Determine whether an object floats based on density data

What is Density?

Density is a measure of how much mass is packed into a given volume. It is written as

$ρ = \\dfrac{m}{V}$

where $m$ is mass (in grams) and $V$ is volume (in cubic centimeters). The unit is usually g/cm³.

Why Density Matters for Floating

When you drop an object into a fluid, it will either sink or float depending on its density compared to the fluid’s density.

• If $ρ_{object} < ρ_{fluid}$ → the object floats.
• If $ρ_{object} > ρ_{fluid}$ → the object sinks.

Think of a boat: a wooden boat is lighter (less dense) than water, so it stays on top.

Calculating Density – Step by Step

1. Measure the mass of the object with a balance.
2. Determine its volume:
   • For regular shapes, use geometry formulas.
   • For irregular shapes, use water displacement.
3. Apply the density formula $ρ = \\dfrac{m}{V}$.

Example: A block of wood has a mass of 150 g and a volume of 200 cm³.

$ρ_{wood} = \\dfrac{150}{200} = 0.75\\,\\text{g/cm}^3$

Since $0.75 < 1.00$ (density of water), the block will float.

Water Displacement Method (for irregular objects)

1️⃣ Fill a graduated cylinder with water. 2️⃣ Note the initial volume $V_i$. 3️⃣ Submerge the object completely. 4️⃣ Record the new volume $V_f$. 5️⃣ The volume of the object is $V = V_f - V_i$.

💡 Tip: Make sure the object is fully submerged and no air bubbles cling to it.

Exam Tip Box

When you see a question like “Will a steel ball float in water?” you can answer quickly:

1. Recall the density of steel (~7.8 g/cm³).
2. Compare it to water’s density (1.0 g/cm³).
3. Since 7.8 > 1.0, the steel ball will sink.

📝 Always write the comparison in words: “Because the density of the object is greater than that of the fluid, it will sink.”

Practice Table – Predicting Floating

🔍 Use this table to practice predicting whether an object will float or sink.

Key Takeaway

Remember: Density comparison is the secret code for floating. If the object’s density is less than the fluid’s, it floats; otherwise, it sinks. Keep this rule in mind for all future physics questions about buoyancy!