Ch. 1: Introduction: Physics and Measurement. Estimating.

1. The Nature of Science2. Models, Theories, & Laws3. Measurement & Uncertainty Significant Figures4. Units, Standards, & the SI System5. Converting Units6. Order of Magnitude: Rapid Estimating7. Dimensions & Dimensional Analysis

Chapter 1 Outline

PhysicsThe most basic of all sciences!

• Physics: The “Parent” of all sciences!

• Physics = The study of the behavior of and the structure of matter and energy and of the interaction between matter and energy.

Sub Areas of Physics• This course (1408, Physics of 16th & 17th Centuries):

– Motion (MECHANICS) (most of our time!)– Fluids & Waves

• Next course (2401, Physics of 18th & 19th Centuries):– Electricity & magnetism– Light & optics

• Advanced courses (Physics of the 20th Century!):– Relativity, atomic structure, condensed matter,

nuclear physics, ….

These are the most interesting & the most relevant to modern technology!

Mechanics“Classical” Mechanics

“Classical” Physics: “Classical” Before the 20th CenturyThe foundation of pure & applied macroscopic physics & engineering!

– Newton’s Laws + Boltzmann’s Statistical Mechanics (&

Thermodynamics): Describe most of macroscopic world!– However, at high speeds (v ~ c) we need Special Relativity: (Early 20th Century: 1905)– Also, for small sizes (atomic & smaller) we need Quantum Mechanics: (1900 through ~ 1930)

“Classical” Mechanics: (17th & 18th Centuries)

Still useful today!

Mechanics: “Classical” Mechanics

“Classical” MechanicsThe physics in this course is limited to macroscopic objects

moving at speeds v much, much smaller than the speed of light

c = 3 108 m/s. As long as v << c, our discussion will be valid.

So, we will workexclusively in the gray region in the figure.

Mechanics • The science of HOW objects move

(behave) under given forces. • (Usually) Does not deal with the

sources of forces. • Answers the question:

“Given the forces, howdo objects move”?

Physics: General Discussion• The Goal of Physics (& all of science): To quantitatively

& qualitatively describe the “world around us”.

• Physics IS NOT merely a collection of facts & formulas!

Physics IS a creative activity!

• Physics Observation Explanation

• Requires IMAGINATION!!

Physics & Its Relation to Other Fields

The “Parent” of all Sciences!• The foundation for & connected to ALL

branches of science and engineering.• Also useful in everyday life and in MANY

professions– Chemistry– Life Sciences (Medicine also!!)– Architecture– Engineering– Various technological fields

Physics Principles are used in many practical applications, including construction.

Communication between Architects & Engineers is essential if disaster is to be avoided.

• Physics is an EXPERIMENTAL science!• Experiments & Observations:

– Important first steps toward scientific theory.– It requires imagination to tell what is important.

• Theories: – Created to explain experiments &

observations. Will also make predictions• Experiments & Observations:

– Will tell if predictions are accurate. • No theory can be absolutely verified

– But a theory CAN be proven false!!!

The Nature of Science

Theory• A Quantitative (mathematical)

Description of experimental observations.• Not just WHAT is observed but WHY it is

observed as it is and HOW it works the way it does.

Tests of Theories: –Experimental observations:

More experiments, more observation.

–Predictions: Made before observations & experiments.

Model, Theory, Law• Model: Analogy of a physical phenomenon

to something we are familiar with. • Theory: More detailed than a model.

Puts the model into mathematical language.• Law: A concise & general statement about

how nature behaves. Must be verified by many, many experiments! Only a few laws.

Not comparable to laws of government!

How does a new theory get accepted?• It’s Predictions:

Agree better with data than those of an old theory• It Explains:

A greater range of phenomena than old theory

Example • Aristotle: Believed that objects would return to rest

once put in motion.• Galileo: Realized that an object put in motion would

stay in motion until some force stopped it.

• Newton:Developed his Laws of Motion to put Galileo’s

observations into mathematical language.

No measurement is exact; there is always some uncertainty due to limited instrument accuracy & difficulty reading results.

The photograph to the left illustrates this – it would be difficult to measure the width of this 24 to better than a

millimeter.

Measurement & Uncertainty;Significant Figures

Measurement & Uncertainty• Physics is an EXPERIMENTAL science!

– It finds relations between physical quantities.– It expresses those relations in the language of

mathematics. (LAWS & THEORIES)• Experiments are NEVER 100% accurate.

There is always an uncertaintyin the final result.

This is known as experimental error.– It is common to state this precision (when

known).

• Consider a simple measurement of the width of a board. Find 23.2 cm.

• However, measurement is only accurate to 0.1 cm (estimated).

We write the width as(23.2 0.1) cm

0.1 cm Experimental uncertainty• Percent Uncertainty:

(0.1/23.2) 100 0.4%

Significant FiguresSignificant Figures (“sig figs”)

The number of significant figures is thenumber of reliably known digits in a number. It is usually possible to tell the number of significant figures by the way the number is written:

23.21 cm has 4 significant figures0.062 cm has 2 significant figures

(initial zeroes don’t count)80 km is ambiguous:

it could have 1 or 2 significant figures.If it has 3, it should be written 80.0 km.

Calculations Involving Several NumbersWhen multiplying or dividing numbers: The number of sig figs in the result the same number of sig figs as the number used

in the calculation with the fewest sig figs.

When adding or subtracting numbers:

The answer is no more accurate than the least accurate number used.

• Example(Not to scale!)

–Area of a board:dimensions 11.3 cm 6.8 cm

–Area = (11.3) (6.8) = 76.84 cm2

11.3 has 3 sig figs , 6.8 has 2 sig figs 76.84 has too many sig figs!

Proper number of sig figs in answer = 2 Round off 76.84 & keep only 2 sig figs

Reliable answer for area = 77 cm2

Sig Figs• General Rule: The final result of

multiplication or division should have only as many sig figs as the number with least sig figs in the calculation.

NOTE!!!!

All digits on your calculator are NOT significant!!

•Calculators will not give you theright number of significant figures;they usually give too many, butsometimes give too few (especiallyif there are trailing zeroes after a decimal point).•The top calculator shows the result

of

2.0 / 3.0•The bottom calculator shows the

result of

2.5 3.2.

Conceptual Example: Significant Figures• Using a protractor, you measure an angle of 30°. • (a) How many significant figures should you quote in this

measurement? • (b) Use a calculator to find the cosine of the angle you

measured.

• (a) Precision ~ 1° (not 0.1°). So 2 sig figs & angle is 30° (not 30.0°).

• (b) Calculator: cos(30°) = 0.866025403. But angle precision is 2 sig figs so answer should also be 2 sig figs. So cos(30°) = 0.87

Powers of 10 (Scientific Notation)READ Appendix B.1

• It is common to express very large or very small numbers using powers of 10 notation.

Examples39,600 = 3.96 104

(moved decimal 4 places to left)

0.0021 = 2.1 10-3

(moved decimal 3 places to right)PLEASE USE SCIENTIFIC NOTATION!!

PLEASE USE SCIENTIFIC NOTATION!!• This is more than a request!! I’m making it a

requirement!!

I want to see powers of 10notation on exams!!

• For large numbers, like 39,600,I want to see 3.96 104 & NOT 39,600!!

• For small numbers, like 0.0021,I want to see 2.1 10-3 & NOT 0.0021!!

On the exams, you will lose pointsif you don’t do this!!

Powers of 10 (Scientific Notation)

Accuracy vs. Precision• Accuracy is how close a measurement

comes to the accepted (true) value.• Precision is the repeatability of the

measurement using the same instrument & getting the same result!It is possible to be accurate without

being precise and to be precise without being accurate!