,252.48509

Multiplication/ Division Calculation Rules

When multiplying or dividing, the answer must be rounded to the same number of significant figures as the factor having smallest number of significant figures.

23.7 x 3.8 = ________ 43.678 x 64.1 = ________

28.367/ 3.74 = ________ 4278/ 1.006 = _________

90. 2,780

7.58 4,252

These calculated values similarly represent the limitations of our measuring devices (ruler, graduated cylinder, mass scale).

Whenever you are reporting any final data, such as an answer in an

examination or quiz – you need to report the answer so that it reflects the proper

number of significant digits.

Do not round off digits until you report the FINAL answer.

Accuracy is a measure of how close a measurement comes to the true value.

Precision is a measure of how close a series of measurements are to one another.

Resolution/ tolerance characterizes the ability of the tool to detect small changes in what is measured.

As already mentioned, all measurements have some degree of uncertainty, or error.

Systematic errors affect every measurement in the same way, and are typically caused by a faulty measuring device, an unseen bias in the protocol of the experiment itself, or an improper procedure. These are the errors that are typically under the control of the experimenter.

Random errors are due to unpredictable and uncontrollable factors, and can’t be eliminated.

Section 1.7

Simplify the following:

(a) 𝑠𝑠𝑣+𝑒𝑎𝑣

𝑙𝑢𝑣 =

𝑣(𝑠2 +𝑒𝑎)

𝑙𝑢𝑣=

𝑠2+𝑒𝑎

𝑙𝑢 (b)

𝑓𝑡

𝑠

𝑠 =

𝑓𝑡

𝑠2

(c)

𝑎2−𝑏2

5𝑥𝑎+𝑏

𝑥2

= 𝑥2(𝑎2−𝑏2)

5𝑥 (𝑎+𝑏) (d)

ℎ

𝐴

5 =

ℎ

5𝐴

(e) 143

2

= 28

3 𝑜𝑟 9

1

3 (f)

𝑘𝑔𝑚

𝑠

= 𝑘𝑔∙𝑠

𝑚



𝑙𝑢𝑣 =


𝑙𝑢𝑣=

𝑠2+𝑒𝑎

𝑙𝑢 (b)

𝑓𝑡

𝑠

𝑠 =

𝑓𝑡

𝑠2

(c)

𝑎2−𝑏2

5𝑥𝑎+𝑏

𝑥2

= 𝑥2(𝑎2−𝑏2)

5𝑥 (𝑎+𝑏) (d)

ℎ

𝐴

5 =

ℎ

5𝐴

(e) 143

2

= 28

3 𝑜𝑟 9

1

3 (f)

𝑘𝑔𝑚

𝑠

= 𝑘𝑔∙𝑠

𝑚



𝑙𝑢𝑣 =


𝑙𝑢𝑣=

𝑠2+𝑒𝑎

𝑙𝑢 (b)

𝑓𝑡

𝑠

𝑠 =

𝑓𝑡

𝑠2

(c)

𝑎2−𝑏2

5𝑥𝑎+𝑏

𝑥2

= 𝑥2(𝑎2−𝑏2)

5𝑥 (𝑎+𝑏) (d)

ℎ

𝐴

5 =

ℎ

5𝐴

(e) 143

2

= 28

3 𝑜𝑟 9

1

3 (f)

𝑘𝑔𝑚

𝑠

= 𝑘𝑔∙𝑠

𝑚



𝑙𝑢𝑣 =


𝑙𝑢𝑣=

𝑠2+𝑒𝑎

𝑙𝑢 (b)

𝑓𝑡

𝑠

𝑠 =

𝑓𝑡

𝑠2

(c)

𝑎2−𝑏2

5𝑥𝑎+𝑏

𝑥2

= 𝑥2(𝑎2−𝑏2)

5𝑥 (𝑎+𝑏) (d)

ℎ

𝐴

5 =

ℎ

5𝐴

(e) 143

2

= 28

3 𝑜𝑟 9

1

3 (f)

𝑘𝑔𝑚

𝑠

= 𝑘𝑔∙𝑠

𝑚



𝑙𝑢𝑣 =


𝑙𝑢𝑣=

𝑠2+𝑒𝑎

𝑙𝑢 (b)

𝑓𝑡

𝑠

𝑠 =

𝑓𝑡

𝑠2

(c)

𝑎2−𝑏2

5𝑥𝑎+𝑏

𝑥2

= 𝑥2(𝑎2−𝑏2)

5𝑥 (𝑎+𝑏) (d)

ℎ

𝐴

5 =

ℎ

5𝐴

(e) 143

2

= 28

3 𝑜𝑟 9

1

3 (f)

𝑘𝑔𝑚

𝑠

= 𝑘𝑔∙𝑠

𝑚



𝑙𝑢𝑣 =


𝑙𝑢𝑣=

𝑠2+𝑒𝑎

𝑙𝑢 (b)

𝑓𝑡

𝑠

𝑠 =

𝑓𝑡

𝑠2

(c)

𝑎2−𝑏2

5𝑥𝑎+𝑏

𝑥2

= 𝑥2(𝑎2−𝑏2)

5𝑥 (𝑎+𝑏) (d)

ℎ

𝐴

5 =

ℎ

5𝐴

(e) 143

2

= 28

3 𝑜𝑟 9

1

3 (f)

𝑘𝑔𝑚

𝑠

= 𝑘𝑔∙𝑠

𝑚



𝑙𝑢𝑣 =


𝑙𝑢𝑣=

𝑠2+𝑒𝑎

𝑙𝑢 (b)

𝑓𝑡

𝑠

𝑠 =

𝑓𝑡

𝑠2

(c)

𝑎2−𝑏2

5𝑥𝑎+𝑏

𝑥2

= 𝑥2(𝑎2−𝑏2)

5𝑥 (𝑎+𝑏) (d)

ℎ

𝐴

5 =

ℎ

5𝐴

(e) 143

2

= 28

3 𝑜𝑟 9

1

3 (f)

𝑘𝑔𝑚

𝑠

= 𝑘𝑔∙𝑠

𝑚

Solve each literal equation for the bolded

variable:

(a) 𝑃𝐸 =1

2𝑘𝒙2 (b) 𝐹𝑖𝒓𝒊 = 𝐹𝑜𝑟𝑜

(c) 𝐹 = 𝑚𝑣2

𝒓 (d) 𝑣𝑓 = 𝑣𝑖 + 𝑎𝒕

(e) 𝐼 = 𝑚𝒓2 (f) 𝑣𝑓 = 𝑣𝑖2 + 2𝑎𝒅

Documents

Section 1.1: The Nature of Science