Technology 6: Mangonels

Today we had a quick brainstorm about siege weaponry: what it was for and what types of seige weapons we could think of. Then we looked at some of the physics of catapults, and mangonels in particular. Here is some of the information we shared:

From http://www.real-world-physics-problems.com/catapult-physics.html

Catapult physics is basically the use of stored energy to hurl a projectile (the payload), without the use of an explosive. The three primary energy storage mechanisms are tension, torsion, and gravity. The catapult has proven to be a very effective weapon during ancient times, capable of inflicting great damage. The main types of catapults used were the trebuchet, mangonel, onager, and ballista.

The Mangonel:

The mangonel consists of an arm with a bowl-shaped bucket attached to the end. In this bucket a payload is placed. Upon release, the arm rotates at a high speed and throws the payload out of the bucket, towards the target. The launch velocity of the payload is equal to the velocity of the arm at the bucket end. The launch angle of the payload is controlled by stopping the arm using a crossbar. This crossbar is positioned so as to stop the arm at the desired angle which results in the payload being launched out of the bucket at the desired launch angle. This crossbar can be padded to cushion the impact.

The mangonel was best suited for launching projectiles at lower angles to the horizontal, which was useful for destroying walls, as opposed to the trebuchet which was well suited for launching projectiles over walls.

However, the mangonel is not as energy efficient as the trebuchet for the main reason that the arm reaches a high speed during the launch. This means that a large percentage of the stored energy goes into accelerating the arm, which is energy wasted. This is unavoidable however, since the payload can only be launched at high speed if the arm is rotating at high speed. So the only way to waste as little energy as possible is to make the arm and bucket as light as possible, while still being strong enough to resist the forces experienced during launch.

The physics behind a mangonel is basically the use of an energy storage mechanism to rotate the arm. Unlike a trebuchet, this mechanism is more direct. It consists of either a tension device or a torsion device which is directly connected to the arm.

The figure below illustrates a mangonel in which the energy source is a bent cantilever, which is a form of tension device. This can consist of a flexible bow-shaped material, made of wood for example.

The point P in the figure is the pivot axle, attached to the frame, about which the arm rotates.

 

In groups of three or four, we researched how we could construct a working model of a mangonel using ice block sticks.

After construction, we took the time to test our creations, recording their capabilities in terms of distance of the projectile and height.

 



Technology 2

Today's challenge was to build a structure which could launch (and steer) a marble towards a target 3 metres away.
The teams only had sheets of newsprint paper to use to create the ramp, plus sellotape. It had to be portable and free standing (they couldn't support it themselves).
All the teams managed the task really well, so accuracy was the testing point. They got 5 points for shooting past the drink bottle (3 metres away), and 10 points for actually hitting it.
There was a tie for first place (with 25 points from three goes):
The team of Danielle, Alena and Stacey, plus the team of Isaac, Aleks and Millie.

Technology 1

Today's challenge was to create a launcher for a table tennis ball with a selection of materials... 2 rubber bands, 6 sheets of paper, 4 straws, 4 ice block stocks, and sellotape. Not all the materials had to be used.
Not all the groups managed to finish, the task, but it was a great activity for practising our team work and for focusing on time management.

Pixar in a Box 2

Today we continued our study of Pixar, and found out more about how this amazing company is able to create such fun and cool new virtual worlds for us every time they release a new movie.
Lesson 2: Crowds
When the designers were planning Wall-e, they wanted him to go from a world where there was only one robot - himself on Earth - to a place where there were hundreds of different robots, all with their own jobs and purposes.
The designers were tasked with creating all these different robots, but instead of inventing a thousand different robots form scratch, they simply used the branch of mathematics known as "combinatorics" to create a few different heads, a few bodies, a few arms, etc, and mixed and matched them.
We also had a design task to carry out or ourselves. The challenge was to create 1000 different dinosaurs by using a limited number of body parts (head, tail, arms, legs and body) - preferably fewer than 25. In the end we worked out that 21 or 24 different body parts is the answer, and we designed what they might look like.
Here's the maths:
2 x 5 x 10 x 5 x 2 = 1000 (24 body parts)
or
4 x 5 x 5 x 2 x 5 = 1000 (21 body parts)

Pixar in a Box 1

The Khan Academy have joined forces with Pixar (the awesome company that brought us films like Toy Story, Brave and Inside Out) to create a series of lessons which combine maths and animation. Through these lessons we are able to learn about some of the techniques the animators use in order to make their films. Plus we're also able to catch a glimpse of what goes on in an enormous company such as Pixar, where so many employees with distinct skills are working together towards a common goal.
Lesson 1: Environment Modelling
This series looked at Brave. One of the challenges when the animators made Brave was creating so much grass which moved in natural ways. We learned how parabolic arcs helped the designers to make single blades of grass, and how they were animated in order to move naturally.

Maths Investigation 3

The Locker Problem
Imagine this: there are 1000 students at a school, each with a locker, which is shut. At the start of the day, the first student comes into school and opens all of the lockers.
Then the second student comes in and touches locker numbers 2, 4, 6, 8 etc... if it's shut, he opens it, if it's open he shuts it.
The third student comes in and touches numbers 3, 6, 9, 12... etc. (If it's shut she opens it, if it's open she shuts it.)
It carries on all day. The students come in, and starting with their own locker, they touch the ones which are multiples of their number.

The challenge is figuring out what state the lockers are in by the end of the day.

PHEW!

There are a couple of things to think about when tackling this problem...
1. Downsize the issue. 1000 is a big number. Try it out with 20 lockers and see if a pattern starts emerging which you can extrapolate.
2. Think about what happens to a specific locker. How many times will locker number 1 be touched? How many times will locker number 21 be touched?

It wasn't long before a few of the students in the group realised that this problem has a lot to do with square numbers - such as 1, 4, 9, 16, and so on. When you write down the factors of each locker number you will realise why.

Maths Investigation 2

Today we looked at a bit of Geometry.
Firstly Polygons: How many diagonal lines are there inside polyhedral shapes? And is there a general rule? Can the number be predicted?
We found that for a four-sided shape the total is 2, five-sided it's 5, six-sided it's 9, seven-sided it's 14, and eight-sided it's 20. So obviously the number of diagonals increases. To find a rule, we looked carefully at each corner, and we found it useful to notice, for every shape, how many diagonals came from each corner.
In the end we did come up with a rule, and used it to predict that the number of diagonals in a 100-sided shape is 4850 (phew!).
Here's our rule, where "s" means the number of sides on the shape:
(s-3) x s / 2. We checked it and it works for all the smaller shapes, so we think it will work for the larger ones too.

Then we had some time to work with Polyhedra. We looked at three nets and noticed that although they are all called pyramids, they were quite different. We folded and made the shapes, then designed our own nets which were made from at least three different 2D shapes.

Maths Investigation 1

Today we worked on a couple of maths investigations that gave us a bit of brain drain.

Firstly, the Corner to Corner counter game... on a 3x3 grid, how many moves does it take to get the red counter from the top right corner to the (empty) bottom left?

We found that the shortest number of moves is 13, and then tried out the game with a 2x2, 4x4 and 5x5 grid. We charted our progress and a pattern emerged. We found that every time a new grid was used the number of moves increased by 8.
We worked toward finding a rule for the pattern.

Lastly we investigated Ninety degree Spirolaterals. This is the pattern for drawing a 3- spirolateral: 1 + 2 + 3 + 1 + 2 + 3 etc. You draw for one square, then turn ninety degrees, draw two squares, turn ninety, draw three squares, turn ninety, and start again at one. We found that some spirolaterals come round to the start, and others (like the four) do not. They continue on indefinitely.

Morse Code and Flanders Fields

Today we had a really interesting session which I so enjoyed - thanks everybody!
Morse Code - what is it, why did they use it, and how is it transmitted?
We learned how to spell our names with the help of a very geeky (but actually very catchy) Morse code song.



Isaac found for us a cooool website which translates any message into a Morse one. Awesome! Click here to be taken to it. Imagine how good you'd have to be at Morse Code before you could interpret it!
It would be like learning another language.
We also added in the International Aviator's Alphabet (just for fun, you know) and learned how to say our names.
Here is a very interesting and rather emotional true story about how the Colombian police department used Morse Code to send a message to 16 hostages, who had all been in the armed forces and all knew Morse Code as part of their training. We spent some time talking about this story, the situation in Colombia, listening to the song, and paying attention to the translated English lyrics.



If you had been trained in Morse Code, I think the pattern would stand out for you just like hearing English lyrics suddenly in amongst Spanish ones. What a clever plan!
Click here to read the whole article.

We also spent a little bit of time looking at the very famous poem "In Flanders' Fields". We talked about the parts of the poem we liked the most, and why. I wonder why this poem is so famous?
Stacey found out a little bit about the poet for us - Major John McRae. Sadly he did not survive the War.

Hard Tack!

Today we created a little booklet for the GD library - World War One in numbers. Each student chose one fact of the Great War to represent in some way on a square card, which was later hole punched and clipped together with book rings.

We researched some New Zealand figures from World War One, such as Sir Harold Gillies - plastic surgeon pioneer - Dave Gallaher - All Black Captain who died at the Somme - and Henare Te Wainohu - chaplain on Gallipoli.

Dave Gallaher

Sir Harold Gillies

Henare Te Wainohu

In the afternoon we attempted to make Hard Tack - the soldier staple which has as many stories told about it as Anzac Biscuits. One is that it saved a man's life when it caught a bullet in his breast pocket. Another is that it was so hard and disgusting that even the weevils didn't try to eat it. Apparently some hard tack from the Great War is still preserved in a museum somewhere (possibly more than one) and it's likely to taste just as it did 100 years ago.

Mrs Armstrong's recipe for Hard Tack

2 cups of flour
3 tsp salt
Mix these together then make a well in the centre and add one cup of water slowly, mixing as you go. When it's all added and looks a bit stringy, use your hands to make a dough. Roll out to a quarter of an inch. Sprinkle with salt. Mark into squares or rectangles (we forgot this step at school), prick with a fork and bake for 30 minutes at 180 degrees. Flip over and bake again for 30 minutes.

Soldiers used to dunk hard tack in their tea or coffee to soften it. They also used to fix it on the end of their bayonets and toast it over the fire - it's definitely more palatable warm.

My strange children have demanded it in their lunchboxes.

What makes a leader great?

Last week we came across an interesting fact: Leaders gain trust by conforming. So today we looked more closely at Leadership. Some of the students had really great insights into this as they have recently been on a leadership course.
First we brainstormed the differences between being bossy and being a leader, jotting down our ideas on a Venn diagram.
Then we shared the traits of the best leaders.
We read together the book of "Yertle the Turtle" which is a story of how not to be a good leader, and the students were able to pick out exact examples of Yertle's mistakes, like his selfishness - the way he put his needs before any of the other turtles.

We ended the session with a suggestion: if you knew that Dr Seuss was writing a book about Hitler and his lack of thought for other humans in his quest for power, how would that change your view of the book?



Social Loafing

What a cool phrase! Today we learned about some other concepts of group psychology, and social loafing is one of them. It's basically the effect that takes place when the tug of war is on, and each individual member of the group chooses to work less hard than they might if pulling on their own.
Deindividuation is what happens when someone feels free to cyber bully, and say things they would never say in person.
Here are some of the interesting facts that have been discovered about groups after lots of studies...

10 Rules That Govern Groups

What most groups of people have in common.

Much of our lives are spent in groups with other people: we form groups to socialise, earn money, play sport, make music, even to change the world. But although groups are diverse, many of the psychological processes involved are remarkably similar.

Here are 10 insightful studies that give a flavour of what has been discovered about the dynamics of group psychology.

1. Groups can arise from almost nothing

2. Initiation rites improve group evaluations

3. Groups breed conformity

4. Learn the ropes or be ostracised

5. You become your job

6. Leaders gain trust by conforming

7. Groups can improve performance…

8. …but people will loaf

9. The grapevine is 80% accurate

10. Groups breed competition

Conformity

Today we looked into some group psychology, and in particular what it is about groups that makes us act in a particular way.
We read a book called Ferdinand, about a bull that is unlike all the others and refuses to conform. It's a wonderful example of the kind of diversity which is not only accepted but promoted in our modern society.
However, that doesn't change the fact that most often than not we will find ourselves behaving in a certain way in order to conform with the group we belong to, even if the group's behaviours are not in line with our usual personality.
There have been many studies done along these lines.
We watched a Khan Academy video and learned some new terms: Groupthink, the Bystander Effect, and Deindividuation.

Bystander effect:

Multiple Intelligences and Social Identity

Today we had a look at the graphs of our Multiple Intelligence quizzes. We talked about why we took three of them and averaged the results, and we talked about the dangers of seeing a test like this as a negative thing. We also talked about how the results are useless if we choose to skew them.
This video from the Khan Academy looks at Self Concept and Social Identity, and Kristy asked a good question about comparisons and whether they are a Good Thing or a Bad Thing. I think in the end it depends on attitude - we could use comparisons to increase our self esteem, or we could use them as a springboard to self motivation.

Self concept, self identity, and social identity:


We read together the book "Frederick" by Leo Lionni. Frederick is a field mouse who does not help his four brothers and sisters collect food stores for the long winter ahead. Instead he tells them that he is gathering the sun, words and colours so that it will keep them going.
The students immediately saw that Frederick had different smarts from the rest of his family. We discussed whether he should be judged negatively for this. It also raised questions about the nature of work, and whether all contributions to a joint goal should be rewarded in the same way. What would happen if all his family decided they were poets? What if they were all collectors? Danielle mentioned that the book is about diversity.
I introduced the students very briefly to the concept of Socialism, its aims and ideals.

Multiple Intelliences

This week we pooled our group: some students from last year's sessions, plus some new students.
Our topic today, Multiple Intelligences, is something that we've all been looking at in our respective classrooms, and we were able to bring together what we've already learned about Gardner's theory.

We talked about the strengths of each smart and also about where we think we fit into the theory. We noted that this is our "self image" and that the multiple intelligence quizzes are all based on this: our self awareness.
We touched on three different aspects of self: how we ARE, how we THINK we are (self image), and how we HOPE to be (self improvement).
Each student took three different Multiple Intelligence quizzes, and we talked about why it might be useful to take a test three different ways.
Here are the links to our quizzes:
Quiz 1
Quiz 2
Quiz 3
Each student then graphed the results, and we talked about how or why the results came out slightly differently in different surveys. We did notice however that in general the results were fairly similar, which is reassuring.
We were quickly running out of time before we got to pool our graphs, and began to touch on the big questions:
1. How do the results of a Multiple Intelligence quiz AID us?
2. How do the results of a Multiple Intelligence quiz LIMIT us?

Back next week with more interesting discussions from the Library at GD!

Cryptography

Today we started our session with two more curly questions: 1. What can you do with a brick? 2. List as many jobs as you can think of that don't exist yet, but will in the future.
It was fun to discuss our answers. We noticed that as soon as we begin to pool our ideas we can think so much more broadly.
We had a look at the Khan Academy website, where you can learn anything. In the applied maths section there is a whole series on Cryptography, including its history and a chance to try it out.
We watched the videos and discussed the Caesar cipher, how it was broken, frequency tables, and how to make it harder to decrypt. We also used the cipher to create our own coded messages.
What is cryptography?: What is Cryptography? A story which takes us from Caesar to Claude Shannon.

The Ship of Theseus

Our first session for 2015!
We had a great session today with 15 brand new faces. First of all the students had to consider their answers to two open ended questions: 1. Name everything you can think of that is orange. 2. What can you make with a pillow and a mirror?
We talked about the reasons we'd asked to bring them together, and discussed what it meant to think outside of the box, and what "curly" questions are.
Together we read the book "The Mixed Up Chameleon", which is a story about a chameleon who wishes to be like other creatures, until no part of his original body remains.
Our discussion centred around identity, what makes you you, and about being grateful for the things you have rather than wishing for others. "Be careful what you wish for," one of the students suggested. It was also a book about social identity; wanting to be like others, and about personality or instinct. We could tell that although the chameleon looked nothing like a chameleon by the end of the book, he was still a chameleon inside, as his first instinct when he saw the fly was to eat it.
The book also raised questions about change - how much can change about something before you can no longer call it the same thing, and it is actually a new thing.
This is a well-known paradox called the Ship of Theseus.
We watched an interesting video which introduced this paradox, and discussed the ship amongst our group. It is very cool that we all had different opinions on the idea, and that all our answers were valid.

 

If you want to explore more about the Ship of Theseus puzzle, the Khan Academy has a good learning video here:

 

Metaphysics: Ship of theseus: Jenn introduces us to a puzzle that has bedeviled philosophy since the ancient Greeks: the Ship of Theseus. She tells the Ship of Theseus story, and draws out the more general question behind it: what does it take for an object to persist over time? She then breaks this ancient problem down with modern clarity and rigor. Speaker: Dr. Jennifer Wang, Lecturer, Stanford University