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 = Vf - Vi\$.

💡 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!