Physics 231 - Michigan State Universitybrown/231/Ch1.pdf · The Strosacker Physics Learning Center...

MSU Physics 231 Fall 2015 1

Physics 231Topic 1: Introduction, Units, Significant Figures

Alex BrownSeptember 2, 2015


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


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


HomeworkHomework 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.


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


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


Information and linksLecture ppt and pdfGrade updates


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!


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.


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


DOs and DON'Ts

DON'T... …use your cell phone in class.


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


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!


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


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


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


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



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



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)


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


A Wide Range of Units


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


Scientific Notation

For very large or very small numbers the scientific notation is advantageous.

Write number as mantissa x 10Exponent

Example: 0.000000001 = 1 × 10‐934000000 = 3.4 × 107

Alternative notation: 3.4E7 (CAPA, computers)1 m = 1000 mm = 1E3 mm


Significant Figures


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


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


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


We will use some of those…

Greek Alphabet


object surface circumference

square Length2 4xlength

triangle ½x base x height Side1+side2+side3

circle x radius2

Radius=diameter/22 x x radius

rectangle Length x height 2xlength + 2xheight

oval xr1xr2 -

2D Geometrical Objects


object surface volume

cube 6xlength2 length3

rectangle 2hw+2lh+2wh hlw

sphere 4r2 (4/3) x r3

cylinder 2rh r2h

3D Geometrical Objects


aacbbx

acbxax

24

00

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


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

aacbbx

acbxax

24

00

2

2

8or33or8

41022

)2(2)48)(2(42222 2

wh

h


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]

Physics 231 - Michigan State Universitybrown/231/Ch1.pdf · The Strosacker Physics Learning Center...

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