I worked out the annoying problem in the calculus book, with the help of a Friendly Scientist as well as my own physics textbooks. The screaming yellow "Solved Physics Problems" book helped me out here, though in previous encounters it had not been helpful at all. Besides, it was there at 4 AM when people would not be. This is one of the good things about a modern literate civilization. Books, or nowadays websites, stand in for people. I don't have to wait for the village wise man to hear my question. And I'm not sure whether the village wise man would know formal physics and mathematics anyway.

The problem was actually somewhat complex for my low level of understanding. Not only did it involve weights tied together which pull against each other in two directions, but it was in the "English system" of ounces, feet, and pounds, which is only prevalent in the USA and in some other English-speaking countries. In this system, mass is not measured in pounds, while force is. Mass is measured in a unit called the "slug," which only a couple of my physics books talked about. From reference sites, the kilogram per square meter appears to be about 1.35 times the mass of a slug per square foot, though I'm not sure how this comparison is worked out. The "slug" unit of mass appeals to me because I have a somewhat perverse fondness for these slow, stupid, slimy molluscs, possibly because they remind me of myself in my math and physics journey.

Once I had found the amount of sluggishness, by dividing the weight by 32 (feet per second²), then I was able, with the help of the physics book, to re-calculate the force = mass x acceleration for the problem's components, and figure out the acceleration for the system, which is what the whole thing was about in the first place. The idea is that the velocity increases, or accelerates, as the system moves, and calculus is going to help me find out just what the velocity is at any given instant while it is changing.

I remember doing problems similar to this back in 2002 when I was doing algebra exclusively. I did problems out of my old 1958 college algebra book which required me to find a number of different values which fit into a parabolic curve. Although my 1958 fellow-students had only slide rules, I had a calculator which made things much easier as I plotted my points. There would be one apex point which could be approached by finer and finer approximations, easy enough for the gadget to do. This was before I learned the art of apex finding and curve fitting for parabolas and other algebraic curves. I suspect I will have to review these processes sometime soon.

Posted at 3:15 am | link