This guide provides detailed answers and explanations for common density practice problems. Understanding density is crucial in various scientific fields, from chemistry and physics to engineering and geology. We'll cover a range of problems, from simple calculations to more complex scenarios, helping you master this fundamental concept.
What is Density?
Before diving into the problems, let's refresh our understanding of density. Density (ρ) is defined as the mass (m) of a substance per unit volume (V). The formula is:
ρ = m/V
Density is typically expressed in units of grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).
Common Density Practice Problems & Solutions
Here are some examples of density problems and their step-by-step solutions:
Problem 1: Finding Density
A block of metal has a mass of 150 grams and a volume of 20 cubic centimeters. Calculate its density.
Solution:
- Identify the knowns: mass (m) = 150 g, volume (V) = 20 cm³
- Apply the formula: ρ = m/V
- Substitute the values: ρ = 150 g / 20 cm³
- Calculate: ρ = 7.5 g/cm³
Therefore, the density of the metal block is 7.5 g/cm³.
Problem 2: Finding Mass
A liquid has a density of 0.8 g/mL and a volume of 50 mL. What is its mass?
Solution:
- Identify the knowns: density (ρ) = 0.8 g/mL, volume (V) = 50 mL
- Rearrange the formula to solve for mass: m = ρV
- Substitute the values: m = 0.8 g/mL * 50 mL
- Calculate: m = 40 g
Therefore, the mass of the liquid is 40 grams.
Problem 3: Finding Volume
A piece of wood with a density of 0.6 g/cm³ has a mass of 30 grams. What is its volume?
Solution:
- Identify the knowns: density (ρ) = 0.6 g/cm³, mass (m) = 30 g
- Rearrange the formula to solve for volume: V = m/ρ
- Substitute the values: V = 30 g / 0.6 g/cm³
- Calculate: V = 50 cm³
Therefore, the volume of the wood is 50 cubic centimeters.
Problem 4: Density and Units Conversion
A substance has a density of 2 kg/m³. What is its density in g/cm³?
Solution:
This problem requires unit conversion. Remember that 1 kg = 1000 g and 1 m = 100 cm. Therefore, 1 m³ = (100 cm)³ = 1,000,000 cm³.
- Convert kg to g: 2 kg * 1000 g/kg = 2000 g
- Convert m³ to cm³: 1 m³ = 1,000,000 cm³
- Calculate the new density: 2000 g / 1,000,000 cm³ = 0.002 g/cm³
Therefore, the density of the substance is 0.002 g/cm³.
Advanced Density Problems (with explanations)
More complex problems might involve:
- Irregularly shaped objects: Finding the volume of irregularly shaped objects often requires water displacement techniques.
- Mixtures and solutions: Calculating the density of a mixture requires considering the densities and volumes of its components.
- Temperature effects: Density is temperature-dependent; changes in temperature will affect the density of a substance.
This guide provides a solid foundation for solving density problems. Remember to always clearly identify the knowns, choose the correct formula, and pay close attention to units. Practice is key to mastering density calculations. By working through various problems, you'll build confidence and develop a strong understanding of this important scientific concept.
