Archive for December, 2013

2013 in review

Posted: December 31, 2013 in Uncategorized

The WordPress.com stats helper monkeys prepared a 2013 annual report for this blog.

Here’s an excerpt:

The concert hall at the Sydney Opera House holds 2,700 people. This blog was viewed about 15,000 times in 2013. If it were a concert at Sydney Opera House, it would take about 6 sold-out performances for that many people to see it.

Click here to see the complete report.

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I first was introduced to this really nice question by Neil Atkin (@natkin) and ever since I have tried to find a good way of showing it. So, look at the question and the explanation that I think is correct, as far as I can tell (but please point out any faults in my reasoning). Then, check out the simple demo I used to show this.

“If I am on a boat in a pond and I hold a 10 kg rock in my hand, what will happen to the level of the water if I drop the rock inside the pond? Will the water level increase, stay the same, or be lower?”

It’s all to do with Archimede’s Principle that states that the upward buoyant force exerted on a body immersed in a fluid is equal to the weight of the fluid displaced by the body.

This should help us think about this problem. In fact, if the boat is floating it means that the weight of the water displaced by the rock when it is inside the boat must be the same as the weight of the rock itself. That is because the upthrust balances the weight of the boat, myself and the rock, or the boat would sink. So the rock displaces a volume equivalent to the space occupied by 10kg of water, i.e. 10 litres.

When I throw the rock inside the pond the water displaced by the rock is only the volume of the rock itself, which is most likely not 10 litres, but much less. So, the level of the water in the pond decreases!

I took these two photos before and after to convince you of this (the measuring cylinder we used in another attempt was to big to appreciate the difference). Click on either photo to enlarge them and see them in Gallery view.