Greenwood press
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book-20600
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SIMILARITY A method to find the height of a tall object, such as a flagpole, based on smaller measurements and principles of similarity. Since an actual tyrannosaurus was about 15 meters long, the ratio of the actual dinosaur to the model is 50 to 1, because 15/0.3 = 50. Use the density ratio of mass volume to determine the mass of the tyrannosaurus. Most animals and reptiles have a density near 0.95 = m v , so the mass of the tyrannosaurus can be calculated once the volume is found. The volume of the actual tyrannosaurus can be calcu- lated by using the cube of the ratio of the lengths of the actual dinosaur to the model. The cube of the ratio is used, because volume is a measure of three dimensions. Therefore the volume of the actual Tyrannosaurus will be 50 3 , or 125,000 times the volume of the dinosaur model. You can measure the volume of an irregular object, such as a dinosaur model, by submersing it in a bucket of water. Place a bucket of water filled to the brim (and larger than the dinosaur model) inside a larger empty bucket. Drop the dinosaur model into the bucket of water, and the excess water will spill over the sides into the empty bucket. Pour the excess water into a graduated cylinder, which is a tool to measure the volume of water. This volume should be the same as the volume of the dinosaur model, because the model replaced the same amount of space in the bucket as the excess water. Suppose that the volume of the model is 61 milliliters. This means that the volume of the actual tyranno- saurus was about 125,000 times 61, or 7,625,000 milliliters, or 7,625 liters. Since density equals mass divided by volume, the equation 0.95 = m 7,625 can be used to predict the mass, m, of the tyrannosaurus. Note that the units of density are kilograms per liter, so volume units are in liters and calculated mass units are in kilograms. The solution to the equation predicts the tyrannosaurus’s mass to equal approximately 7,243 kilograms, which is about 16,000 pounds. That is the same as 100 people that have an average mass of 160 pounds. Most football coaches would like to recruit a tyrannosaurus for their teams! Similarity is sometimes not used in models, which as a result can cause mis- conceptions about length and size. Most models of the solar system are inaccu- rately proportioned so that they can be easily stored, carried, and viewed within a reasonable amount of space. If a teacher wants to illustrate planetary motion on a solar-system model, he or she needs to be able to move the planets around fairly easily, and students need to see all of them. Realistically, however, this type of model is inaccurate, because the planet sizes vary tremendously and are spread apart by vastly different distances. For example, if an accurate scale model of the planets in the solar system were used in a classroom with the sun at the center of the room, then the first four planets would be within 227 cm of the center, and the remaining planets would be stretched out to almost 6 meters away! The large variability in distances among the planets would make it diffi- cult to build a movable model that illustrates rotation around the sun. Further- more, the volumes of the planets vary considerably. Large planets, like Jupiter and Saturn, have diameters that are about ten times larger than the earth. If the planets were built to scale, these giant planets would have to be a thousand times larger than the earth, because the ratio of volumes between similar figures is Download 1.81 Mb. Do'stlaringiz bilan baham: |
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