Chapter 4: Problem 14

Believe it or not, canoes have been made out of concrete (and they actually float). But even though concrete has a lower density than aluminum, a concrete canoe weighs a lot more than an aluminum one of the same size. Why is that?

Short Answer

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Answer: A concrete canoe can float in water because the average density of the whole canoe (concrete + air inside) is less than the density of water, thanks to its thicker walls and greater internal volume (air-filled). Although concrete is denser than aluminum, using more concrete in the canoe's construction achieves an average density that allows it to float. On the other hand, the concrete canoe weighs more than an aluminum one because it requires a greater volume of material (thicker walls) to achieve floatability.

Step by step solution

Understanding Density

First, the understanding of density is crucial. Density is defined as mass per unit volume (ρ=m/v). That is, how much matter (mass) is packed into a specific volume.

Understanding the relationship between density and flotation

The principle of flotation, based on Archimedes' principle, states that an object submerged in a fluid (water in this case) will experience an upward force (buoyancy) equal to the weight of the fluid displaced by the object. That means, to float, an object must displace a weight of fluid equal to its own weight.

Delving into the reason concrete canoes float

The fact that concrete canoes can float despite concrete being denser than water might seem counterintuitive. But it is important to remember that it's the average density of the canoe (concrete + air inside) that determines whether it floats or sinks. If the average density of the canoe is less than the density of water, it will float.

Investigating the weight difference between concrete and aluminum canoes

Now, considering the fact that concrete has a lower density than aluminum, wouldn't it result in a concrete canoe being lighter than an aluminum canoe? Actually, no. The key factor here is that to make a concrete boat that floats, we must use a lot more concrete (making the walls thicker) to ensure it has enough internal volume (air-filled) to achieve an average density less than water. In contrast, given aluminum's higher density, a smaller quantity is necessary to build a canoe of the same size. The aluminum canoe, therefore, ends up weighing less than the concrete one because the amount of aluminum used is less than the amount of concrete necessary to achieve the floatability.

Summing up

In summary, while concrete has a lower density than aluminum, a concrete canoe weighs more than an aluminum one due to the need for thicker walls, thus using a greater volume of material. The flotation of a canoe (or any object) is determined by the average density of the whole canoe (material + air inside), and if it's less than the density of the fluid, in this case, water, the canoe will float.

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Believe it or not, canoes have been made out of concrete (and they actually float). But even though concrete has a lower density than aluminum, a concrete canoe weighs a lot more than an aluminum one of the same size. Why is that?

Short Answer

Step by step solution

Understanding Density

Understanding the relationship between density and flotation

Delving into the reason concrete canoes float

Investigating the weight difference between concrete and aluminum canoes

Summing up

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