Understanding Floating and Sinking Based on Density

Whether an object floats or sinks in a liquid depends on the comparison between the density of the object and the density of the liquid. If the object's density is less than the liquid's density, the object will float. If the object's density is greater than the liquid's density, the object will sink. If the densities are equal, the object will remain suspended within the liquid.

Calculating the Density of the Sealed Packet

We are given the volume and mass of the sealed packet. We can calculate its density using the formula:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

The given values are:

• Volume of the packet = 1 liter
• Mass of the packet = 800 g

First, we need to convert the volume from liters to cubic centimeters (cm³) to match the units of the liquid densities (g/cm³). We know that 1 liter is equal to 1000 cubic centimeters.

\[ \text{Volume} = 1 \text{ liter} = 1000 \text{ cm}^3 \]

Now, we can calculate the density of the packet:

\[ \text{Density of packet} = \frac{800 \text{ g}}{1000 \text{ cm}^3} = 0.8 \text{ g/cm}^3 \]

So, the density of the sealed packet is 0.8 g/cm³.

Comparing Packet Density with Liquid Densities

Now we compare the density of the packet with the densities of water and liquid B.

The density of the packet is 0.8 g/cm³.

Packet in Water

The density of water is given as 1 g/cm³.

Comparing the densities:

\[ \text{Density of packet} \, (0.8 \text{ g/cm}^3) \, \text{ vs. } \, \text{Density of water} \, (1 \text{ g/cm}^3) \]

Since 0.8 g/cm³ < 1 g/cm³, the density of the packet is less than the density of water. Therefore, the packet will float in water.

Packet in Liquid B

The density of liquid B is given as 1.5 g/cm³.

Comparing the densities:

\[ \text{Density of packet} \, (0.8 \text{ g/cm}^3) \, \text{ vs. } \, \text{Density of liquid B} \, (1.5 \text{ g/cm}^3) \]

Since 0.8 g/cm³ < 1.5 g/cm³, the density of the packet is less than the density of liquid B. Therefore, the packet will float in liquid B.

Conclusion on Floating and Sinking

Based on the density calculations and comparisons:

• The packet floats in water because its density (0.8 g/cm³) is less than the density of water (1 g/cm³).
• The packet floats in liquid B because its density (0.8 g/cm³) is less than the density of liquid B (1.5 g/cm³).

Thus, the packet will float in both water and liquid B.

Revision Table: Density and Buoyancy

Additional Information: Archimedes' Principle

The concept of floating and sinking is explained by Archimedes' Principle. This principle states that a body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the body. The buoyant force acts opposite to gravity.

• If the buoyant force is greater than the object's weight, the object floats.
• If the buoyant force is less than the object's weight, the object sinks.
• If the buoyant force is equal to the object's weight, the object remains suspended.

Relating this to density: The weight of the object is \( \text{Volume}_{\text{object}} \times \text{Density}_{\text{object}} \times g \). The buoyant force is the weight of the displaced fluid, which is \( \text{Volume}_{\text{submerged}} \times \text{Density}_{\text{fluid}} \times g \).

For a fully submerged object with Volume \(V\):

• If \( V \times \text{Density}_{\text{object}} \times g \, > \, V \times \text{Density}_{\text{fluid}} \times g \), the object sinks. This simplifies to \( \text{Density}_{\text{object}} \, > \, \text{Density}_{\text{fluid}} \).
• If \( V \times \text{Density}_{\text{object}} \times g \, < \, V \times \text{Density}_{\text{fluid}} \times g \), the object floats (partially submerged). This implies \( \text{Density}_{\text{object}} \, < \, \text{Density}_{\text{fluid}} \).
• If \( V \times \text{Density}_{\text{object}} \times g \, = \, V \times \text{Density}_{\text{fluid}} \times g \), the object is suspended. This implies \( \text{Density}_{\text{object}} \, = \, \text{Density}_{\text{fluid}} \).

Our density comparison method is a direct application of Archimedes' Principle.