|MadSci Network: Physics|
Greetings, Case: Unfortunately, there is no single/simple Answer for your Question. At least three major factors play a part, and any one of them, by itself, could be the crucial difference. First, while you specified the lengths of the skis and snowboard, you did not specify widths. The total amount of friction between these devices and the snow depents partly upon the total amount of surface area that contacts the snow. A snowboard that is wider than two skis could easily have more total surface area in contact with the snow, and more total friction, and thus be slower. Next, there are the various varnishes and/or other coatings that are applied to skis and snowboards, to reduce friction. If the coating on the skis is better quality than the coating on the snowboard, then again the latter will experience more friction, and thus be slower. Finally, there is air resistance, and at least two different aspects of it come into play here. For the first, consider the position of the body taken by someone on skis, as compared to the position of the body taken by someone on a snowboard. The former is facing the oncoming air, while the latter is posed sideways. By inspection, it is obvious that the latter offers less air resistance than the former -- but the person directly facing the "wind" can crouch in such a way as to reduce air resistance a great deal. The snowboarder can crouch, also, but SAME sideways surface area is still presented to the "wind"! Thus, if the skier can crouch enough, air resistance will always be greater for the snowboarder -- who thus is slower. For the second aspect of how air resistance is a factor in the Answer to your Question, I need to begin by digressing into an explanation of something known as the "Square-Cube Law". ******************** First noticed/described by Galileo, the Square-Cube Law associates the strength and mass of an object with its size. For example, consider a fat mouse: It has pretty skinny legs to support the weight of its plump body. Now consider the big legs that an elephant has, to support its body. If you simply enlarged a picture of a mouse to be the same size as an elephant, you would plainly see that the mouse's legs are comparatively much skinnier than the elephant's. Why? Well, if you started with a mouse having height/width/length dimensions of X, Y, and Z, and simply doubled it to 2X, 2Y, and 2Z, then any area-related measurment of the mouse goes up by a factor of 4 (or 2 times 2, because only two dimensions are used to compute areas/squares), while any volume-related measurement of the mouse goes up by a factor of 8 (2 times 2 times 2, because all three dimensions are used to compute volumes/cubes). As it happens, the strength of the mouse's legs is an area-related thing (think "cross-section"), while the overall mass and weight of the mouse is a volumne-related thing. You know that the weight of the mouse must be carried by its legs, of course. So, if the ordinary mouse easily carries its mass around on skinny legs, what of the double-sized mouse that has 8 times the mass but only 4 times the strength in its legs? They might break under the load! As a result, all through Nature, larger animals have EXTRA thickness in their legs, to increase their cross-sectional areas, to thus have the strength to carry larger body weights, with the elephant being today's extreme example. (Yet the Square-Cube Law has applied all through Natural History, and the giant dinosaurs had legs of a thickness to put trees to shame.) There are plenty of other physical phenomena that are linked in some way with the Square-Cube Law. Several years ago I decided that it can explain the traditional complaint that parents have, about how their little kids run them (the parents) "ragged". See, the average little kid is about half the size of the adult, and so has only one-quarter the strength -- but also has only one-eighth the weight. The kid has twice the strength-to-weight ratio as the adult! Trying to keep pace with the antics of little children is something that no ordinary adult will EVER have an easy time attempting, thanks to the Square-Cube Law. ******************** Now let's apply the Square-Cube Law to skiers and air resistance. Suppose Person A is half the size of Person B: The math is easier to figure that way, but the essence of the results apply to any two people of differing size, if overall proportions are maintained. The surface area presented by Person A is 1/4 the surface area of Person B, so Person B will experience 4 times the air resistance as Person A (ALL other things being equal). Next, please note that air resistance is a Force, as in the equation F=ma (Newton's Second Law of Motion: Force equals Mass times Acceleration). To figure how a mass accelerates in response to air resistance rephrasing the equation as a=F/m, and plugging in appropriate values. (Person B has eight times the mass of Person A, remember.) So, for Person A, we shall use unitary values of Force and Mass (exactly as in the prior rephrased equation), while for Person B, the equation is (1/2)a=4F/8m. Now, since air resistance attempts to SLOW DOWN a skier, the results of this figuring is that we discover that air resistance acts to slow Person B, the larger person, at less than the rate at which it could slow the smaller Person A (one-half the rate, in this particular case). THAT is the second aspect of how air resistance can be a factor associated with your Question. One more factor, about which I don't know enough, involves the change in friction between ski and snow, as the weight of the skier increases. Generally it is thought that pressure can cause a thin layer of ice (and presumably snow as well) to melt, forming water that acts as a lubricant. Thus the heavier skier might have yet another advantage over the lighter, speed-wise, due to more water/lubricant being present. But I don't know that for sure, and anything else I might add here would only be speculation, so I can only hope that the things I do know have Answered your Question satisfactorily.
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