Question

State whether the following will sink or float when dropped into water. (a) redwood \((d=1.2 \mathrm{~g} / \mathrm{mL})\) (b) bamboo \((d=0.40 \mathrm{~g} / \mathrm{mL})\)

Short answer

Redwood will sink; bamboo will float.

Step-by-step solution

Understanding Density and Buoyancy

An object will float in a fluid if its density is less than the fluid's density. Water has a density of approximately \(1.0 \; \mathrm{g/mL}\). If an object's density is greater than \(1.0 \; \mathrm{g/mL}\), it will sink. If it's less, it will float.

Analyze Redwood's Density

Redwood has a density of \(1.2 \; \mathrm{g/mL}\). Since \(1.2 \; \mathrm{g/mL}\) is greater than the density of water, which is \(1.0 \; \mathrm{g/mL}\), redwood will sink in water.

Analyze Bamboo's Density

Bamboo has a density of \(0.40 \; \mathrm{g/mL}\). Since \(0.40 \; \mathrm{g/mL}\) is less than the density of water, which is \(1.0 \; \mathrm{g/mL}\), bamboo will float in water.

Key concepts

Water Density

When we talk about water density, we are referring to how much mass is packed into a specific volume of water. For water, this density is typically around \( 1.0 \; \text{g/mL} \). This means every milliliter of water weighs about one gram. However, it's essential to note that this value can slightly change with temperature.

A liquid's density determines its ability to support an object floating on it. In most cases under normal conditions at room temperature, we consider water's density to be \( 1.0 \; \text{g/mL} \) for simplicity when solving problems about buoyancy and flotation. This baseline comparison helps us determine whether another object will sink or float.

Object Density

Object density, on the other hand, is a measure of how much mass is contained within a unit volume of that object. It helps us understand how the object will interact with different fluids, like water.

For instance, if an object like redwood has a density of \( 1.2 \; \text{g/mL} \), that means it is heavier for its size compared to water. Redwood sinks because it is denser than water. Similarly, bamboo with a density of \( 0.40 \; \text{g/mL} \) is lighter, allowing it to float.

It's quite straightforward: compare the density of any object with the density of water. If the object's density is lower, it will float! Otherwise, it sinks. Always remember that density is all about how compact the mass inside an object is relative to its volume.

Floatation Theory

Floatation Theory helps us predict whether an object will float or sink in a fluid. The basic principle is that an object will float if it is less dense than the fluid it is placed in. Conversely, it will sink if it is denser.

In simpler terms, imagine you are placing a log in water. If the log is compact and heavy for its size, it will likely sink. But if it's light and has lots of air trapped inside, like bamboo, it will float.

• If an object's overall density is less than the fluid, it displaces a volume of fluid equal in weight to itself.
• If it's denser, it cannot displace enough fluid to support its weight, so it sinks.

Understanding floatation in this way lets us predict and explain why things behave the way they do in different fluids.