Density Definition in Physics: Explained with Examples for AP Physics 2

📚 Quick Study Guide

🔍 Definition: Density is a measure of mass per unit volume. ⚛️ Formula: $\rho = \frac{m}{V}$, where $\rho$ is density, $m$ is mass, and $V$ is volume. 📏 Units: Common units include kg/m³ (kilograms per cubic meter) and g/cm³ (grams per cubic centimeter). 🌡️ Temperature Dependence: Density can change with temperature, as volume typically increases with temperature. 💧 Density of Water: The density of pure water is approximately 1000 kg/m³ or 1 g/cm³ at 4°C. 💡 Key Concept: An object will float if its density is less than the density of the fluid it is placed in. 📐 Applications: Density is used in various applications, including buoyancy calculations, material identification, and fluid dynamics.

🧪 Practice Quiz

1. A metal block has a mass of 500g and a volume of 200 cm³. What is its density?
   1. 2.5 g/cm³
   2. 0.4 g/cm³
   3. 100 g/cm³
   4. 700 g/cm³
2. Which of the following is the correct formula for density?
   1. $\rho = m \times V$
   2. $\rho = \frac{V}{m}$
   3. $\rho = \frac{m}{V}$
   4. $\rho = m + V$
3. A liquid has a density of 1.2 g/mL. What volume will 60g of this liquid occupy?
   1. 72 mL
   2. 50 mL
   3. 0.02 mL
   4. 61.2 mL
4. If an object floats in water, what can you conclude about its density?
   1. Its density is greater than water.
   2. Its density is equal to water.
   3. Its density is less than water.
   4. Its density is unrelated to water.
5. Which of the following units is NOT a unit of density?
   1. kg/m³
   2. g/cm³
   3. lb/ft³
   4. m³/kg
6. A balloon filled with helium rises in air. Why?
   1. Helium is heavier than air.
   2. Helium is less dense than air.
   3. Helium has the same density as air.
   4. Helium is attracted to the Earth.
7. The density of a substance is $2 g/cm^3$. What is its density in $kg/m^3$?
   1. 200 kg/m³
   2. 2000 kg/m³
   3. 0.002 kg/m³
   4. 20 kg/m³