|MadSci Network: Physics|
Greetings, Jake: Let's start with a simple stick of wood. How many fundamentally different ways can you apply a force to it? For the most part, you already know that pushing or pulling constitute the main types of application of force. But what about variations on those themes? Depending on where a force is applied to the stick, or how much is applied, or even how rapidly it is applied, very different results can occur. If the stick is secured so that one end cannot move, then if you try to pull the other end directly away, the stick experiences "tension". Molecular bonds become stressed (and stretched a bit) throughout the length of the stick. If you push the free end directly toward the secured end, the stick experiences "compression". Molecules resist being squished into each other, as you may expect. Different substances respond to different degrees; wood is not as responsive to forces of tension and compression as is, say, a stick of rubber, but be assured that wood IS affected. Next, suppose the stick of wood is placed horizontally, supported at both ends, with nothing under its middle (like a miniature bridge). If you apply a force to its middle, pushing downwards, the stick may flex a bit. (Very likely, it flexes a minute amount anyway, thanks to the force of gravity.) The wood may withstand a considerable amount of force before it breaks; we say that a "shear" force has been applied. As mentioned above, the rapidity of application of a force can be as important as the total amount of force: Consider a mini-bridge that can support a slowly- accumulated mass of 1000 kilograms -- yet it may break if a karate chop is instead applied, even though the "normally computed" maximum force is less than that associated with 1000Kg of resting mass. (In the field of engineering, the INITIAL application of a force has effects that are usually described with such terms as "jerk", "kick", or "starting transient". Physicists generally don't pay a lot of attention to these effects, because they are difficult to measure precisely and consistently -- and they only last for milliseconds at best. What evidence there is suggests [and this qualifies as Mad Science!] that while forces are normally computed in association with "acceleration", which is "a rate of change in velocity", there MAY be additional forces associated with "a rate of change in acceleration". It would be these additional forces that let the karate chop -- or kick -- break the wood.) You're probably wondering when I'll get to the topic of see-saws. In a way, I just did! Take that mini-bridge above and turn it upside-down, and you GET a see-saw, with the 1000Kg mass in the middle becoming the fulcrum, and the bridge-support points becoming the kids on each end. Obviously, if there are too many kids at each end there will be too much mass, and the see-saw will break in the middle (shear force again). So as we detour into the topic of geometry, keep in mind that see-saws aren't being neglected. Below is a sketch of several arcs: 1 - - - - - - - - - - - - 2 - - - - - - - - - - - - 3 - - - - - - - - - - - - 4 - - - - - - - - - - - - 5 - - - - - - - - - - - . 6 - - - - - - - - - - . . 7 - - - - - - - - - . . - - - . . . - - . . . - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 6 5 4 3 2 1 By simple inspection of these arcs, it is obvious that #1 is longer than any of the others, and #7 is the shortest. Now suppose you take a thin stick and bend it into an arc. The OUTSIDE edge of the bent stick might correspond to arc #1 above, while its inside edge might correspond to #2. Because the stick is thin, the difference in distance bewteen #1 and #2 is quite small, and you are able to bend the stick easily. Now ask yourself, "When I let go of one end of the bent stick, what causes it to straighten out again?" To reach the answer, let us pretend we have a big magnifying glass, and look at the bent stick. NOW the stick may look as thick as the distance between arcs #1 and #7 above, instead of arcs #1 and #2. Arc #4, of course, corresponds to the MIDDLE of the bent stick. Note that when the stick was straight, all edges were the same length. When bent, however, one edge has been forced to imitate arc #1 (stretched under tension), and one edge has been forced to imitate arc #7 (squished under compression). Without needing a lot of math, it is reasonable to state that arc #4 is close to the original length of the stick. So: If bending the stick involves forces that cause parts of it to compress and parts of it to stretch, any resistance to those forces is going to reverse that compression and tension. THIS is what causes the stick to straighten out again. Now take away the big magnifying glass, and remember that you only have a thin stick. What if you had a thick stick, that really was equal to the distance between #1 and #7? You can't bend that so easily at all! One of the differences here is simply that the thick stick has a lot more material (wood) in it than the thin stick. Trying to bend it means compressing and tensioning much more material than before -- and this is naturally associated with much more resistance to those forces. Furthermore, the greater distance outside and inside edges of a thick stick, the greater the DIFFERENCE in the lengths of the arcs they would form when bent. That is, much more tension and compression must be applied, to cause the edges to imitate arcs #1 and #7, than to cause those edges to imitate arcs #1 and #2. Perhaps now it is pretty obvious why one end of a see-saw goes up when the other end goes down. It is made of pretty thick wood, or even steel, after all. As you press down on one end, a force of tension grows along the top surface, and a force of compression grows along the bottom surface. These two forces work together to lift the other end of the see-saw. ---------- With respect to constraints on motion, that will entirely depend on how the see-saw is mounted. As a child I encounterd an unusual type of see-saw that was cone-shaped. The fulcrum was at the top of a short tower, just under the top of the cone, and seats for kids were spaced along the lower circular edge of the cone. The whole cone could sway in any direction, and it could also rotate around the fulcrum. With respect to predictive formulae, there are almost certainly heavy-duty equations in the literature describing the tension and compression effects in vastly more detail than presented here. You would primarily use them to determine how much a see-saw (or a bridge) would flex under a given load. Feel free to pursue those equations at your leisure.
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