Question

What happens to the density of a filled water balloon as it is pulled to the bottom of the ocean?

Short answer

The density of the filled water balloon increases as it is pulled deeper into the ocean.

Step-by-step solution

Understanding the Concept of Density

Density is defined as mass per unit volume, mathematically represented as \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). To understand how density changes, we need to know how mass and volume might change.

Analyzing Changes to Volume

As a water balloon is pulled to the bottom of the ocean, the pressure exerted on it increases. Increased pressure often compresses the volume of an object. For a water balloon, this compression reduces its volume since water is slightly compressible and the balloon material may also compress.

Considering Changes to Mass

The mass of the filled water balloon remains constant as it descends because there is no addition or loss of mass while it moves through the water column.

Applying the Density Formula

Since the mass remains constant and the volume decreases due to compression, the density of the water balloon increases. This is because density is inversely proportional to volume in \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). When volume decreases and mass is unchanged, density increases.

Key concepts

Pressure

Pressure is a fundamental concept that describes the force exerted over a unit area. In everyday terms, it explains how a force applied to a surface influences that surface. When we talk about the pressure on a water balloon, especially as it descends into the ocean, it becomes important to understand how this pressure increases.
Oceans exert a lot of pressure at greater depths. This pressure comes from the weight of the water above pushing down on anything below, like a balloon. The deeper the balloon goes, the more pressure it feels because all that water is pressing on it. So, pressure increases with depth in the ocean.

Volume Compression

Volume compression refers to the decrease in the volume of an object when pressure is applied. In the context of a water balloon sinking into the ocean, the increased pressure leads to volume compression.
Imagine squeezing a soft ball; it shrinks under your hand. Similarly, the ocean's pressure pushes on the balloon, making it smaller.

• This is because the water inside and the balloon's material itself become slightly compressed.
• Compression is more noticeable when the object is flexible, like a water balloon.

As pressure adds up, the balloon's volume shrinks, directly affecting its density.

Inversely Proportional

When two quantities are inversely proportional, as one increases, the other decreases. A classic example is the relationship between volume and density in the formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]As volume decreases due to compression, density must increase if the mass stays the same.
Imagine you have a fixed amount of something, like clay. If you squish it into a smaller space, it becomes denser.

• This relationship helps us understand why the density of the balloon increases despite no change in mass.

The balloon's shrinking volume, caused by ocean pressure, inversely affects its density.

Ocean Pressure

Ocean pressure is an incredibly powerful force acting on objects as they descend into the sea. With increasing depth, water pressure grows due to more water piling on top.
For an object diving deeper, every meter it descends adds pressure: each meter adds a force from the water column above. The balloon experiences this as a squeezing effect.

• Ocean pressure can compress air, liquids, and even seemingly incompressible materials slightly (like water).
• It's important for divers and underwater explorations to consider ocean pressure.

While ocean pressure impacts volume compression, it does not change the mass of the balloon.

Mass Conservation

Mass conservation is a key principle in physics stating that mass cannot be created or destroyed in an isolated system. For our water balloon descending in the ocean, the mass remains constant. Despite changes in pressure or volume, the mass of the balloon and its water content doesn’t change.
Even while the balloon might shrink, the same amount of water is inside.

• Knowing the mass stays the same explains why any increase in density results only from a decrease in volume.

This principle simplifies understanding how pressure affects density in scenarios like descending through ocean depths.