MSU Physics 231 Fall 2015 1 Physics 231 Topic 1: Introduction, Units, Significant Figures Alex Brown...
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Transcript of MSU Physics 231 Fall 2015 1 Physics 231 Topic 1: Introduction, Units, Significant Figures Alex Brown...
MSU Physics 231 Fall 2015 1
Physics 231Topic 1: Introduction, Units, Significant Figures
Alex BrownSeptember 2,
2015
MSU Physics 231 Fall 2015 2
Today's Lecture:Key Concepts
Syllabus International System of Units (SI)
Mass: kilograms (kg) Length: meters (m) Time: seconds (s)
Units and conversions Dimensional Analysis Scientific Notation (e.g., 4.3x1012 and 2.3E4) Significant Figures
Covers chapter 1 in Rex & Wolfson
MSU Physics 231 Fall 2015 3
Textbook & Reading
Essential College Physics, Volume 1
•The syllabus lists the relevant chapters for each lecture and homework
•Read the material before class
•Not everything can be covered in class
•Lectures are not a replacement for the textbook
MSU Physics 231 Fall 2015 10
Homework
Homework is to be done online using LON-CAPA
http://msu.lon-capa.org
Homework assignments are due Tuesdays at 10 PMThe deadline is strict. Being away from a network connection is no excuse.
Do not wait until the last minute!
Assignments are somewhat unique to each student
Discussion boardYou are encouraged to use the discussion board inside LON-CAPA. If you don't understand a problem, or you
need help, just click on the "Post Discussion" link and post your question. If you know the answer to somebody
else's question, don't be afraid to post you answer. Don't forget: The best way to learn is to teach.
But – to do well in the exams you should try the problem on your own first, and if you use the discussion board,
be sure you understand the concepts and the reasoning behind the solution.
MSU Physics 231 Fall 2015 11
Extra Credit Quizzes
We will be doing in-class quizzes using i>Clickers
Quizzes will be given almost everyday You must have in i>Clicker to participate
Start to count them on Monday September 14th
Be on time, quizzes are sometimes at the beginning of class.
There are NO make-ups for quizzes all of the points are for extra credit
You must take quizzes in this section. No credit for quizzes in other sections.
Quiz points: 3 for correct answers, 1 for incorrect answers
Scores will be posted on my website occasionally – check to ensure you're registered
You must register your i<Clicker on lon-capa before Monday September 14th
Even if you have registered before, you need to re-register for this course!
You MUST enter the preceding “A” before your student ID
MSU Physics 231 Fall 2015 12
You must use your own and ONLY your own
i>Clicker in class
If you are found to be using another
person's i>Clicker, all clickers will be
confiscated
This will be considered a violation of
the rules governing academic
dishonesty
Extra Credit Quizzes
MSU Physics 231 Fall 2015 16
Physics Learning Center (PLC)
The Strosacker Physics Learning Center is located in BPS 1248
Details and schedule TBA
The PLC is a cooperative learning center, not a help room. TAs
will encourage group work and will help groups who get stuck.
Group work A very effective learning tool for both strong and weak students
You must do your own assignments and must learn how to do problems on
your own
Do as much as you can of the assignments before group work – PREPARE!
MSU Physics 231 Fall 2015 17
How to Suceed in PHY231
Read the book before coming to class. Go to the Physics Learning Center frequently! The TAs are there to help you learn. Always attend the lectures.
Recognize that learning physics is different than many other subjects Physics is about understanding concepts and connecting your knowledge with
these concepts. Physics is not just about memorizing facts. Some physics concepts will be contrary to your instincts, but not contrary to
your intellect. Be willing to think things through! Keep working continuously – do the reading assignments, think about what you
learned in lecture, keep thinking AS WE GO. Memorizing facts is not sufficient, so cramming before an exam is not effective.
Understanding the concepts helps you set up solutions to problems. Equation hunting is not a good strategy.
Little is learned by copying or memorizing the solution of another student.
MSU Physics 231 Fall 2015 18
DOs and DON'Ts
DON'T... ...use LON-CAPA postings from others before you have given a problem a genuine attempt yourself. If you have to frequently look at how others solved the problem, it means you aren't understanding the material well.
...try to memorize LON-CAPA problems; it is unlikely that you will get many problems in exams that are exactly like the homework
...base your entire study routine on LON-CAPA. Bring variation in your studies and practice questions that are not phrased like LON-CAPA (eg, questions in the book)
...wait until the last weeks of the semester to ask for help if you need it (ie, if you're working hard but still are not doing well)
...cheat on exams, quizzes, homework
MSU Physics 231 Fall 2015 20
Why Learn Physics?Example:
Tacoma Narrows Bridge
Golden Gate
Bronx-WhiteStone
Tacoma Narrows
Year 1937 1939 1940
Cost $35M $20M $6.4M
Length 4200 ft 2300 ft 2800 ft
Width 90 ft 74 ft 39 ft
Ratio: Width to Length
1 : 47 1 : 31 1 : 72
MSU Physics 231 Fall 2015 21
Why Learn Physics?Example: Mechanics of the Skeleton
Key concept for:• Human medicine• Veterinary medicine• Sports training• Ergonomic engineering
In other classes, you learn the namesof bones, how to treat broken bones, where to drill to replace things.
Physics teaches you HOW and WHY it works (and how to understand the system as a whole)
Combination is the key to innovation!
MSU Physics 231 Fall 2015 22
Why Learn Physics?
Example: Dark Matter & Dark Energy
•Cosmological measurements have told us that our universe is not made the way we thought.
•IE, what we see in telescopes corresponds to what we are all made out of: atoms (stars, gases, planets)
Bullet Cluster
MSU Physics 231 Fall 2015 23
Why Learn Physics?
Example: Dark Matter & Dark Energy
•Cosmological measurements have told us that our universe is not made the way we thought.
•IE, what we see in telescopes corresponds to what we are all made out of: atoms (stars, gases, planets)
•But this is only 4% of what’s out there!
Bullet Cluster
MSU Physics 231 Fall 2015 24
Système Internationale (SI) Units
Also called the MKS unit system
Based on powers of 10 relative to base units
All other units derive from these (Area: m2, Speed: m/s, etc)
(ones used for this course)
Unit Abbreviation Base unit for
meter m lengthkilogram kg masssecond s timeKelvin K temperaturemole mol amount of substance
(others)ampere A electric current candela cd luminous intensity
MSU Physics 231 Fall 2015 25
Defining Standard Units
Original definition of the meter: 1/10,000,000 of earth's arc length Today: 1m = distance light travels in 1/299,272,458 s
MSU Physics 231 Fall 2015 26
Defining Standard Units
The kilogram defined by a fixed “prototype” of matter
Standards are important: when you buy 1kg of gold, you want to get it right!
Platinum-IridiumKilogram Prototype
MSU Physics 231 Fall 2015 27
Defining Standard Units
Original definition of the second: 1/86,400 of a solar day 1960: based on a tropical year
Since 1967: 9,192,631,770 periods of radiation corresponding to the transition
between two hyperfine states of the ground state of 133Cesium
Cesium Atomic ClockNational Institute of
Standards and Technology (NIST)
MSU Physics 231 Fall 2015 28
Unit Conversion Example
Treat conversions as algebraic equivalencies:
Convert by multiplying your existing units by a numerical equivalent of 1.0
Jon has walked 3 miles in 1 hour, what is his average speed in m/s?
Given: 1 mile = 1609.3 m ie, 1.0 = ( 1609.3 m/ 1 mile )
Velocity (speed) = distance / time = ( 3 miles ) / ( 1 hour )
= ( 3 miles/hr ) x ( 1609.3 m / mile ) = 4827.9 m/hr
= ( 4827.9 m/hr ) x (1 hr / 60 min) x (1 min / 60 sec) = ( 4827.9 m/hr ) x (1 hr / 3600 s) = ( 4827.9/3600 ) m/s = 1.341 m/s
Equal to 1.0
MSU Physics 231 Fall 2015 30
0.000000000000001 = 10-15 = 1E-15 femto (f)0.000000000001 = 10-12 = 1E-12 pico (p)0.000000001 = 10-9 = 1E-9 nano (n)0.000001 = 10-6 = 1E-6 micro ()0.001 = 10-3 = 1E-3 milli (m)0.01 = 10-2 = 1E-2 centi (c)0.1 = 10-1 = 1E-1 deci (d)1 = 100 = 1E+010 = 101 = 1E+1 deca (da)100 = 102 = 1E+2 hecto (h)1000 = 103 = 1E+3 kilo (k)1000000 = 106 = 1E+6 mega (M)1000000000 = 109 = 1E+9 giga (G)10000000000 = 1012 = 1E+12 tera (T)
Very Large and Very Small Numbers
MSU Physics 231 Fall 2015 31
Scientific Notation
For very large or very small numbers the scientific notation is advantageous.
Write number as mantissa x 10Exponent
Example: 0.000000001 = 1 × 10-9
34000000 = 3.4 × 107
Alternative notation: 3.4E7 (CAPA, computers)1 m = 1000 mm = 1E3 mm
MSU Physics 231 Fall 2015 34
Significant Figures
Two statements: The population of the USA is 294,109,799 The population of the USA is 294,000,000=2.94×108
First statement implies precision that is probably not warranted Second statement claims that the population is somewhere between 293M
and 295M. This is reasonable!
General Rules: The number of digits we write down in a number specifies the precision
with which we can claim to know the number
All non-zero figures are signficant (except exponent in scientific notation)
Zeros only count whenThey are between non-zero figuresThey are to the right of a non-zero figure and there is a decimal point
MSU Physics 231 Fall 2015 35
Significant Figures Example
An athlete must bicycle around a circular track for a time trial. His coach tells him that the radius of the circular track is 40.2 m. How far does he ride?
Formulae: C = π D = 2 π RD = diameter of the circleR = radius of the circleπ = 3.14159265.....
We know π to many decimal places, but we only know the radius is between 40.2 and 40.3 m (ie, 3 significant figures).
Thus we can only know the circumference to 3 significant figures! What is the answer?
C = 2 × 3.14159265... × 40.2 m = 253 m
MSU Physics 231 Fall 2015 36
There are no general rules but here are some pointers:
1) READ the problem carefully!2) Summarize (throw away unnecessary info)3) Visualize (drawing can often help)4) Convert units (consistency)5) Set up equations:
Plug in numbers if not comfortable with solving sets of equationsIf confident, plug in numbers at last moment
6) Check whether answers (and units) make sense7) In exams: once you have solved a problem, check calculations one more time at the end of exam. Especially important if you tend to make small mistakes
How to Solve Problems
MSU Physics 231 Fall 2015 38
object surface circumference
square Length2 4xlength
triangle ½x base x height
Side1+side2+side3
circle x radius2
Radius=diameter/2
2 x x radius
rectangle
Length x height 2xlength + 2xheight
oval xr1xr2 -
2D Geometrical Objects
MSU Physics 231 Fall 2015 39
object surface volume
cube 6xlength2 length3
rectangle 2hw+2lh+2wh
hlw
sphere 4r2 (4/3) x r3
cylinder 2rh r2h
3D Geometrical Objects
MSU Physics 231 Fall 2015 40
a
acbbx
a
cbxax
2
4
0
0
2
2
In general there are 2 solutions. In physics problems,One of them is usually not realistic and is thrown out.
Solving Quadratic Equations
MSU Physics 231 Fall 2015 41
Calculate the length of the shorter of two sides of a rectangle, which has an area of A = 24 m2 and a perimeter of p = 22 m. Example of two equations and two unknowns.
w
hA = whp = 2w+2h
24 = wh so w = 24/h22 = 2w + 2h = (2x24/h) + 2h = (48/h) + 2h
-2h2 + 22h - 48 = 0
a
acbbx
a
cbxax
2
4
0
0
2
2
8or3
3or8
4
1022
)2(2
)48)(2(42222 2
w
h
h
MSU Physics 231 Fall 2015 42
Dimensional Analysis
Dimensions should be treated as algebraic quantities If you know the dimensions you want in the end of a calculation, it helps you plan
your work and check your math
Example: Calculate the distance traveled in 10 seconds by an object starting at rest and
traveling at constant acceleration
Given : x = (1/2) a t2
What are the units for a (acceleration)? [m] = [?] [s2]
Rearrange to get units for a:[?] = [m] / [s2] )= m/s2 Units of acceleration go here
Check your math: [m] = [m/s2] [s2] = [m]