Thanks for replying to my post.
Perhaps I should explain why I wrote this response on this (nearly year old) thread, how I came to this forum, and why I signed up to it.
The following is the text of an email which I sent to a friend of mine earlier today:
Dear Sir
Daughter was doing some physics homework, and we come across the bit that says that, if it weren't for differential air resistance, all objects would fall at the same rate of gravitational acceleration, and so, if dropped at the same time from the same height, would hit the ground at the same time, irrespective of their mass.
Basic law of physics, which has been branded into our brains since our earliest youth, no?
Well, I had been thinking how to make a demonstration of this, that was practical to set up (ie, that didn't involve both or even either of a spacecraft and the Leaning Tower of Pisa). So, I thought that things sinking in water should obey the same physical law, with water resistance taking the place of air resistance.
Inference: two objects of the same external shape and size (thus having equal hydrodynamics) should sink equally fast, even if one of them is much denser than water, and the other one is only slightly denser than water.
But, I thought "that doesn't sound right" (just as I sometimes find it difficult to imagine a feather falling at the same rate as a rock, if dropped on the moon, despite "knowing" it as an almost Biblical truth ).
So, I came up with this experimental plan:
Two glass test-tubes, same size and weight.
If one were sealed, full of air, it would float.
If the other were filled with water, it would sink (doesn't matter about sealing it, but do so, for the sake of experimental uniformity).
Now, if a tube had just a little bit of water in it, it would still float. There would be an amount of water that, if put in the tube and sealed up, the average density of this part-full tube would be the same as that of water.
If there were more water than this critical amount, it would sink; if less, it would not sink.
Now, if we have one tube completely filled with water, and the other filled with just over the critical amount of water, and both sealed identically, and arrange to let them go just below the surface of a column of water at the same time (and of course in the same orientation), then, as I understand Galileo, they should fall at the same rate, and hit the bottom of the water container at the same time.
Today, I (with daughter) transformed the gedankenexperiment into a wirklichexperiment, and the result is quite clear - the tube filled right up with water hits the bottom of the bucket before the less-filled tube.
Why is it so? You are the only person that I am in contact with who could be smart enough to give me an explanation. Please help! My whole world view, my faith in the fundaments of science, and the respect of my intellect in the eyes of my daughter are at stake!
Your simple friend,
Adam
Obvious, now, where I went wrong - but it has taken a lot of digging around to find the answer - which I finally found on this forum (your post, and one of Simon's, in this thread). However, there was not a nice, simple, easily understandable explanation, such as the OP (and indeed anyone starting out in science) needed. There was too much detail, both in the maths, and in all the extraneous suggestions, like quibbles about "acceleration", rather than "speed", and worrying about terminal velocity.
The suggestion "Why not just do the experiment?" is usually a good one, but wasn't particularly helpful here, and the Cartesian Diver doesn't solve the problem either, just shows again that it exists.
FactChecker came closest to a good simple explanation, but perhaps went too far in the simple direction, as I did not initially realize what it meant.
