Density Notes

Density Describes How Much Mass Is Packed Into a Volume

1. When you compare two objects of the same size, one might feel much heavier than the other.
2. This is not only about how big the object is, but it is also about what it is made of.

Comparing Size and Mass

1. Objects can be compared by their size (volume) and mass, but this does not fully describe the material.
2. Two objects can:
   1. have the same size but different masses,
   2. have the same mass but different sizes.
3. These differences are caused by how tightly matter is packed inside the object.

What is Density?

1. Density describes how much mass is contained in a given volume.
2. It explains why materials with the same size can have different masses.
   1. High-density materials have particles packed closely together.
   2. Low-density materials have particles spaced further apart or contain air gaps.

$$\text{density} = \frac{\text{mass}}{\text{volume}}$$

Units of Density

1. Standard SI unit of density: kilograms per cubic metre (kg m⁻³).
2. Other commonly used units: grams per cubic centimetre (g cm⁻³).
3. Volume units are cubic, not linear.

Measuring Mass

1. Mass is measured using a balance.
2. Common units are grams (g) and kilograms (kg).
3. Mass must be measured carefully before calculating density.

Measuring Volume of Regular Solids

1. Regular shapes have measurable dimensions.
2. Volume is calculated using geometric formulas.
3. Common shapes include cubes and rectangular blocks.

Measuring Volume of Liquids

1. Liquids are measured using a measuring cylinder.
2. The volume is read at the bottom of the meniscus.

Using an Archimedes Can

1. An Archimedes can allows displaced water to flow out.
2. The displaced water is collected and measured.
3. The volume of displaced water equals the volume of the object.

Why Some Dense Materials Can Float

1. Objects may contain air spaces.
2. These air spaces reduce the object’s average density.

Floating Depth

1. Floating objects sink until they displace enough liquid to balance their weight.
2. The deeper an object floats, the greater its average density.

Density Helps Explain Floating Through Upthrust

1. When an object is placed in a fluid (a liquid or gas), the fluid pushes upward on it. This upward force is called upthrust.
2. If you submerge a stone in water, it displaces a volume of water equal to its submerged volume. The weight of that displaced water is the upthrust pushing up on the stone.
   1. If the object's weight is larger than the upthrust, it sinks.
   2. If the upthrust equals the object's weight, it floats (in equilibrium).

Why Does Ice Float On Water, Even Though It Is Made From Water?

1. Most substances become denser as they cool.
2. Water behaves differently near its freezing point.
3. When water freezes, its particles form a more open structure.
4. This increases the volume and reduces the density.
5. Ice, therefore, has a lower density than liquid water and floats.

Units Of Volume And Area Require Cubing And Squaring

1. A common difficulty is converting between units such as m$^3$ and cm$^3$.
2. The key idea is that length conversions get squared for area and cubed for volume.
3. Because $1\text{ m} = 100\text{ cm}$:
   1. $1\text{ m}^2 = (100\text{ cm})^2 = 10\,000\text{ cm}^2$
   2. $1\text{ m}^3 = (100\text{ cm})^3 = 1\,000\,000\text{ cm}^3$

Useful Unit Conversions For Density Work

1. $1\text{ cm}^3 = 1\text{ mL}$ (common in lab work)
2. $1\,000\text{ cm}^3 = 1\text{ L}$
3. $1\text{ g cm}^{-3} = 1\,000\text{ kg m}^{-3}$

Density Connects To Environmental Physics

1. Air density helps you estimate how much gas is in a room, which links to quantities like the mass of greenhouse gases present.
2. Water density differences help drive ocean currents (denser water sinks), influencing climate.
3. Ice and liquid water have different densities, which affects floating ice and can connect to discussions about sea level.