We have not posted for some time but I am pleased to announce that the next few weeks should lead to some interesting posts.

We are going to take the ideas we had about balancing the coke can introduced earlier in the year and conduct a “model exploration”. The outcome of this exercise should be an exploration that could be graded against IB criteria for Internal Assessment.

The object of this exercise is NOT to produce a perfect IA exploration, though we hope it will be quite good. However, more important is to observe the approaches and ways of thinking involved.

**Finding a Focused Topic**

The second post called more balancing matters actually began to look quite deeply into the problem in hand. In this post we managed to create a Geogebra file modeling the situation and start to propose what the problem of finding a balance point for a cylinder filled with liquid might be. The first thing to note is that creating this Geogebra file was no easy matter and by creating the file it became clear that one of teh primary issues was how to find out how the liquid behaved as the can was tipped in order to conserve the volume of the liquid in the can. This seems like a really tough problem.

Perhaps this is too difficult a problem for the exploration. Is there an easier problem we could solve that might be a good exploration in itself or if quite doable lead to a solution method for the actual problem of finding the tipping point of the actual can. The real challenge of the coke can is that it is 3 – dimensional. Perhaps we can solve a 2 – dimensional problem first.

Consider the following image in 2 – dimensions of a rectangle on a slope with a 2 – dimensional “liquid” inside it.

Note that the “liquid” inside the rectangle is in the shape of a trapezium since the “liquid”must keep a horizontal surface. This trapezium needs to preserve its area (the 2 d equivalent of volume) as the slope is changed. We also need to know how to find the “centre of gravity” of the trapezium.

Already we have two quite nice problems to solve. These are

- Finding the centre of gravity of a trapezium.
- Preserving the area of a trapezium as its base is “tipped”.

Perhaps these questions will make a good exploration on their own. If they do we will then need to construct a topic around this that is of interest as a whole. Of course, if we can make rapid progress with the 2 – d problem we may be able to tackle 3 – dimensions and then our topic would simply be “finding the balance point of a partially filled coke can”.

We will shortly post about finding the centre of gravity of a trapezium.

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