Question

The canoe gliding gracefully along the water in the photograph is made of concrete, which has a density of about \(2.4 \mathrm{g} / \mathrm{cm}^{3}\). Explain why the canoe does not sink.

Short answer

The concrete canoe does not sink because the overall density of the canoe (concrete + air) is less than the water density. Therefore, it can displace a weight of water equal to its own weight, resulting in floating due to Archimedes' principle.

Step-by-step solution

Understanding the question

We must explain why the concrete canoe does not sink in water even though the density of concrete is greater than the density of water, which is \(1 \mathrm{g} / \mathrm{cm}^{3}\). The exercise is based on the principle of Archimedes or buoyancy.

Understanding Archimedes' Principle

Archimedes' Principle states that the buoyant force on an object is equal to the weight of the fluid it displaces. This is why a hollow canoe floats; the weight of the water it displaces is equal to its own weight.

Applying the principle to our canoe

Although the canoe is more dense than the water due to the concrete, there is also air inside the canoe. This contributes to the overall density of the canoe, making it to be less than the density of water. Hence, the canoe can displace a weight of water equal to its own weight, making it able to float.

Key concepts

Buoyancy

Buoyancy is a fascinating force that acts on objects submerged in a fluid, influencing whether they float or sink. When an object is placed in water, it experiences an upward force called the buoyant force. This force is equal to the weight of the fluid the object displaces. If the buoyant force is greater than or equal to the object's weight, it will float.
This concept is the core idea behind Archimedes' Principle, which helps us understand how even a concrete canoe can glide smoothly on water without sinking. Despite the heavy nature of concrete, the design of the canoe allows it to have sufficient displacement of water, creating enough buoyant force to support its weight.

Density

Density is a measure of how much mass is contained in a given volume. It tells us how compact or concentrated a substance is. The density of concrete, for instance, is higher ( 2.4 ext{g/cm}^3 ), compared to water ( 1 ext{g/cm}^3 ).
When considering flotation, it’s important to think about the overall density of the object, not just the material it's made of. A concrete canoe doesn’t sink because its overall density, including the hollow spaces and air inside, is less than that of water. This allows it to successfully float, even though the density of concrete itself is greater than water.

Displacement of Water

When an object like our concrete canoe is placed in water, it pushes water out of its way. This is known as displacement of water. The key idea here is that the canoe displaces enough water to match its own weight.

• The displaced water generates a buoyant force opposite to the weight of the canoe.
• If the weight of the displaced water equals the weight of the canoe, it achieves flotation.

This balance between the weight of the canoe and the weight of the displaced water explains why it stays afloat, illustrating the practical application of Archimedes' Principle. By designing the canoe to have a shape that displaces enough water, regardless of the heavy material, engineers ensure its stability in water.