Determine whether an object floats based on density data

IGCSE Physics 0625 – Topic 1.4: Density

Learning Objective

Determine whether an object will float or sink in a fluid using density data.

Key Concepts

• Density (\$\rho\$) is the mass of a substance per unit volume.
• Formula: \$\rho = \frac{m}{V}\$ where \$m\$ is mass (kg) and \$V\$ is volume (m³).
• Typical units: \$\text{kg·m}^{-3}\$ or \$\text{g·cm}^{-3}\$.
• An object will float if its average density is less than the density of the fluid it is placed in.
• If the object's density is greater than that of the fluid, it will sink.

Relationship Between Density and Buoyancy

The buoyant force (\$F_B\$) acting on an object immersed in a fluid equals the weight of the displaced fluid:

\$FB = \rho{\text{fluid}} \, g \, V_{\text{disp}}\$

Where:

• \$\rho_{\text{fluid}}\$ – density of the fluid
• \$g\$ – acceleration due to gravity (≈ 9.81 m·s⁻²)
• \$V_{\text{disp}}\$ – volume of fluid displaced

Floating occurs when the buoyant force is equal to or greater than the weight of the object (\$mg\$). This condition reduces to the density comparison above.

Steps to Decide if an Object Will Float

1. Obtain the mass (\$m\$) and volume (\$V\$) of the object, or its given density (\$\rho_{\text{obj}}\$).
2. Identify the density of the fluid (\$\rho_{\text{fluid}}\$) – e.g., water ≈ 1.0 g·cm⁻³ (1000 kg·m⁻³).
3. Compare the densities:

   • If \$\rho{\text{obj}} < \rho{\text{fluid}}\$, the object will float.
   • If \$\rho{\text{obj}} > \rho{\text{fluid}}\$, the object will sink.
   • If \$\rho{\text{obj}} = \rho{\text{fluid}}\$, the object will remain suspended in the fluid.

4. State the conclusion clearly, referencing the density values used.

Common Materials and Their Densities

Worked Example

Problem: A solid block has a mass of 150 g and a volume of 100 cm³. Will it float in water?

1. Calculate the block’s density:

   \$\rho_{\text{block}} = \frac{150\ \text{g}}{100\ \text{cm}^3} = 1.5\ \text{g·cm}^{-3}\$

2. Density of water is \$1.0\ \text{g·cm}^{-3}\$.
3. Compare: \$1.5\ \text{g·cm}^{-3} > 1.0\ \text{g·cm}^{-3}\$.
4. Conclusion: The block will sink in water.

Practice Questions

1. A piece of cork has a mass of 2.5 g and a volume of 5.0 cm³. Determine whether it will float in water.
2. Calculate the density of an object that just remains suspended in water (neutral buoyancy). What is its density?
3. Given a metal alloy with density \$8.0\ \text{g·cm}^{-3}\$, will a shape made from this alloy float in oil of density \$0.92\ \text{g·cm}^{-3}\$?