W15 Physics2CL Lec1 FIN.pdf

7/26/2019 W15 Physics2CL Lec1 FIN.pdf

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Physics 2CLLecture 1

"You do not really understand something unless

you can explain it to your grandmother."

--Albert Einstein


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Introduction

Welcome to Physics 2CL!

The Physics 2 series is a four quartercourse designed as an introductory levellook into physics for engineers andphysical scientists.

Physics 2CL, in particular, exploreselectricity, circuits, magnetism, and waves.


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IntroductionWho is this guy?

My name is Brian Maple

I am a Professor in thePhysics Department

My Ph.D. degree is incondensed matterphysics from UCSD

I have taught Physicsand carried outresearch at UCSD for

more than 40 years

My research interests

include superconductivity,magnetism, properties ofmaterials at low tempera-tures, high pressures,

and high magnetic fields


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Introduction

My office is located in 1230Mayer Hall.

The Lab TA Coordinator (LTAC)for this course is:

Paul Rozdeba.

Pauls LTAC office is located in2544 Mayer Hall Addition.

Pauls office hours:Will be announced on TED

Discussion Board on TED

administered by Paul.


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Administrativa

There is a lot of help available for you to completeyour homework and understand the concepts:

The LTAC and I will

hold office hours(announced on TED).

The book we will be

using is:

Taylor, An Introductionto Error Analysis.


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AdministrativaYour grades will be determined by your performance in

lab and the final exam.

Each lab will be worth 14 points. 2 of these points willbe from the weekly reading quiz, 2 of these points fromassigned Taylor problems, and 10 of these points will be

from the final lab report.Your lowest lab score will be dropped (except for Lab 06).

The final exam will be worth 25 points.

The cumulative final exam will be Monday, March 9 from8:00 am - 9:00 am in 2722 York Hall.

You will be given an equation sheet of relevant equations

and constants for the final exam.


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AdministrativaThe Lab 01 Write-up is available in the Physics

2CL Laboratory Manual which can be obtainedfrom the UCSD Bookstore.

You should read the Lab 01 Writeup before thebeginning of your lab session.

You should attend the lab section you signed upfor (i.e., there are no make-up lab sessions foryou to attend).

Every lab will start with a short reading quiz(worth 2points) based upon the lab writeup andthat weeks lecture. You will also turn in your

Taylor problems.


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AdministrativaYou should download the Academic Integrity Policy

and bring it to your lab meeting for Lab 01 (nextweek). (You can bring it to lab this week, as well.)

You need to sign it and hand it in to the TA toacknowledge our expectations of how you shouldcomplete your final lab reports.

No Taylor problems are assigned for this week.

Yet, you will have a Data Studio MATLABassignment that is posted on TED (this will countas 5 points towards your final grade).

It is due at the beginning of your meeting for the

first lab (Lab 01) next week.


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"I think, however, that there isnt any solution to this problem of

education other than to realize that the best teaching can be done

only when there is a direct individual relationship between a

student and a good teachera situation in which the studentdiscusses the ideas, thinks about the things, and talks about the

things. Its impossible to learn very much by simply sitting in a

lecture, or even by simply doing problems that are assigned. But

in our modern times we have so many students to teach that we

have to try to find some substitute for the ideal. ..."

--Richard Feynman in the Preface to The Feynman Lectures

on Physics, 1963

My Feelings Regarding Labs


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ErrorsYour first reading assignment is Chapters 1 and 2 ofTaylor.

Error analysis will play a significant role in how youinterpret the data obtained in lab.

You must understand the limitations of your data. Youmay, for example, have to compare your results toanother set of results.

For every measurement, x, you make in lab:

x = xbest

!x

measured value

of x best estimate

of x

uncertaintyOR

error in the

measurement


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ErrorsWhen dealing with errors, you may have to estimate theuncertainty of a measurement.

For example, if you measurethe length of an object usinga ruler (in cm here):

Be reasonable in what couldbe the maximum and minimumvalues for this measurement.

What is the highest

reasonable value for length?What is the lowestreasonable value for length?

9.3 cm

9.1 cm

What is the best estimate forthe length? 9.2 cm

x= 9.20.1cm


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ErrorsYou may also have to calculate an error due torepeatable measurements.

For example, you may be asked to measure the periodT of a pendulum with a stopwatch.

Lets say you make four separate attempts and get:

2.3s, 2.4s, 2.5s, 2.4s

Sometimes you will compare your measurements toknown constants, like g (acceleration due to gravity).

Always report what your data tells you, NOT whatyou think the answer should be!

It is reasonable to then saythat for this experiment: T = 2.40.1s


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Significant FiguresExperimental uncertainties should be rounded to one

significant figure (although it is okay to leave twosignificant figures if the leading digit in theuncertainty is a 1).

The last significant figure in any answer should be

of the same order of magnitude as the uncertainty.

g = 9.820.02385ms2 g = 9.82 0.02 m

s2

g = 9.823780.02 m

s2 g = 9.82 0.02

m

s2


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Significant FiguresSo, in lab you may make the following measurementregarding the velocity of an object (like a chargedparticle in a magnetic field):

According to the rules of significant figures, first setthe uncertainty of your measurement:

v = 6051.7832 ms

v = 6051.7830 ms

Then adjust your best estimate based upon theleading value of your uncertainty:

v = 605030 m

s


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Propagation of UncertaintiesMany times you will have to calculate a value based

upon measurements made in lab. You must propagatethe errors in each independent measurement.For example, you may have to add two independentmeasurements (x and y).

The sum of these

two values is:

x = xbest

!x y =ybest!y

q =x +y = xbest!x( )+ ybest!y( )

The maximum possible value for the length is:

qmax

= xbest+!x( )+ ybest+!y( )

qmax = xbest+ybest( )+ !x +!y( )


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Propagation of Uncertainties

Such that:

We could naively conclude then that:

The minimum possible value for the length is:

qmin = xbest!

!x( )+ ybest!!y( )qmin

= xbest+ybest( )! !x +!y( )

q = xbest+ybest( ) !x+!y( ) q = qbest!q

qbest =xbest+ybest !q = !x+!y

But this overestimates q because you aresimultaneously overestimating x and y.As it turns out the quadraticsum is the best q: !q = !x( )

2

+ !y( )2


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For This Week


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First LabDuring the first lab you will be

exploring the base concepts for theclass along with the equipment andtools you will be using throughout thequarter.

A lab activity will be to explore theVan de Graaff generator located in thelab.

This generator transfers charge to thedome by means of a rotating belt.

The generator is creating a potential

difference, (V).


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+Q

R


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ResistorsResistors are put in circuits to control

the current available.When we draw a resistor in a circuit, wewill draw it as a choppy, connectedsection.

If a wire has negligible resistance, then we will

represent it with a straight line.

We will consider all wires in a circuit diagram tohave negligible resistance unless stated otherwise.

All resistors will have a potential difference

across them (if current passes through them).

i t


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Measuring CurrentThe potential difference created by a battery

terminal is also called EMF (ElectroMotive Force).

This is a rather confusing name as EMF ismeasured in Volts.

We physically measure the amount of current ina circuit with an ammeter.

You connect the ammeter inthe circuit in series with theelement whose current youare trying to measure.

Want resistance of ammeter

to be very small.


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Break opento detect flow

Ammeter

+

A

M i V lt


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Measuring VoltageA voltmeter is used to measure electric potential

difference (or voltage).You connect a voltmeter in the circuit in parallelwith the element whose voltage (potential

difference) you are trying to measure.

You basically want tomeasure what the potential

is before and after theelement.

Want resistance of

voltmeter to be very large.


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Voltmeter

Connect on bothsides of element

+

V

R i ti it


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ResistivityIf you were constructing a wire, for a givenbattery how could you lower its resistance?

Use a good conductor.

Increase its cross-sectional area.

Decrease its length.

is called the electrical resistivity (depends onthe type of material of the conductor).

L is the length of the conductor and A is the

cross-sectional area of the conductor.

The resistance of an ohmicconductor is given by:

R i ti it


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Resistivity

Resistivity is measured in units of: [#m]

Metals typically have very low resistivity:

We actually define the resistivity of a material as

the amount it resists current flow due to anapplied electric field.

Insulators have very high resistivity:

Oh L


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Ohms LawNo matter how good your conductor is, you arealways going to have a minute reduction ofcurrent due to the conductor (excludingsuperconductors).

Ohms Law quantifies the ability of a given

material to resist the flow of charge for a givenelectric potential difference.

where R is called the resistance and ismeasured in #(Ohms).

[#]=[Volt]/[Ampere]

Oh L


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Ohms LawA good conductor will have a low resistance; this

means that current will easily flow through it.A good insulator will have a high resistance; thismeans that current will have a very hard time

flowing through it.With Ohms Law, as you increase electric potential

(V), then current will increase linearly.

The resistance in a circuit arises due to collisionsbetween the electrons moving against the electricfield and the electrons that are fixed in theatoms.


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For This WeekDownload the Academic Integrity Policy for your

lab meeting for Lab 01 next week. (You canbring it to your lab meeting this week, as well.)

Download the Data Studio Assignment from TED

for your lab meeting this week.

Download the Syllabus and read it and Lab 01for your lab meeting to perform Lab 01 (nextweek).

Read Chapters 1 and 2 of Taylor.


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Supplementary material notcovered in lecture due to

lack of time

R i ti it


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ResistivityFor most metals, as you increase the temperature,

the resistivity of the metal increases.

The following equation takes temperature intoaccount for resistivity:

is the resistivity at some temperature T.

ois the resistivity at some reference

temperature To.

is the temperature coefficient of resistivity.

Tois usually taken to be 20o

C.


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Oh s L


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Ohms LawOhms Law is not really a law in the technicalsense. It merely defines the resistance forcertain materials.

Certain materials obey Ohms Law; these arecalled ohmic materials.

There is a linearrelationship betweencurrent and electricpotential.

Certain materials do notobey Ohms Law; these are

called nonohmic materials.

E l ( t i l t )


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Example (not in lecture)

Next calculate the uncertainties (use general formula):

First calculate the best estimate for momentum(leave digits, round later):

Find the momentum of a body with massm=0.530.01kg moving with a velocityv=9.10.3m/s.

qbest =xbest!ybest pbest

=

mbest!

vbest

pbest = 0.53kg( ) ! 9.1ms( ) = 4.823kg !ms

!p

!m= v = 9.1m

s( )

!p

!m!m

"

#$

%

&'

2

=

9.1ms( 0.01kg( )( )

2

=

0.00828 kg (ms( )

2

E l


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ExampleAgain using the general formula:

!p

!v=m = 0.53kg( )

!p

!v!v

"

#$

%

&'

2

= 0.53kg ( 0.3ms( )( )

2

= 0.02528 kg (ms( )

2

This gives us:

!p =!p

!m!m

"

#$

%

&'

2

+

!p

!v!v

"

#$

%

&'

2

!p = 0.00828( )+ 0.02528( )

!p = 0.18319 kg !ms" 0.2 kg !m

s

Our reported result would be:

p = 4.8 0.2 kg!ms

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W15 Physics2CL Lec1 FIN.pdf