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# The Effect of the Height of an Object's Center of Gravity

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Author: Janice VanCleave

Some toys are designed so that when they are pushed, they may wobble back and forth but they don't fall down. No matter how far this kind of toy is pushed, it returns to its upright position. This ability to be moved and to return to the original position is an example of mechanical stability. An object is in equilibrium when all the forces acting on it are balanced. There are three types of equilibrium—stable, unstable, and neutral.

In this project, you will move different objects and trace the paths of their centers of gravity. You will investigate the effect of the height of an object's center of gravity, as well as the width of the object's base, on mechanical stability. You will construct an object with great mechanical stability, or stable equilibrium. You will also learn about the differences among stable, unstable, and neutral equilibriums.

### Getting Started

Purpose: To model the motion of an object's center of gravity when the object is tilted.

### Materials

• pencil
• ruler
• 6-by-10-inch (15-by-25-cm) piece of poster board
• 2-by-8-inch (5-by-20-cm) piece of poster board
• one-hole paper punch
• 4-by-8-inch (5-by-20-cm) piece of graph paper
• transparent tape

### Procedure

1. Use the pencil and ruler to draw a line across the large piece of poster board, 2 inches (5 cm) from one long edge. This will be line A.
2. Draw a line down the center of the small strip of poster board from one short edge to the other. Make a dot in the center of this line. Using the paper punch, make a hole through the poster board at this dot.
3. Label one short edge of the poster board strip "Bottom," then cut a second hole in the strip in the right corner of the bottom edge.
4. Lay the small strip of poster board on the larger piece of poster board so that their bottom edges are together and the left side of the strip is on line A.
5. Use the pencil to trace the bottom hole in the strip on the large piece of poster board. lift the paper strip and use the paper hole-punch to cut out the tracing on the poster board.
6. Lay the strip on the large piece of poster board as in step 4. Then insert the paper brad through the holes (bottom hole in the strip and hole in the poster board). The brad will secure the two pieces together.
7. Lay the piece of graph paper under the paper strip and secure it with tape, then tape the large poster board piece to a table (see Figure 2.1).
8. Hold the pencil with its point through the hole in the center of the poster board strip.
9. Use the pencil to rotate the poster board strip, marking a line to the edge of the graph paper.
10. Remove the pencil, then rotate the strip to the left and observe the path marked on the graph paper.

### Results

The path on the graph paper shows that the hole in the poster board strip initially rises as the strip is rotated.

### Why?

Since the poster board strip is symmetrical with uniform density, its center of gravity is in the center, where you made the hole. Before being rotated, the strip represents an object in static equilibrium (the state of an object that is not in motion, that is at rest). When rotated a small angular distance, the center of gravity of the poster board initially rises as indicated by the path of the hole traced on the paper. This demonstrates that if an object's center of gravity is in the center of the object, the center of gravity initially rises when the object is rotated or tilted slightly.

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