Current Reading

This blog is primarily for me to blog my responses to books that I'm reading. Sometimes I blog about other stuff too, though.

I'm currently reading Notes on the Death of Culture: Essays on Spectacle and Society by Mario Vargas Llosa.

Word cloud

Word cloud

Sunday, July 26, 2015

Everybody must have stones

I'm reading Chapter 10, excerpts from Two New Sciences (published in 1638, while he was under house arrest).  I like his argument for free fall speed being independent of the mass of the object:  If we take a heavy and light stone and tie them together, then the small stone should retard the large stone while the large stone drags the small stone along, so they should go at a pace intermediate between their "natural" rates.  However, they also form one large composite stone, and the larger stone should go even faster.  So we get a contradiction.

Unfortunately, this argument is not entirely correct.  If we drop the stones from a sufficiently tall building or cliff, they will reach terminal velocity (due to air resistance) and then the larger stone will indeed go faster (if they have the same shape).  However, if we tie them together then the resulting speed will depend on both the increased mass (which, all else equal, will increase the speed) and the new shape (which could potentially increase the drag force).

However, Galileo's argument is sufficient to show that a model that only considers mass, to the exclusion of all other variables, is indeed defective.  It just isn't sufficient to show the universality of free fall.

I first came across this argument a very, very long time ago, back when dinosaurs roamed the earth and was a good buy and I was in grad school.  I read Jacob Israelachvili's book on intermolecular forces, and he included Galileo's argument in the first chapter, along with an assertion that the argument is wrong, but he left it as an exercise for the reader to figure out why the argument was wrong.  It took me a while to figure out the problem with the argument.

No comments: