Friday, December 5, 2014

GEOGEBRA angle at centre equal twice angle at circumference

GEOGEBRA angle at center equal twice angle at circumference
customized from https://www.geogebratube.org/material/show/id/37863 by damienchew

http://tube.geogebra.org/student/m359109

students must be able to understand why $ \angle $ at Centre = 2 times $ \angle $  at Circumference.

Steps:


  1. Compare angles at the centre of a circle with angle touching the circumference.
  2. vary the $ \angle $ at Centre O for which it is acute less than 90 °
    example of acute angle at centre O, what is the value of $ \angle $ at Circumference point A?
  3. write down the value of  $ \angle $ at Centre O and $ \angle $ at Circumference point A
  4. vary the $ \angle $ at Centre O for which it is obtuse more than 90° and less than 180°.
    example of obtuse angle at centre O, what is the value of $ \angle $ at Circumference point A?
  5. do step 3
  6. vary the $ \angle $ at Centre O for which it is reflex more than 180°.
  7. example of reflex angle at centre O, what is the value of $ \angle $ at Circumference point A?
  8. do step 3

Thinking:

looking at the evidence of the table of recorded values, suggest a relationship between 
$ \angle $ at Centre O and $ \angle $ at Circumference point A.


Conclusion:

$ \angle $ at Centre = 2 times $ \angle $ at Circumference.


Proof:


Let $ \angle $AOC = 2a

Let $ \angle $BOC = 2b

Then $ \angle $AOB = 360° - 2a – 2b

$ \angle $ OCA = 90° – a (isosceles triangle)

$ \angle $BCO = 90° – b (isosceles triangle)

Therefore, $ \angle $ACB = (90° – a) + (90° – b) =  180° – a – b

Hence, $ \angle $AOB = 2$ \angle $ACB ($ \angle $ at Centre = 2 times $ \angle $ at Circumference) Proven

Hydrogen, Bromine, Hydrogen Bromide equilibrium Model by Andy Luo Kangshun

Hydrogen, Bromine, Hydrogen Bromide equilibrium Model by Andy Luo Kangshun
another artifact of learning by a Chemistry Tampines JC teacher who attended the EJS-OSP Singapore workshop.
http://weelookang.blogspot.com/2014/12/hydrogen-bromine-hydrogen-bromide.html
Hydrogen, Bromine, Hydrogen Bromide equilibrium Model
run: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_EQB17/EQB17_Simulation.xhtml
scr: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_EQB17.zip
author: Andy Luo Kangshun, Paco and Wolfgang


This simulation emulates the gas phase equilibria between hydrogen, bromine and hydrogen bromide molecules.


$H_{2}$ + $Br_{2}$ ⇌ 2HBr (∆H = -103 kJ mol-1) 


Constants:


$ k_{B}  = \frac{R}{ N_{A}}  = 1.38060445x10^{23} $

R = 8.314

$ N_{A} = 6.022x10^{-23} $



Parameters:


Hydrogen are yellow particles. (mass = 2*1.00794 u)

Bromine are red particles. (mass = 2* 79.904 u)

Hydrogen bromide are green particles. (mass = 79.904 + 1.00794 u)

N = 200 molecules

H-H bond: 436 kJ mol-1

Br-Br bond: 193 kJ mol-1

H-Br bond: 366 kJ mol-1

∆H = -103 kJ mol-1

$kf = A \exp{(\frac{-629}{(8.314)(T)})} $

$ kb = A \exp{(\frac{-732}{(8.314)(T)})} $

$ K_{eq} = \frac{kf}{kb} = \exp(\frac{10^{3}}{8.314(T)} $



Fixed relations



 v = Math.sqrt(3*8.314/6.022*10E23*T/mass)


or 


$ v = \sqrt( \frac{(3)(8.314)(T)}{6.022x10^{23}m}  )$

Thursday, December 4, 2014

Lower Secondary Science Chapter

Lower Secondary Science Chapter
.
For Lawrence tan yong Chong.
How did it landed on my desk? :)
Lower Secondary Science Chapter

Physics Chapter Core Team

Physics Chapter Core Team

Physics Chapter Core Team

MUST Watch, This will revolutionize education explained

MUST Watch, This will revolutionize education explained. An excellent video that deserve more views. Thank you Veritasium !



 

My take ways includes

Who Learn?

20 participants of the workshop

Why they learn?

The high levels of mental and hands-on efforts by the participants to create models that can be readily used in their own area of work

What they Learn?

computer modelling

What are teachers for?

Professor Wolfgang and Paco Francisco Esquembre, skillful and inspiring teaching and facilitation by the consultants (see Facebook post by Leong Tze Kwang thanking them). 

Facebook post by Leong Tze Kwang November 30 ·
Prof Wolfgang and Paco didn't just teach us how to make amazing JavaScript applet but also inspire us to become better teachers. Thanks Lookang for organizing the workshop. I finally get down to work. Will start making more JavaScript applet. — with Lye Sze Yee,Thomas Yeu, Dave Lommen, Ezzy Chan, Loo Kang Lawrence Wee,Francisco Esquembre, Andy Luo Kangshun and Ng Boon Leong.

the excellence service from the local organizers loo kang, sze yee and tat leong.

brief summary of EJS Workshop in Singapore

artefacts of performance http://iwant2study.org/lookangejss/00workshop/


Title: Computational Modeling with Open Source Physics (OSP) Easy Java/JavaScript (EJSS) Simulations: Funded by eduLab NRF2011-EDU001-EL001 Java Simulations for Teaching and Learning

Date: November 25-28, 2014
Venue: Academy of Singapore Teachers,eduLab@AST Block J Level 4.
Leaders: Wolfgang Christian, Francisco Esquembre
Local Organizer: Wee Loo Kang Lawrence, Lye Sze Yee, Lee Tat Leong
Sponsor: Singapore Ministry of Education, National Institute of Education & National Research Foundation


1.Background of Visit

The purpose is to allow Singapore Teachers involved in this project to directly benefit from expert knowledge that the creators of Open Source Physics OSP and Easy Java/JavaScript (EJSS) Simulations research projects.

2) Activities

This 3.5 day workshop and consultations aims to provide a hands-on bootstrapping experience to the ComPADRE Open Source Physics (OSP) project and the Easy Java/JavaScript Simulations (EjsS) modelling and authoring tool. This 3.5-day workshop combines morning expositions and practical sessions where participants will work in teams/individually on computers provided by the organizers followed by afternoon one-on-one consultations with some references to NRF2011-EDU001-EL001 customized models and worksheets with the workshop leaders. Participants will study and explore, step by step, important computational and pedagogical examples, such as the gravitational N-body and the simple harmonic oscillator models, to learn how they have been implemented in EjsS, and then modify these examples to add new capabilities.

On Day 2 PM, CPDD Director, Deputy Director and Officers had a rich up close discussions on topics on the Student Leaning Space (Blended-Face to Face&Online Learning, Massive Online Open courses, Open educational Resources)  for Physics resource development, curation etc. 

3) Impact

As of 04 Dec 2014, out of 20 participants, there are 8+2=10 creator/users of models, 7 customisers and 1 starting a NIE-MOE grant and 2 yet to confirm their models.

This outstanding achievement is possible largely due to 
  1. skillful and inspiring teaching and facilitation by the consultants (see Facebook post by Leong Tze Kwang thanking them) 
  2. the high levels of motivation of the participants to create models that can be readily used in their own area of work. 
  3. the excellence service from the local organizers loo kang, sze yee and tat leong. 


Facebook post by Leong Tze Kwang November 30 ·
Prof Wolfgang and Paco didn't just teach us how to make amazing JavaScript applet but also inspire us to become better teachers. Thanks Lookang for organizing the workshop. I finally get down to work. Will start making more JavaScript applet. — with Lye Sze Yee,Thomas Yeu, Dave Lommen, Ezzy Chan, Loo Kang Lawrence Wee, Francisco Esquembre, Andy Luo Kangshun and Ng Boon Leong.

4) Follow-Up/Learning

We have achieved the aim to provide a hands-on bootstrapping experience for 20 participants (14 teachers, 5 HQ officers and 1 NIE researcher) to the ComPADRE Open Source Physics (OSP) project and the Easy Java/JavaScript Simulations (EjsS) modelling and authoring tool.

The benefits to teachers include 10 creating new models, 7 adopt and adapt EjsS material on ComPADRE for their own teaching and more advance teachers to teach physics using computer-based modeling.

Total funding cost is around S$ 15,000 from NRF, managed by NIE and MOE, for both professor’s 4 full days of workshop, consultation, public lectures at NIE5-LT12 and close up discussions with DCPD, DD Sc and their team of CRDO officers. The professional development for teachers/ HQ officers is high in terms of the artifacts of learning and networking with international world-best researchers. DCPD and DD Sc also glean insights to the student learning space creation and population of resources from day 2 PM rich discussions.

5) Reference:


Monday, December 1, 2014

EJSS Vertical Spring-Mass (N08/III/6) Model

EJSS Vertical Spring-Mass (N08/III/6) Model by Lee Tat Leong and Ng Kar Kit.

http://weelookang.blogspot.com/2014/12/ejss-vertical-spring-mass-n08iii6-model.html
run: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/lookangejss/00workshop/ejss_model_verticalSpringMass_N08P3Q6/verticalSpringMass_N08P3Q6_Simulation.xhtml
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/lookangejss/00workshop/ejss_model_verticalSpringMass_N08P3Q6.zip
author: Lee Tat Leong and Ng Kar Kit.
author EJS: Paco

The model


Spring: spring constant k = 19.62 N/m, natural length of spring Lo = 0.650 m, equilibrium length yo = 0.850 m

Load: mass m = 0.400 kg, displacement from equilibrium position y

Mathematical model: 

$ \frac{\delta y}{\delta t} = v_{y} $

$ \frac{\delta v_{y}}{\delta t} = -\frac{k(y_{0}+y)}{m} + g $

Energies:

kinetic energy (green)  $ KE = \frac{1}{2}mv^{2}_{y} $
elastic potential energy (red) $ EPE =\frac{1}{2} k (yo+y)^{2} $
gravitational potential energy (blue) $ GPE = m g (L_{o}+y_{o} + y + reference level) $
total potential energy (magenta) $ TPE = EPE + GPE $ elastic and gravitational potential energy,
total energy (black) $ TE = KE + EPE + GPE $ sum of all the energies

Controls:

The gravitational potential energy is calculated with respect to the reference level (blue horizontal line). This reference level can be adjusted by (1) dragging the blue box at the right end of the reference level or (2) entering the value of the position in the text box at the lower right hand corner.

fine < > control buttons for learners to manipulate the model with single incremental precision
Reset button to bring simulation back to original (default)setting.