This worksheet provides a comprehensive guide to density calculations, including practice problems with detailed solutions. Density is a fundamental concept in physics and chemistry, representing the mass of a substance per unit volume. Mastering density calculations is crucial for understanding various scientific principles and applications.
What is Density?
Density (ρ) is defined as the mass (m) of a substance divided by its volume (V):
ρ = m/V
The SI unit for density is kilograms per cubic meter (kg/m³), but other units like grams per cubic centimeter (g/cm³) are also commonly used. Remember to maintain consistent units throughout your calculations to avoid errors.
Understanding the Formula:
The formula ρ = m/V allows us to solve for any of the three variables if we know the other two. We can rearrange the formula as follows:
- m = ρV (to find mass)
- V = m/ρ (to find volume)
Practice Problems:
Here are several practice problems of varying difficulty to help you solidify your understanding of density calculations. Remember to show your work!
Problem 1: A block of wood has a mass of 150 grams and a volume of 200 cubic centimeters. What is its density?
Answer:
First, identify the knowns:
- m = 150 g
- V = 200 cm³
Use the density formula: ρ = m/V
ρ = 150 g / 200 cm³ = 0.75 g/cm³
Therefore, the density of the wood block is 0.75 g/cm³.
Problem 2: A metal object has a density of 8.9 g/cm³ and a volume of 5 cm³. What is its mass?
Answer:
First, identify the knowns:
- ρ = 8.9 g/cm³
- V = 5 cm³
Use the mass formula: m = ρV
m = 8.9 g/cm³ * 5 cm³ = 44.5 g
Therefore, the mass of the metal object is 44.5 g.
Problem 3: A liquid has a density of 1.2 g/mL and a mass of 36 g. What is its volume?
Answer:
First, identify the knowns:
- ρ = 1.2 g/mL
- m = 36 g
Use the volume formula: V = m/ρ
V = 36 g / 1.2 g/mL = 30 mL
Therefore, the volume of the liquid is 30 mL.
Problem 4 (Challenge): A irregularly shaped rock is placed in a graduated cylinder containing 50 mL of water. The water level rises to 75 mL. If the rock has a mass of 125 grams, what is its density?
Answer:
First, calculate the volume of the rock:
- Volume of rock = Final volume - Initial volume = 75 mL - 50 mL = 25 mL
Now, identify the knowns:
- m = 125 g
- V = 25 mL
Use the density formula: ρ = m/V
ρ = 125 g / 25 mL = 5 g/mL
Therefore, the density of the rock is 5 g/mL.
Advanced Concepts (Optional):
- Specific Gravity: This is the ratio of a substance's density to the density of water. It's a dimensionless quantity.
- Density and Temperature: Density is usually temperature-dependent; most substances become less dense as temperature increases.
- Archimedes' Principle: This principle explains buoyancy and is closely related to density.
This worksheet provides a foundational understanding of density calculations. Remember to practice regularly to build your skills and confidence in solving density-related problems. Further exploration of related concepts will enhance your comprehension of this crucial scientific principle.
