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# Achievement of Equilibrium and Position of the Center of Mass

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Source:
Author: Jerry Silver

### The Idea

You have four equal books. Each is 10 inches long. You can stack them up any way you like. How far from the edge of the table can you place the far edge of the top book, so all four books still balance over the edge of the table? This can be done by intuition or analytically. It also makes a good competition activity.

### What You Need

• stack of objects: bricks, blocks, books, or empty CD cases
• ruler

### Method

1. Before you start, state your prediction. How far beyond the edge of the table will the four books go, so they balance without falling? See Figure 46-1.
2. Take the four books and arrange them, so the fourth object extends as far from the edge of the table as possible.
3. Repeat with any other number of books. This makes a good friendly competition to see who can produce the greatest overhang.

### Expected Results

If you have four similar objects, 10 inches long, the maximum overhang will be just under 9.4 inches. In general, if you have four objects whose length is L, the maximum overhang is (just under) 0.94 × L.

### Why It Works

The books (or other objects) will balance on the table if the center of mass for all the books lies over the table. If the center of mass is positioned over the edge of the table, the entire stack of books will topple.

Let's start with one book. The book balances with the overhang no greater than halfway. With a second book added, the equilibrium is maintained with the added book extending one-quarter of its length beyond the first. As books are added, the added distance that the entire stack can be pushed out is one-half the length of that of the previous book, as indicated in Figure 46-2.

### Other Things to Try

Now that you got past four books, how about 100? Extending this to a large number of books, the overhang is extended by the book length divided by one-half of the total number of books.

The total overhang is the sum of all the individual extensions. As an example, for 100 books, each of a length 10 inches, the maximum overhang would be 25.9 inches as pictured in Figure 46-3.

### The Point

Equilibrium is maintained when the center of mass is centered over the area of support.