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## Student Worksheet for the Demonstration The Density Ball

### Flotation

Whether an object floats or not depends on the object’s density. Water has a density of about 1 g/mL. If an object has a density less than 1 g/mL, such as a cork, the object will float. If an object has a density greater than 1 g/mL, such as a coin, the object will sink. Things get interesting, however, when objects have a density very close to the density of water. If an object has exactly the same density as the surroudning water it is said to be neutrally buoyant and it can float at any level under or at the surface of the water.

### Temperature and Phase Changes

The discussion so far assumes that water always has the same density. For most purposes, that is true but under certain circumstances subtle changes in the density of water can be detected. For example, warm water has a lower density than cold water. Why should this be? It has to do with the nature of temperature, which is a measure of the average speed of molecules. A low temperature means that molecules move more slowly while a high temperature means they move more quickly. Water molecules, when they move slowly enough, stick together to make a liquid or a solid. When the temperature is low enough, the molecules are stuck together too strongly for them to separate from one another. In this case, the water is a solid and we call it ice. When the temperature of the ice is raised the molecules move more quickly. Generally, they still stay stuck in place but they move back and forth a little bit and it’s this motion that increases. If the temperature rises high enough the water molecules’ motion increases so much that the forces holding the molecules together are no longer strong enough to confine the water molecules to their positions. When ice melts the water molecules are free to move around, though there are still forces that hold them together in a mass. You can think of it this way. In a solid, the water molecules act like people seated in an auditorium—they move around in their seats but stay put. In a liquid it’s as if the people have risen from their seats but stay together as a tightly packed crowd. A person can move through the crowd and everyone is walking around but no one moves very far from anyone else. Now, if temperature continues to rise then eventually the water will be transformed into a gas, which we call steam. In the gas phase molecules of water are moving so fast that the forces that held them together in the liquid and solid states are too weak to keep them from flying apart.

### Thermal Expansion

The important thing for this discussion is what happens before the water evaporates. The water molecules move faster and faster as the temperature rises. Think about the molecules of water as people in a crowd again. As the temperature rises the people in the crowd start bumping into each other faster and harder. A natural result of this is that the people (or molecules) get pushed a little bit farther apart. The size of the space the crowd is standing on gets larger even though there are still the same number of people. The liquid expands in volume as the temperature rises. As temperature falls, volume decreases. As temperature rises, volume increases. There is a direct proportion between the temperature of water and its volume. Different materials expand and contract with changes in temperature by different amounts. For some materials, a small change in temperature can make a relatively large change in volume when compared with other materials.

Density is a function of both mass and volume. For a particular sample of a material the mass is unchanging, but the volume can change as a result of changes in temperature. There is an inverse proportion between the volume of a sample and its density. The bigger the volume, the smaller the density. Consider the equation for density below. As the value of V grows, the value of D must fall.

```         m
D = -----
V
```
This demonstration requires a specially manufactured metal ball. The ball is hollow and partially filled with water and sealed. The density of the ball is such that it will float in water at or below about 16°C and sink in water above about 29°C. 1-L or 2-L beakers filled with water cooled with ice (but with the ice remomved) and water heated on a hot plate (with the hot plate out of view). The presentation is just a description of the ball and then showing students the behavior of the ball in each container of water. After this, students are enjoined to read the text together in groups of 3 or 4. Then they work on answering the questions together. After they have written an explanation they may share it with the teacher who may make some suggestions. Once they have the correct explanation, the teacher should allow the students to try the ball in each of the two containers.
Questions
1. Describe what you observed in the demonstration.
2. What happens to the volume of a liquid when its temperature is raised?
3. Why, based on the behavior of molecules, does the volume of a liquid change as a result of changes in temperature?
4. What happens to the density of a liquid when its temperature is raised? Explain by reference to the mathematical definition of density.
5. Assuming the mass of the ball did not change and that its volume was not much affected by any changes in temperature, will the ball in the demonstration sink in colder water or warmer water? Explain.
6. Explain the floating behavior of the ball in the two containers of water in one or two well-crafted sentences. Once you have written your explanation show it to your teacher. After you have done so, you may approach the front of the room to test your hypothesis about the behavior of the ball.

Last Updated: Oct 11, 2018
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