# Archimedes principle: think carefully

Benjamin has recently acquired a 'new' book from Grandma and Grandad: Mr Archimedes' Bath (by Pamela Allen – here's the amazon link – the reviews are as interesting as the content). The story-line is reasonable guessable from the title. Mr Achimedes puts water into his bath, gets in, and the water overflows. What's going on? So we've been doing some copycat experiments – not by filling the bath right up and having it slosh all over the bathroom floor (Waipa District Council – you can rest easy about water usage)  but filling up rather more sensible-sized containers and dropping objects in.

Archimedes principle is actually a little more involved than simply saying that putting an object in the water will raise the water level. It says that the weight of water displaced is equal to the force of buoyancy acting on the object.  This picture summarizes it. That is, if an object of 2 kg floats, then 2 kg of water will be displaced. If an object is unable to displace enough water for this to be the case, it will sink. That still should be pretty easy to get, especially if you've done some experimenting. However, it can still be the basis of some really hard questions. I had one in my third year  physics exams at Cambridge. In our 'paper 3', as it was called then, the examiners had free reign to ask about ANYTHING that was on the core curriculum from any of our years of study – plus ANYTHING that was considered core knowledge for entry into the degree (which meant basically anything at all you were taught in physics or general science from primary school upwards). This paper was feared like anything – it was basically impossible to revise for*.

Here is a question then, as I recall it from the exam.

An ice cube contains a coin. The ice completely surrounds the coin. The cube is floating in a container of water.  The cube melts. Does the water level rise, fall, or stay the same?