Question

Different types of wood have different densities. For example, the density of pine \(\left(0.5 \mathrm{~g} / \mathrm{cm}^{3}\right)\) is less than that of ebony \(\left(0.9 \mathrm{~g} / \mathrm{cm}^{3}\right)\) but more than the density of balsa wood \(\left(0.14 \mathrm{~g} / \mathrm{cm}^{3}\right)\). All would float in water but with different proportions of each block lying above and below the surface. 1\. Draw a diagram to show what would happen if equalsized blocks of each type of wood were added to a container of water. 2\. What would happen to the blocks if we replaced the water with a liquid with higher density, such as corn syrup?

Short answer

All wood blocks will float higher in corn syrup than in water.

Step-by-step solution

Understanding Densities Relative to Water

We need to first understand how density affects whether an object floats on water. Water has a density of approximately \(1.0\, \text{g/cm}^3\). Objects with a density less than water will float. Since all three woods (pine, ebony, balsa) have densities less than water, they will all float. Balsa wood, with the lowest density, will have the most of its volume above water, followed by pine, and then ebony.

Diagramming the Water Scenario

For the diagram, draw a container filled with water and three equally sized blocks labeled as balsa, pine, and ebony placed in the water. The balsa block will be mostly above the water line, while the pine block will have a lesser proportion above the water. The ebony block will have the least volume above the water, with the most submerged, but all will stay afloat as their densities are less than water.

Assessing Effects of Denser Liquid

When water is replaced with corn syrup, which has a higher density than water (approximately \(1.4\, \text{g/cm}^3\)), all blocks will float even more than they did in water. Objects float better in denser liquids because they displace a volume of the liquid that equals their own weight more quickly. Therefore, more of each block's volume will be above the surface of the corn syrup compared to water.

Conclusion of Liquid Density Effects

In conclusion, replacing water with corn syrup will cause all blocks to rise, with even more of each type of wood above the syrup surface than when in water. The order of rising will remain the same, with balsa having the most above, followed by pine and then ebony.

Key concepts

Density

Density is a fundamental concept in physics that governs how objects interact with the liquids they are immersed in. It is defined as the mass of an object per unit of volume, and its formula is \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). The unit of density is typically grams per cubic centimeter (\( \text{g/cm}^3 \)) for solids and liquids.

Understanding density is key to predicting whether an object will float or sink in a liquid. If the density of an object is less than that of the fluid, the object will float. Conversely, an object with a density greater than the fluid will sink. In this exercise, we see various blocks of wood with different densities and how they behave in water, demonstrating the practical implications of density.

Floating Objects

When considering floating objects, the main principle to remember is that an object less dense than a liquid will float on it. In our exercise, we have three types of wood: pine, ebony, and balsa. All of these woods have densities lower than water's, which is roughly measured at \( 1.0 \, \text{g/cm}^3 \).

The hierarchy of the woods from balsa, pine to ebony, shows us how density affects the height at which objects float. Balsa wood, having the lowest density (\(0.14 \, \text{g/cm}^3\)), will float with most of its volume above water surface. Pine wood, with an intermediate density (\(0.5 \, \text{g/cm}^3\)), will have some of its block submerged but with a reasonable proportion still above the water. Ebony, being more dense yet still lighter than water (\(0.9 \, \text{g/cm}^3\)), will show the least volume above water. This example highlights the floating behavior due to density differences.

Liquid Displacement

Liquid displacement is a process that occurs when an object enters a liquid and pushes the liquid aside to make space for itself. This principle is pivotal in understanding buoyancy—the force that allows objects to float. As an object floats, it displaces a volume of liquid equal to its own weight.

• If an object displaces more liquid than it weighs, it will float.
• If it displaces less liquid than its weight, it will sink.

In the exercise, we see blocks of wood added to water and corn syrup, experiencing buoyancy. In denser liquids like corn syrup, blocks displace less liquid before equaling their weight, thus floating better and more of their volume remains above the surface compared to less dense liquids like water. This explains why denser liquids provide a greater "floating" capacity for objects.

Density of Liquids

The density of a liquid plays a critical role in determining the buoyancy of objects. For example, water has a density of \( 1.0 \, \text{g/cm}^3 \), while corn syrup is denser at approximately \( 1.4 \, \text{g/cm}^3 \).

The higher the density of the liquid, the better the flotation of objects with densities below that threshold. When substituting water with a denser liquid like corn syrup, the objects (in this case, wood blocks) float higher. This occurs because denser liquids can support more weight before the object is completely submerged.

Thus, understanding liquid density allows predictions of how objects will behave when placed in those liquids. In practical terms, this knowledge helps design crafts that float and efficiently analyze fluid interactions with various materials.