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# The Effect of the Height of an Object's Center of Gravity (page 2)

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Author: Janice VanCleave

### Try New Approaches

What effect does the location of the center of gravity have on an object's motion when that object is tilted? Cut two additional holes in the poster board strip, one 3 inches (7.5 cm) above the center hole and one 3 inches (7.5 cm) below the center hole. Repeat the experiment twice: First place the pencil in the top hole. This represents the higher center of gravity. Then repeat, placing the pencil in the bottom hole. This position represents a lower center of gravity. Compare the path of the center of gravity from the original experiment to the paths of the higher and lower centers of gravity.

1. A ball has neutral equilibrium, the state of the object when pushing it over will not change the height of its center of gravity. Design a way to trace out the path of the center of gravity of a ball. One way is to cut a circle from corrugated cardboard, then make a hole in the center of the circle. (The circle represents a slice through the center of the ball, with the hole marking its center of gravity.) Place a sheet of paper on a table. Lay a book with a flat binding edge on the paper. Then lay the paper circle on the paper next to the binding edge of the book. Stand a pencil in the hole of the circle. Use the pencil to trace the motion of the hole as the circle is rolled across the edge of the book.
2. An object is in a state of stable equilibrium or mechanical stability when it falls back to its original position after being tilted slightly. This happens when the center of gravity of the object is initially raised during the object's rotation. Design an experiment to determine the effect of the height of the center of gravity on mechanical stability. One way is to fill two identical bottles with different amounts of water and seal the bottles. Fill one bottle about one-fourth full and the other totally full. ('The more water, the higher the center of gravity.) Place the bottles side by side; tilt each bottle slightly, then release. Continue increasing the amount of the tilt until one of the bottles falls over. The first to fall will be the one with the lesser mechanical stability.
3. You can make a model that demonstrates mechanical stability (stable equilibrium) using a plastic egg. Find the kind of plastic egg that you can open. Shape a ball from a grape-size piece of clay. Open the egg and press the clay into the bottom of the more rounded end. Close the egg and stand it on that end. If the egg does not stand upright, reposition the clay. Give the standing egg a gentle push to one side. It should rock back and forth several times and stand upright again. If it lays on its side, remove some of the clay. For more information about the three types of equilibrium, see Mary Jones, Physics (New York: Cambridge University Press, 1997), pp. 50-51.
4. An object has stable equilibrium as long as a vertical arrow from the center of gravity of an object passes through its base (side it rests on) (see Figure 2.2). Design a way to determine how the width of the base affects the mechanical stability of an object. One way is to use a block of wood with edges of different lengths, such as a 2-by-4-by-6-inch (5-by-10-by-15-cm) block. Let the base of the block be one of the 2-by-6-inch sides. Set the block near one end of a shallow baking pan or piece of stiff cardboard. To prevent the block from sliding, place a length of clay on the pan in front of the block. The width of the base is determined by measuring the side adjacent to the clay, as shown in Figure 2.3. Slowly raise the end of the pan opposite the clay until the block falls over. Hold the board in this position and ask a helper to measure the angle the board is raised above the table. Repeat three or more times, and average the measured angles. Rotate the block so that one of the 2-inch (5-cm) edges of the base faces the clay. Then repeat as before, determining the average angle that the board must be raised for the block to fall. Use the results to explain how the width of the base of an object being tilted affects the angle at which the object will tip over.

### Get the Facts

Objects that are in motion but are not accelerating are in equilibrium. What is the difference between linear and rotational equilibrium? How do static and dynamic equilibrium compare? For information, see Corinne Stockley, Illustrated Dictionary of Physics (London: Usborne, 2000), p. 15.

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