January 1, 2007

Quote of the Day

"For when two things are raised by one and the same exertion, the lesser quantity will invariably yield more readily and the greater (which offers more resistance) less readily, to the force applied." - Plato (tr. Donald J. Zeyl), Timaeus 63c

So what you're saying is that an object's acceleration is directly proportional the force applied and inversely proportional to its mass. Didn't some other guy get famous for saying that? Hmm...

Posted by Kenny at January 1, 2007 2:38 PM
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How do you know that "yield" refers to acceleration, as opposed to velocity?

Posted by: Lauren at January 1, 2007 2:50 PM

Well, I suppose he doesn't give an equation and so is open to a number of interpretations (the Timaeus is also notoriously difficult to read/translate). However, the principle does, in context, seem to be overcoming inertia rather than overcoming friction: "When he ... drags fire into the alien air, applying force to it, clearly the lesser quantity of fire somehow gives way to his force more easily than the greater." That is, he implies, at the very least, that the force required to set a resting object in motion varies directly as the mass of the object. This is a change in velocity, rather than a velocity. I suppose it is open to question whether the mathematical relationship is supposed to hold against the final velocity or against the rate of acceleration. It is also, I suppose, open to question whether Plato had the concept of moving objects being subject to inertia (i.e., of it requiring a force to cause a moving object to come to rest). I don't know enough about Plato's physics to answer these sorts of questions. I just thought it was a bit amusing to find a line like that in the fourth century BC rather than the 17th century AD.

Posted by: Kenny at January 1, 2007 3:02 PM

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