Density: Mass vs Volume Guide

PhysicsBeginnerReading time: 3 min

Overview

Why is a plastic block much lighter than an iron block of the same size? Why does oil always float on water? It all depends on an inherent property of matter—density. By measuring the mass of different substances (aluminum, iron, copper, wood) at different volumes, this experiment aims to reveal the quantitative relationship between mass and volume, and intuitively present the physical meaning of density using 'graph slope'.

Background

In ancient times, people were often puzzled by questions like 'Which is heavier, a pound of cotton or a pound of iron?'. It was not until the establishment of the concept of density that we understood that heaviness has two meanings: one is the total mass (weight) of the object, and the other is the compactness of the material itself. Density reflects the compactness of the arrangement of microscopic particles inside a substance. It is an important 'ID card' for identifying types of matter, and it is also the core basis for Archimedes' verification of the authenticity of the golden crown.

Key Concepts

Mass ( $m$ )

m

The amount of matter contained in an object. In the International System of Units, the basic unit is the kilogram ( $kg$ ), and the gram ( $g$ ) is commonly used in this experiment.

Volume ( $V$ )

V

The amount of space occupied by an object. Cubic centimeters ( $cm^3$ ) or milliliters ( $mL$ ) are commonly used as units in experiments.

Density ( $\rho$ )

\rho = \frac{m}{V}

The mass of a substance per unit volume. It is a property of the substance itself, determined by the type of substance, and is unrelated to the magnitude of mass or volume.

Formulas & Derivation

Density Definition

\rho = \frac{m}{V}

The unit is usually

g/cm^3

kg/m^{3}

. Conversion relation:

1g/cm^3 = 1.0\times10^3 kg/m^3

Experiment Steps

1
Microscopic Conjecture
Switch between different 'Substances' (such as aluminum or wood) in the control panel. Observe the density of particle arrangement in the microscopic view on the left. Which substance's particles do you think are more crowded? Will this correspond to a greater or smaller density?
2
Explore Mass vs. Volume
Drag the volume slider to increase $V$ . Observe how the electronic balance reading $m$ changes. When the volume becomes 2 times the original, does the mass also become 2 times?
3
Find the Invariant
Record at least 3 sets of $m$ and $V$ data. Calculate the ratio $\frac{m}{V}$ for each set. What pattern do you find in this ratio for the same substance?
4
Graph Analysis
Switch to another substance and repeat the measurement. Observe the generated $m-V$ graph and compare the steepness (slope) of the two lines. What physical meaning does a steeper slope represent?

Learning Outcomes

Understand that the mass of the same substance is directly proportional to its volume ( $m \propto V$ ).
Master the definition of density and its physical meaning: a property of matter.
Learn to use $m-V$ graphs to analyze material properties, understanding that slope represents density ( $k=\rho$ ).
Recognize through microscopic comparison that macroscopic differences in density stem from the mass of microscopic particles and their arrangement gaps.

Real-world Applications

Material Identification: By measuring density, one can preliminarily determine whether a metal ring is pure gold.
Industrial Material Selection: The aerospace field prioritizes 'lightweight materials' with low density and high strength, such as aluminum alloys and titanium alloys.
Agricultural Application: Using brine for seed selection. Full seeds have a density greater than brine and sink, while shriveled seeds have a low density and float.
Product Design: Mobile phone manufacturers pursue a thin and light feel, choosing high-strength composite materials with lower density.

Common Misconceptions

Misconception

The density of a large piece of aluminum is greater than that of a small piece of aluminum.

Correct

Incorrect. Density is a property of matter, just like a name. As long as the type, state, and temperature of the substance remain unchanged, its density is constant. A large piece of aluminum has a large mass but also a large volume, so the ratio (density) remains unchanged.

Misconception

1kg

of iron is heavier than

1kg

of cotton.

Correct

Incorrect. Both have a mass of

1kg

, so their gravity is equal. When people normally say 'iron is heavier than cotton', they physically mean 'the density of iron is greater than that of cotton'.

Ready to start?

Now that you understand the basics, start the interactive experiment!

Start Experiment Start Quiz

Overview

Background

Key Concepts

Mass (mmm)

Volume (VVV)

Density (ρ\rhoρ)

Formulas & Derivation

Density Definition

Experiment Steps

Microscopic Conjecture

Explore Mass vs. Volume

Find the Invariant

Graph Analysis