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# Center of Gravity of Symmetrical and Asymmetrical Objects (page 2)

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Author: Janice VanCleave

### Try New Approaches

1.
1. Where is the center of gravity if the object is not symmetrical with uniform density? Repeat the experiment placing a weight, such as a walnut-size piece of modeling clay, on one end of the dowel. Where is the center of gravity in relation to the added weight?
2. Repeat the investigation, placing the weight at different points along the dowel.

Science Fair Hint: Make display diagrams for each investigation similar to the one in Figure 1.2.

### Design Your Own Experiment

1. If an object is supported at any point other than at or in line with its center of gravity, unbalanced torque on either side of the center of gravity causes the object to rotate about the support until its center of gravity is as low as possible. Design a way to demonstrate how this fact makes it possible to find the center of gravity of a plane figure (a geometric figure that lies on a flat surface) with an irregular shape. One way is to cut an irregular shape from a stiff piece of thin cardboard (see Figure 1.3). Use a one-hole paper punch to cut four or more holes around the edge of the cardboard. Hang the cardboard on a tackboard by inserting a pushpin through one of the holes. Make sure the figure can swing freely on the pin. Cut a piece of string slightly longer than the widest part of the cardboard. Tie a weight, such as a metal washer, to one end of the string and make a loop in the other end large enough to slip over the head of the pushpin. While the cardboard is suspended by the pin, slip the loop of the string over the pin's head and allow the string to hang freely. The string should almost touch the cardboard. Mark two points on the cardboard under the string, one near the hole and the other near the edge of the cardboard (see Figure 1.3). Take the cardboard down and draw a line between the two points. Repeat the procedure using the other holes in the cardboard. The lines overlap on the center of gravity.
2.
1. The measure of the ability of an object to resist falling over is known as its mechanical stability. How does the relationship between the height of the center of gravity of an object and the height of the object affect its mechanical stability? Design a way to measure the effect of a high or low center of gravity on mechanical stability. One way is to measure the angle at which an object such as an empty film canister, with its center of gravity at its center near the cap end, tips over (see Figure 1.4). Place the canister on a flat surface, such as a yardstick (meterstick), and use a protractor to measure the angle of the measuring stick at which the canister tips over. Tape a piece of sandpaper on the surface to keep the canister from sliding. One edge of the yardstick (meterstick) should be placed against a heavy book so the yardstick does not slide as you lift the other edge.
2. The position of the center of gravity of the canister can be lowered by filling the canister one-fourth full with modeling clay. Repeat the experiment, pressing the clay against the bottom of the canister so the clay stays in place. The center of gravity of the canister is near its clay-filled bottom.
3. An object falls over when its center of gravity is not on an imaginary vertical line that passes through the base of the object. How does the width of the base affect mechanical stability? Using the previous investigation for testing stability, test objects with varied base sizes.
4. The center of gravity can be located outside the balancing object. For example, tightrope walkers are able to more easily balance when they hold a curved bar with weights on its ends that extend below the rope they walk on (see Figure 1.5 on page 15). The weight of the bar lowers the center of gravity of the tightrope walker to a point below the rope. Design a way to demonstrate this, such as by using a tightrope walker cut from a 4-inch (10-cm) -square piece of corrugated cardboard. Note: The cardboard grooves must run left and right, not up and down. Insert a 12-inch (30-cm) pipe cleaner through the bottom of the cardboard, and add metal washers to the ends to represent the weights on the pole. Balance the figure on a stretched string. Redesign the figure and/or move the pipe cleaner to determine the answers to the following questions:
• Is it easier for a tall or a short tightrope walker to balance on the wire?
• Which helps more—a short or a long balancing pole?
• Does the distance the pole is held above the wire affect the stability of the figure? The center of gravity of the figure is on an imaginary line running through the balancing point, and is below the body of the cardboard figure.

### Get the Facts

The center of mass is the point on an object where the whole mass of the object appears to be concentrated. On Earth, the center of mass and the center of gravity of an object are at the same place. However, for larger objects, such as planets and moons, the location of the center of mass will be slightly different from that of the center of gravity. How does the size of the object affect the location of the center of gravity? For information, see P. Erik Gundersen, The Handy Physics Answer Book (Detroit: Visible Ink, 1999), p. 106.

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