Orientation for Physics Lab for Chemists 2304191¹€อกสาร Download/ภาคปลาย_62... · 9 General rules Be in class no later than 10 minutes, After 10 minutes

1

Orientation for

Physics Lab for Chemists

2304191

Email physicslabchulaacth

This document is available at Physicslab Homepage

Website httpwwwphysicslabscchulaacth

Facebook PhysicsLab CHULA

A Glimpse of Physics

Experiments

2

3

Why experiment is important Experiment is used to identify a value of unknown quantity from the

known physics formula ie to find a gravitational constant (g) from

a swing of pendulum using an equation

Results from experiments can help formulate the relationship

between two quantities despite precise formula is yet to be

identified

It is well accepted that any new theoryhypothesis must be

physically verified by a real observation (experiment)

Sometimes an advanced experiment can lead to a new physics

phenomenon

2l

Tg

4

Goals of the physics lab courses

Measurement skills that minimize errors -

discrepancy between result and theoretical values

The use of instruments - understand how it works

and basic operation

Data recording with appropriate accuracy and

precision

Error analysis of the results

Data analysis by statistical and graphical methods

Gaining physics concept

Important Accessories

Pen

Pencil

RubberEraser

Transparent Ruler (make sure it is long enough to

draw graph)

Scientific Calculator (use of Calculator Apps on

smartphone is not allowed)

5

List of 2nd Year Physics Experiments

Number Experiment name Post-Test

1 Measurement and UncertaintiesYes

2

Simple Pendulum Linear Graph and Statistical

AnalysisNo

4 Simple Harmonic Motion and Hookersquos Law No

7 Rotational Motion No

8 Speed of sound in air Yes

11 Electrical MeasurementYes

17 Lenses and Spherical Mirrors Yes

19 Interference and Diffraction of Light No

20 Radioactivity No

21 Heat Capacity No

6

Lab Schedule

7

BSAC 191Friday 900 - 1200 AM

Week Date

Orientation 10-Jan-2020

Sport Day 17-Jan-2020

1st 24-Jan-2020

2nd 31-Jan-2020

3rd 7-Feb-2020

4th 14-Feb-2020

5th 21-Feb-2020

6th 28-Feb-2020

Midterm Week (NO LAB) 6-Mar-2020

7th 13-Mar-2020

8th 20-Mar-2020

9th 27-Mar-2020

10th 3-Apr-2020

Review 10-Apr-2020

Make -up lab 17-Apr-2020

Final Exam As announced

8

Grading policy

Experimental part (10 Labs) 70 points

7 points for each lab

2 points for general evaluations

On time for class

Manner in class

Behavior in class

5 points for

Data sheet

Post-Test in class (see course syllabus)

Final exam (written) 30 points

9

General rules Be in class no later than 10 minutes

After 10 minutes is considered being late (1 point reduction)

After 30 minutes student is not allowed to enter the lab

Dress properly according to the university code of uniforms IF NOT

you may be refused to enter the lab or 1-2 points of score will be

deduced

No use of mobile phoneTablet PCPC in class Keep those devices in a

provided plastic box on your table

2 points reduction for 1st warning on use of devices

Additional 5 points reduction for 2nd warning on use of devices

Students are required to bring the laboratory handbook and present to

the staff when signing for attendance One point will be deducted from

your total score if the laboratory handbook is not presented

10

General rules Do not leave the laboratory room at any time without notifying an

instructor

Stay at your table until the experiment is finished unless necessary

Do not make unnecessary loud noise

No food or drink in the laboratory room

11

General procedures 2-3 students per group for each experiment

Check your lab schedule and partners at the front of room 506-507 MHMK

Building or on the Website httpwwwphysicslabscchulaacth

Sign your name before getting into the lab room and obtain the data sheet

Sign up for other person is considered cheating All parties involved will

get a punishment - maximum of 7 points score deduction The issue will

also be reported to your course administrator

In some lab student is required to sign up for checking out an experiment kit

After finishing the lab all checked-out items must be returned

If damage occurs student(s) will be held responsible (charge or replacement)

Submit your data sheet on time (informed at the briefing)

Do not take your data sheet out of the lab room

It is not accepted after the class is already over

A Make-Up Class Policy If you miss more than 2 classes you have no right to take the final

examination (lt80 attendance) You are advised to ldquoWITHDRAWrdquo

before the final exam otherwise an F grade will be given

If you miss any class please contact the laboratory staff within 7 days

with supporting documents ie a medical certificate official letter from

a respected organization etc sufficiently explaining why you could not

attend the class The laboratory instructorstaff retains the right to

acceptreject those documents

Only ONE make-up experiment can be arranged for any student during

the MAKE-UP week Beware that attending a make-up class does not

necessarily reduce the number of your absences in normal class

12

Personnel amp Staff Security Issue

Threatening or injuring instructorsstaffs is a very

serious issue The issue will be reported to your

course administrator and your family If seriously

punishment will be executed to the maximum extend

by university law and criminal law

13

Personnel amp Staff Security IssueEvacuation Procedure

In Case of FireWhen you hear fire alarm or are

instructed to leave the building you should

- Bring valuable items eg money or cellphone

- Follow the staff who carries the ldquoPhysics

Room XXXrdquo sign

- Leave the building quickly and calmly to the

nearest ldquoFire Exitrdquo

- Do not use an elevator during an evacuation

- Do not use the central stairwell as emergency

exit

- Gather for a head count at the ldquoFire Assembly

Pointrdquo behind the Geology-Botany building

- Do not enter the building again until it has

been declared safe to enter by the local Fire Department

14

Personnel amp Staff Security IssueFIRE ESCAPE PLAN

General Physics Laboratory Room 501-503

Department of Physics Faculty of Science Chulalongkorn University

Fire Escape Plan Fire Exit

fire extinguisher Fire Alarm

fire extinguisher

Hallway Hallway

Hallway Faculty Office

Room 502

Room 503Room 501

15

What to do if a fire starts

If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them

Press the fire alarm located near the fire exit

If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669


16

Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the

clamp Therefore during the experiment do not move the wheel

or the axle and beware of the loaded mass ndash when it moves it

may hit you or your partners

Laboratory Room 503


17

Experiment 11 Electrical Measurement

bull Be careful about electronic devices eg multimeters or

resistors before connecting them to a power supply

Check whether devices work well before doing the

experiment

Laboratory Room 503


18

Experiment 19 Interference and Diffraction of Light

bull Be careful when using a laser do not aim it at

personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8

Speed of sound in air

bull Be careful when pulling up the

pipe higher than your height

bull Check the electrical wires before

connecting them in a circuit

Experiment 20 Radioactivity

bull Do not touch radioactive substances

without protection and do not put

them in your mouth

bull Radioactive source should be used

carefully to avoid damage (If

damage occurs inform instructors or

staffs immediately)

Laboratory Room 505-507


21

Experiment 21

Heat Capacity

This experiment involves

heat students should use

provided equipment to

hold a pot or any hot

equipment and beware of

the stream coming from

the tube end

Students must wear heat

protection gloves while

doing the experiment







fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17

Lenses and Spherical

Mirrors

bull Beware of dropping

or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4

Simple Harmonic Motion

and Hookersquos Law

bull Beware not to drop loaded

masses on your feet

bull Do not pull or push a

spring too hard

Laboratory Room 202


25

Comments Form

The comment form is available at every lab room in a box near the entrance door

Student can evaluate or comment on each lab and drop the form into the box nearby

Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab

Your comments are important and useful to make things better

Comment can also be sent to physicslabchulaacth

26

Error analysis and graph

bull Types of errors

bull Preliminary description of error analysis

bull Propagation of uncertainties

bull How to report and use uncertainties

bull Straight line

Note that the following details appear in

Lab books 2304191

27

Types of errors

bull Personal error

ndash Individual mistake - must be avoided or minimized

bull Systematic error (ONE WAY error)

ndash Instruments that always give too high or too low value (corrected

by instrument calibration)

ndash Example the measuring tape that its end start from 1 not 0

Without this notice length will always be TOO SHORT

ndash We cannot reduce systematic error merely by taking an average

bull Statistical error (TWO WAY error)

ndash Reading that is randomly sometimes too high sometimes too

low

ndash Taking an average can reduce this random errorness

Accuracy and Precision

Not accurate not precise

Not accuratebut precise

Quite accurate

(around the

target) but not precise

Accurate and

precise

We want this one

in doing the measurement

28

29

Preliminary Description of

Error Analysis

use error in the sense of ldquouncertaintyrdquo error

do not involve lsquomistakersquo in a scientific

measurement

no scientific measurement can yield exact

value

knowing the uncertainty is important

30

Example Is the crown made of gold

Perform the density measurement of the crown

gold = 155 gcm3 and alloy = 138 gcm3

Measurement report Student A Student B

Best estimate of crown 15 gcm3 139 gcm3

Uncertianty() for crown 15 gcm3 02 gcm3

135 165

137 141Student A

(not sure)

Student B

(certainly NO)

138 gcm3 155 gcm3alloy gold

density

31

Estimating uncertainties in repeatable

measurements

Same quantities obtained from several readings

repeating

Best estimate = average value

Standard deviation () is 68 confidence limit

Uncertainty of the mean () is

2

1

( )

1

N

i

i

x x

N

68 of 100 readings will fall

within and x S D x S D

N

32

Propagation of uncertainties

Question If A = 15 1 and B = 10 2 what is the maximum and

minimum value of A+B (which give the range of answer)

14 A 16 8 B 12

Answer So maximum of A+B is 16+12 = 28 and minimum of A+B

is 14+8 = 22

Question What about the maximum and minimum value of A-B

Is it 16-12=4 and 14-8=6 respectively

Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8

The minimum of A-B is minA ndash maxB = 14-12 = 2

A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3

which gives maximum value of 8 and

minimum value of 2


33

Question If A = 15 1

and B = 10 2 what is the

maximum and minimum of

A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112

Another way of thinking is that

A has uncertainty around 667

(this come from 115 x 100)

B has uncertainty around 20

(210 x 100)

So we would expect maximum

uncertainty of around 2667

A x B = 150 and 2667 of this is

40 So our answer is 15040 which

is close to the exact answer on the

left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)



A B = 15 and 2667 of this is

04 So our answer is 15 04

which is close to the exact answer

on the left

35

What we did on two previous slides are equivalent to the following

formula

maximum uncertainty products or quotients

A x B = (a x b) AB AB = (ab) AB

the ratio added up

example W = 13 01 cm and L= 21 03 cm

area = WL = 13 x 21 = 273 cm2

Uncertainty of area WL= [(0113) + (0321)] x 273

= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36

Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from

A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b

Prove it yourself that statistical uncertainties is always

LESS THAN the maximum uncertainty

37

more example

q =

max uncertainty

stat uncertainty

Read more in your lab manual

zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38

How to report and use uncertainties

bull Always include the units

(measured value of x) = best estimate uncertainty

bull Rule for stating uncertainties

In an introductory laboratory experimental

uncertainty usually be rounded to one significant

figure

example (measured of g) = 982 002385 ms2

should be reported as 982 002 ms2 or the

mass of 524 04637 g should be reported as 52

05 g

39


bull Rule for stating answers

The last significant figure in any stated answer

should usually be of the same order of

magnitude (in the same decimal position) as the

uncertainty

Example

best estimate uncertainty stated answer

92855 005 9286 005

92855 05 929 05

92855 5 93 5

40


bull Using scientific notation for a very

large or small value

Example

1 (measured charge) = 159x10-19 5x10-21 C

should report as (159 005 ) x 10-19 C

2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line

bull Linear equation y = m x + c

m is slope and c is y-intercept

They can be evaluated using either graphical

analysis or statistical analysis (lab 2)

bull Usually data are plotted to see if they satisfy

linear equation (straight line)

42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di

di2 = (yline- ydata)

2 is minimum

Best fit for a straight line

bull Number of data

points above the line

is about the same to

that of under the line

bull Summation of the

vertical distances for

each data point to the

line is minimum

bull Number of data points above the line is about the same to that of

under the line

bull Summation of the vertical distances for each data point to the line is

minimum

43

Homework

bull Read the Introduction part in the lab book

bull Bring your calculator and learn how to use it

to get the mean and standard deviation of a

set of data

wwwphysicslabscchulaacth

44

A Glimpse of Physics

Experiments

2

3






identified




phenomenon

2l

Tg

4





and basic operation


precision





Pen

Pencil

RubberEraser


draw graph)



5




2


AnalysisNo







20 Radioactivity No

21 Heat Capacity No

6

Lab Schedule

7


Week Date



1st 24-Jan-2020

2nd 31-Jan-2020

3rd 7-Feb-2020

4th 14-Feb-2020

5th 21-Feb-2020

6th 28-Feb-2020


7th 13-Mar-2020

8th 20-Mar-2020

9th 27-Mar-2020

10th 3-Apr-2020

Review 10-Apr-2020



8

Grading policy




On time for class

Manner in class

Behavior in class

5 points for

Data sheet



9






deduced








10


instructor




11

























12







13






Room XXXrdquo sign





exit





14






fire extinguisher

Hallway Hallway


Room 502

Room 503Room 501

15






16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

3






identified




phenomenon

2l

Tg

4





and basic operation


precision





Pen

Pencil

RubberEraser


draw graph)



5




2


AnalysisNo







20 Radioactivity No

21 Heat Capacity No

6

Lab Schedule

7


Week Date



1st 24-Jan-2020

2nd 31-Jan-2020

3rd 7-Feb-2020

4th 14-Feb-2020

5th 21-Feb-2020

6th 28-Feb-2020


7th 13-Mar-2020

8th 20-Mar-2020

9th 27-Mar-2020

10th 3-Apr-2020

Review 10-Apr-2020



8

Grading policy




On time for class

Manner in class

Behavior in class

5 points for

Data sheet



9






deduced








10


instructor




11

























12







13






Room XXXrdquo sign





exit





14






fire extinguisher

Hallway Hallway


Room 502

Room 503Room 501

15






16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

4





and basic operation


precision





Pen

Pencil

RubberEraser


draw graph)



5




2


AnalysisNo







20 Radioactivity No

21 Heat Capacity No

6

Lab Schedule

7


Week Date



1st 24-Jan-2020

2nd 31-Jan-2020

3rd 7-Feb-2020

4th 14-Feb-2020

5th 21-Feb-2020

6th 28-Feb-2020


7th 13-Mar-2020

8th 20-Mar-2020

9th 27-Mar-2020

10th 3-Apr-2020

Review 10-Apr-2020



8

Grading policy




On time for class

Manner in class

Behavior in class

5 points for

Data sheet



9






deduced








10


instructor




11

























12







13






Room XXXrdquo sign





exit





14






fire extinguisher

Hallway Hallway


Room 502

Room 503Room 501

15






16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44


Pen

Pencil

RubberEraser


draw graph)



5




2


AnalysisNo







20 Radioactivity No

21 Heat Capacity No

6

Lab Schedule

7


Week Date



1st 24-Jan-2020

2nd 31-Jan-2020

3rd 7-Feb-2020

4th 14-Feb-2020

5th 21-Feb-2020

6th 28-Feb-2020


7th 13-Mar-2020

8th 20-Mar-2020

9th 27-Mar-2020

10th 3-Apr-2020

Review 10-Apr-2020



8

Grading policy




On time for class

Manner in class

Behavior in class

5 points for

Data sheet



9






deduced








10


instructor




11

























12







13






Room XXXrdquo sign





exit





14






fire extinguisher

Hallway Hallway


Room 502

Room 503Room 501

15






16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44




2


AnalysisNo







20 Radioactivity No

21 Heat Capacity No

6

Lab Schedule

7


Week Date



1st 24-Jan-2020

2nd 31-Jan-2020

3rd 7-Feb-2020

4th 14-Feb-2020

5th 21-Feb-2020

6th 28-Feb-2020


7th 13-Mar-2020

8th 20-Mar-2020

9th 27-Mar-2020

10th 3-Apr-2020

Review 10-Apr-2020



8

Grading policy




On time for class

Manner in class

Behavior in class

5 points for

Data sheet



9






deduced








10


instructor




11

























12







13






Room XXXrdquo sign





exit





14






fire extinguisher

Hallway Hallway


Room 502

Room 503Room 501

15






16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

Lab Schedule

7


Week Date



1st 24-Jan-2020

2nd 31-Jan-2020

3rd 7-Feb-2020

4th 14-Feb-2020

5th 21-Feb-2020

6th 28-Feb-2020


7th 13-Mar-2020

8th 20-Mar-2020

9th 27-Mar-2020

10th 3-Apr-2020

Review 10-Apr-2020



8

Grading policy




On time for class

Manner in class

Behavior in class

5 points for

Data sheet



9






deduced








10


instructor




11

























12







13






Room XXXrdquo sign





exit





14






fire extinguisher

Hallway Hallway


Room 502

Room 503Room 501

15






16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

8

Grading policy




On time for class

Manner in class

Behavior in class

5 points for

Data sheet



9






deduced








10


instructor




11

























12







13






Room XXXrdquo sign





exit





14






fire extinguisher

Hallway Hallway


Room 502

Room 503Room 501

15






16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

9






deduced








10


instructor




11

























12







13






Room XXXrdquo sign





exit





14






fire extinguisher

Hallway Hallway


Room 502

Room 503Room 501

15






16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

10


instructor




11

























12







13






Room XXXrdquo sign





exit





14






fire extinguisher

Hallway Hallway


Room 502

Room 503Room 501

15






16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

11

























12







13






Room XXXrdquo sign





exit





14






fire extinguisher

Hallway Hallway


Room 502

Room 503Room 501

15






16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44












12







13






Room XXXrdquo sign





exit





14






fire extinguisher

Hallway Hallway


Room 502

Room 503Room 501

15






16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44







13






Room XXXrdquo sign





exit





14






fire extinguisher

Hallway Hallway


Room 502

Room 503Room 501

15






16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44






Room XXXrdquo sign





exit





14






fire extinguisher

Hallway Hallway


Room 502

Room 503Room 501

15






16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44






fire extinguisher

Hallway Hallway


Room 502

Room 503Room 501

15






16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44


16





Laboratory Room 503


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44


17





experiment

Laboratory Room 503


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44


18



personrsquos eyes

Laboratory Room 503






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44






fire extinguisher

Hallway Hallway


Room 506

Room 507Room 505

19






20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44


20

Experiment 8









them in your mouth




staffs immediately)



21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44


21

Experiment 21

Heat Capacity







the tube end










fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44






fire extinguisher

Hallway Hallway


Room 602

Room 603Room 601

22






23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44


23

Experiment 17


Mirrors


or damaging lenses

or mirrors

Laboratory Room 601

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

24

Experiment 4


and Hookersquos Law


masses on your feet


spring too hard

Laboratory Room 202


25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

25

Comments Form






26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

26






bull Straight line


Lab books 2304191

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

27

Types of errors

bull Personal error










low





Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44




Quite accurate

(around the


Accurate and

precise

We want this one


28

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

29


Error Analysis



measurement


value


30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

30







135 165

137 141Student A

(not sure)

Student B

(certainly NO)


density

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

31


measurements


repeating




2

1

( )

1

N

i

i

x x

N



N

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

32




14 A 16 8 B 12


is 14+8 = 22





A BA B

Maximum uncertainty

Example (15-10) (1+2) = 5 3


minimum value of 2


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44


33




A x B

14 A 16

8 B 12

Max = 16 x 12

= 192

Min = 14 x 8

= 112





(210 x 100)






left


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44


34




A B

14 A 16

8 B 12

Max = maxA minB

= 168 = 2

Min = minA max B

= 14 12

= 117





(210 x 100)






on the left

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

35


formula



the ratio added up


area = WL = 13 x 21 = 273 cm2


= 0600054 = 06 cm2

b

b

a

a

ba

AB

b

b

a

a

ba

BA


36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

36


A =a a B=b b

sums or differences

products

quotients

2 2( ) ( ) ( )A B a b a b

2 2A a a a b

B b b a b


2 2a b

AB ab aba b



37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

37

more example

q =

max uncertainty

stat uncertainty


zy

baq

|||||||||| z

z

y

y

b

b

a

a

q

q

2222

z

z

y

y

b

b

a

a

q

q


38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

38







figure




05 g

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

39






uncertainty

Example


92855 005 9286 005

92855 05 929 05

92855 5 93 5

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

40




Example



2 1857000 40000

1857 x 106 4 x 104

( 186 004 ) x 106

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

41

Straight line







42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

42

000

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

x

y

di


2 is minimum


bull Number of data







line is minimum


under the line


minimum

43

Homework




set of data


44

43

Homework




set of data


44


44

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Orientation for Physics Lab for Chemists 2304191¹€อกสาร Download/ภาคปลาย_62... · 9 General rules Be in class no later than 10 minutes, After 10 minutes