**Tumbling** Note that the top two blocks fall to the left in diagrams 1, 3, and 5 and fall to the right in diagrams 2, 4, and 6. The top two blocks fall to the left when the red block is heavier than the orange block; they fall to the right when the red block is lighter than the orange block. Start with diagrams 1, 3, and 5, in which the top blocks fall to the left. There are three combinations of weight in which the top block is heavier than the middle block: 3-1-9, 9-3-1, and 9-1-3. We know that diagram 1 is 3-1-9. To determine which of the remaining combinations goes with the other diagrams, consider this: Blocks that have the same weight ratios will behave almost the same, with minor differences due mostly to friction. Therefore the top two blocks in the weight combination 9-3-1 should tip to the left in about the same way that 3-1-9 does. Diagram 5 is similar to diagram 1, except that the lighter bottom block tips easily to the right. So the combination of weights in diagram 5 is 9-3-1. That leaves diagram 3 with the weight combination 9-1-3. Note that the top block is nine times the weight of the middle block, causing it to tip to the left faster.

The same logic works for diagrams 2, 4, and 6, in which the top two blocks fall to the right. The two similar diagrams are 2 and 6; diagram 2 has the lighter bottom block, which tips over more quickly. Therefore diagrams 2 and 6 have the weight combinations 3-9-1 and 1-3-9, respectively. In diagram 4, which has the weight combination 1-9-3, the middle block is nine times the weight of the top block, causing it to tip to the right faster.

**Spinning ** 1. 15°, 0°, 90°, 180° = C

2. 180°, 180°, 180°, 180° = A

3. 120°, 210°, 300°, 150° = F

4. 60°, 0°, 240°, 120° = E

5. 240°, 300°, 210°, 150° = B

6. 0°, 60°, 150°, 300° = D

**Plummeting ** 1. The main reason the experiment would fail is air resistance, which slows down lighter objects more. Two objects dropped in a vacuum do fall at the same speed, as was verified on the moon by

*Apollo 15* astronauts David Scott and James Irwin, when Scott simultaneously dropped a feather and a hammer.

2. If one of the balls is lighter than air, it will float up, not fall down.

3. Measuring the height of the drop from Earth's surface is misleading because Earth's surface varies in height. The farther away objects are from Earth's center, the more slowly they fall. So if two balls of the same size are dropped simultaneously, one from 50 meters above the top of a mountain, and the other from 50 meters above the floor of a valley, the object in the valley will hit the ground first.

By the way, Galileo proposed a thought experiment that cast doubt on Aristotle's theory of falling objects. Suppose a two-pound ball falls faster than a one-pound ball. Cut the two-pound ball into two one-pound halves and link them loosely with a string. Does the compound object fall at the speed of a one-pound ball because the effect of the string is negligible, or does it fall at the speed of a two-pound ball because the compound object has a weight of two pounds?

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