Dynamic balance
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P-prim: Dynamic Balance Balance and Equilibrium
This section sketches an apparently rich and important class of p-prims having to do with balance, equilibrium, imbalance, and overcoming. Again and again, one hears novices explaining situations by things being "in balance" or a system "returning to equilibrium."
Dynamic Balance
Dynamic balancing is likely abstracted from situations in which two opposing forces "try" to achieve mutually exclusive results but happen to cancel each other out. A paradigmatic case is two people pushing against each other with equal force, accomplishing nothing. Canceling itself is an important naive p-prim (see diSessa, 1982). Canceling is likely a common abstraction for many cases of joint, although not necessarily simultaneous, application of "equal and opposite" tendencies. For a situation involving dynamic balancing, canceling justifies lack of result.
Dynamic balancing entails agents in interaction and conflict as important elements in the cuing priority. Recall that the case of a person pushing on a wall is not, in the naive sense, an instance of dynamic balancing. For the pushedupon wall, there is only one agent, the person, and there is no motion simply because the wall resists the push on it.
One frequent use of dynamic balancing at novice stages of physics problem solving occurs in explaining circular motion. It is said that force pulling toward the center of the circle-gravity in the case of an orbit or string tension in the case of a rock on a string-"balances out" the centrifugal force, which pulls the rock or satellite outward." Centrifugal force is sometimes justified as the "resistance" to the tug of gravity.
In view of the acceptance of balancing forces as an explanation of circular motion, apparently circular motion is taken to be a relative primitive. Novices who declare "centrifugal balances centripetal" do not ask further what else causes the circular motion, as opposed to straight-line motion, which would be the actual result of balanced forces, or as opposed to no motion at all. The relative primitiveness of circular motion is not hard to understand. The world offers many examples of circular motion where no evident agency is needed to maintain the motion (e.g., parts of a spinning wheel). If it were not the case that physics training increases the salience of centripetal forces (causing worry about the lack of motion toward the center), one could just start out with the end stance in the previous argument: Circular motion sometimes just happens. Note further that clamping might increase confidence that the pair of forces, inward gravitational and outward centrifugal, "lock" the object in orbit. Some subjects verbalize "locking in."
Symmetry, such as having an obvious center, encourages novices to think about circular motion problems so as to view circular motion as primitive. Many novices who propose dynamic balancing to explain circular motion have great difficulties explaining less natural elliptical orbits, especially if they know or if it is pointed out to them that the center of attraction is not at the center of the ellipse. Note here that visual patterns, as opposed to reasoning about mechanical or dynamic causality, play a role in judgments of plausibility. Such a role for visual patterns is a case in which the naive sense of mechanism attends to substantially different attributes than a Newtonian sense of mechanism. In contrast, whereas F = ma and force as a mover are technically at odds, they share in many circumstances a basically mechanical causal focus on contact intervention.
Gravitational orbits and ball-on-a-string situations are sometimes seen differently from what is a physics-identical motion, a ball in a circular tube. In the latter, the guiding primitive and lack of any overt force toward the center make the countering centrifugal force also unnecessary, and it may be denied in these circumstances by students who affirm it in other situations.
I have considered this p-prim since I was kid sliding around the back seat of my parents car in the 1970's when seat belts and speed limits were not strictly enforced as in our more saftey conscious (and litigious) world. Later in life roller coasters became the phenomenon to more excitedly consider the 'forces" centrifugal versus centripetal forces being in 'balance' way so I do not fly off into space (or the air and then the hard ground or some poor park attendee or visitor below). I witness objects tending to move in straight vectors unless affected by some obtuse force but why? Do forces always need to be opposed--can a string holding a ball in circular motion really be equivalent to the gravitational attraction of the sun holding the earth in its slightly eliiptical orbit? Also, when does one force overpower another one--is it indicated simply by movement toward the "winning' force? Why should acceleration feel so similar to gravity (movement through space is not the same as a force is it)? Don't get me started on space-time continuums and mutlidimensional universe we may or may not exist in. We don't live in the Newtonian or even an Eisteinian physics-based universe ultimately but they effectively work with hypothetical astronauts traveling at the speed of light and launching cannon balls at hapless dukesin their castles.
