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Barycenter: The Balancing Point (page 2)

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Author: Janice VanCleave

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Different masses affect the distance of each body from the barycenter. Mold the clay into one large ball and one tiny ball. Weigh the balls on the food scale and prepare a Celestial Body Mass vs. Distance table like Table 11.1. Call the mass of the smaller ball m1. Let the mass of the larger body equal m2. Call their distances from the center of each clay ball to the barycenter d1 and d2, respectively. Use the dowel and sling to find the barycenter as in the original experiment (see Figure 11.2). Measure d1 and d2.

For example, when m1=1 ounce (28 g) and m2=15 ounces (426 g), and d1 = 45 inches (112.5 em), then d2 = 3 inches (7.5 em). Notice that mass and density have an inverse relationship, which means that when one term increases, the other decreases.

In our example, m1 × d1 = m2× d2, or m1/m2 = d2/ d1 = 3/45, which reduces to 1/15. Thus, m1 lies 15 times farther from the barycenter than does m2, and m2 is 15 times more massive than m1.