Significant Figures - Texas Tech University

Syllabus: PHYS 1408,
Principles of Physics I, Fall 2008
Welcome to
the Physics 1408-002
Principles of Physics I
Spring, 2009
Prof. Sung-Won Lee
Dept. of Physics
Texas Tech University
Class room: Science Building Room 7
Class Time and Attendance
You are expected to read the chapters indicated in the “Class
Schedule” before coming to class. I will assume that you have
read the material and we will discuss the concepts in class.
Class attendance is strongly encouraged and will be taken
randomly. Also it will be used for extra credits.
Course Advice
This course has several components:
!! Lecture: lecture, demos and Active learning
!! Reading: study the text BEFORE lecture
!! Homework: individual Web based problem solving
!! Labs: group exploration of physical phenomena
!! SI (Supplemental Instruction) session - to be named
•! The pace is fast. It is important to keep up!
Homework problems are assigned and graded on the web through the commercial
site MateringPHYSICS.
Once you are registered, you will be able to download the assignments.
The assignments are posted each Monday and are due by 11:pm on the Tuesday a
week later.
There are total of ~10 homework sets for this course.
Pay attention to the instructions on the HW website about how HW is scored.
To access MateringPHYSICS, you must register at
Instructions are in the Student Access Kit.
Your course ID is LEE2009
If you do not have the Student Access Kit which comes with a new textbook, you
can purchase one on the MateringPHYSICS site. Please do this ASAP.
This web site is not at TTU and you should give yourself plenty of time for
submitting answers –sometimes the network can be slow or down. !
There will be “3” in-class exams and a final exam
(see Class Schedule for dates).
The exams are closed book. You may bring one hand-written
a 3” by 5” index card with formulae, etc. Telephones, pagers,
PDAs, iPods, iPhone and other gizmos are not allowed.
Calculators are needed.
The lowest exam grade (not the final) will be dropped since
there are no makeup exams.
Lab & Homework 25%, each exam 25%, and the final will
count 25% towards your final course grade.
•!Lab, Homework
•!2(out of 3) in class exams 50%
Final Exam
•!Final Exam
25% Exam
The final exam is comprehensive and is a common exam for
all sections.
There will be no make-up exams.
The grading scale is A=100-90%, B=89-80%, C=79-65% and
D=64-50%, F=49 to 0.
Course Objectives
You will learn:
Please do not wait until the last second to seek help. If you do
not understand the material or feel that you are falling behind,
seek help as soon as possible.
Your instructor is available during office hours. If you cannot
make it, call me or e-mail me.
Dr. Sung-Won Lee,
where: Sci 117, when: MWF 2:00-3:00
contact phone #: 742-3730
e-mail:: [email protected]
TA:: Physics 1408 Lab (2 hr) /Recitation (1hr). Use their help.
How to use Newton’s laws to solve problems with static and
dynamic bodies.
Use of conservation of energy and linear and angular
momentum to solve problems.
How to represent wave motion and solve problems about
sound propagation.
Learning Assessment: certain problems on the final exam will
explicitly require facility with the course objectives and be
used as learning assessment tools.
Lecture Notes!
End of
Administrative Details
Go to Chapter 1
Fundamental Science
!! concerned with the basic principles of the
!! foundation of other physical sciences
Divided into 6 major areas
!! Classical Mechanics
!! Relativity
!! Thermodynamics
!! Electromagnetism
!! Optics
!! Quantum Mechanics
Our study will start with Classical Mechanics
Also called Newtonian Mechanics
Includes Mechanics
Major developments by Newton, and continuing through the latter part of the
19th century
All of these were not developed until the latter part of the 19th century
Began near the end of the 19th century
!! Phenomena that could not be explained by classical
!! Includes theories of relativity and quantum
Still important in many disciplines
!! Wide range of phenomena that can be explained with
classical mechanics
!! Many basic principles carry over into other
!! Conservation Laws also apply directly to other areas $&"
Mechanics and electromagnetism are basic to all other
branches of classical physics
Classical physics developed before 1900
To find the limited number of fundamental laws that govern
natural phenomena
To use these laws to develop theories that can predict the
results of future experiments
Express the laws in the language of mathematics
Should complement each other
When a discrepancy occurs, theory may be modified
Theory may apply to limited conditions
Example: Newtonian Mechanics is confined to objects traveling slowing
with respect to the speed of light
Try to develop a more general theory
Brief History of Physics!
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What do we want to learn in this class?!
Physics is everywhere around you.!
!! Understand the fundamental principles that surrounds
you in everyday lives…!
!! Identify what laws of physics applies to what
phenomena and use them appropriately!
!! Understand the impact of such physical laws!
!! Learn how to research and analyze what you observe.!
!! Learn how to express observations and measurements
in mathematical language!
!! Learn how to express your research in systematic
manner in writing!
!! I don’t want you to be scared of PHYSICS!!!!
Most importantly,
let us have a lot of FUN!!
PHYS 1443-002, Fall 2008!
Dr. Jaehoon Yu!
Chapter 1
•!The Nature of Science
•!Physics and its Relation to Other Fields
•!Models, Theories, and Laws
•!Measurement and Uncertainty; Significant
•!Units, Standards, and the SI System
•!Converting Units
•!Dimensions and Dimensional Analysis
1-1 The Nature of Science
How does a new theory get accepted?
•!Predictions agree better with data
•!Explains a greater range of phenomena
Physics and Its Relation to Other Fields
Communication between architects and engineers is
essential if disaster is to be avoided.
1-2 Physics and Its Relation to Other Fields
Physics is needed in both
architecture and engineering.
Other fields that use physics,
and make contributions to it:
physiology, zoology, life sciences,
1-4 Measurement and Uncertainty;
Significant Figures
No measurement is exact; there is always some
uncertainty due to limited instrument accuracy
and difficulty reading results.
1-4 Measurement and Uncertainty;
Significant Figures
Measured quantities are never known precisely
Scientist use significant figures to indicate the level of
accuracy in their measurement data.
Estimated uncertainty is written with a ± sign; for
Percent uncertainty is the ratio of the uncertainty to
the measured value, multiplied by 100:
1-4 Measurement and Uncertainty;
Significant Figures
0.0075 [m] has 2 significant figures
!! The leading zeros are placeholders only
!! Can write in scientific notation to show more clearly:
7.5 x 10-3 [m] for 2 significant figures
10.0[m] has 3 significant figures
!! The decimal point gives information about the reliability
of the measurement
1500 [m] is ambiguous
!! Use 1.5
x 103 [m] for 2 significant figures
!! Use 1.50 x 10
[m] for 3 significant figures
!! Use 1.500 x 10
[m] for 4 significant figures
The number of significant figures is the number of
reliably known digits in a number.
23.21 cm has 4 significant figures
0.062 cm has 2 significant figures (the initial zeroes don’t
80 km is ambiguous – it could have 1 or 2 significant
figures. If it has 3, it should be written 80.0 km.
1-4 Measurement and Uncertainty;
Significant Figures
When multiplying or dividing numbers, the result
has as many significant figures as the number used
in the calculation with the fewest significant figures.
Example: 11.3 cm x 6.8 cm = 77 cm
When adding or subtracting, the answer is no more
accurate than the least accurate number used.
1-4 Measurement and Uncertainty;
Significant Figures
Calculators will not give you the right
number of significant figures; they usually
give too many but sometimes give too few
(especially if there are trailing zeroes
after a decimal point).
The top calculator shows the result of 2.0 /
The bottom calculator shows the result of
2.5 x 3.2.
Units, Standards, and the SI
These are the standard SI
prefixes for indicating powers of
10. Many are familiar.
Prefixes correspond to powers of 10
Each prefix has a specific name
Each prefix has a specific
The prefixes can be used with any
base units
1 mm = 10-3 m
1 mg = 10-3 g
Units, Standards, and the SI System
We will be work in the SI system, basic units
kilograms, meters, seconds.
Other systems: cgs; units are grams,
centimeters, and seconds.
British engineering system has force
instead of mass as one of its basic
quantities, which are pounds, feet,
and seconds.
1-5 Units, Standards, and the SI System
We will use mostly SI units, but you may run across some problems
using British units. You should know how to convert back & forth. !
Defined in terms of a meter
– the distance traveled by
light in a vacuum during a
given time
See Table 1.1 for some
examples of lengths
SI – meter, m
SI – kilogram, kg
Defined in terms of a
kilogram, based on a
specific cylinder kept at
the International Bureau
of Standards
See Table 1.2 for masses
of various objects
seconds, s
Defined in terms of the
oscillation of radiation
from a cesium atom
See Table 1.3 for some
approximate time intervals
Time (s)!
Age of universe!
5 x 1017!
Age of Grand Canyon
3 x 1014!
32 years!
1 x 109!
One year!
3.2 x 107!
One hour!
3.6 x 103!
Light travel from Earth to Moon 1.3 x 100!
One cycle of guitar A string!
2 x 10-3!
One cycle of FM radio wave!
6 x 10-8!
Lifetime of neutral pi meson
1 x 10-16!
Lifetime of top quark! !
4 x 10-25!
1.5 Converting Units
Density is an example of a derived quantity
It is defined as mass per unit volume
Converting between metric units, for example from
kg to g, is easy, as all it involves is powers of 10.
Converting to and from British units is
considerably more work.
Units are kg/m3
See table 1.5 for some density values
e.g , given
1 m =3.28084 ft,
this 8611-m mountain is
28251 feet high.
The atomic mass is the total number of protons and
neutrons in the element
Can be measured in atomic mass units, u
1 u = 1.6605387 x 10-27 kg
Useful Conversion factors:
!! 1 inch
= 2.54 cm
!! 1 m
= 3.28 ft
!! 1 mile
= 5280 ft
!! 1 mile
= 1.61 km
Example: convert miles per hour to meters per second:"
1 m
1 hr
= 1 ! 5280
= 0.447
mi 3.28 ft 3600 s
1-6 Order of Magnitude: Rapid Estimating
1-7 Dimensions and Dimensional Analysis
A quick way to estimate a
calculated quantity is to round
off all numbers to one
significant figure and then
calculate. Your result should at
least be the right order of
magnitude; this can be
expressed by rounding it off to
the nearest power of 10.
Dimensions of a quantity are the base units that
make it up;
Written using square brackets.
Example, speed, v = “distance / time”
Dimensions of speed: [L/T]
e.g. …. Quantities that are being added or
subtracted must have the same dimensions. !
Diagrams are also very useful
in making estimations.
#!On-line HW: MateringPHYSICS registration
#!Before the next lecture, read the text book,
Chapter 2.
#!Next lecture: Tuesday, 1/13