Fluids and density: compare equal volumes
You will be able to: Calculate density and distinguish real fluids from the ideal-fluid model.
Why can a small metal object have more mass than a larger piece of foam?
A 1 L sample has mass 2 kg; another 1 L sample has mass 1 kg. The first contains twice as much mass in the same volume. Density captures this comparison without confusing mass, size and weight.
A useful starting point: Choosing a system →
Words and symbols before equations
- Fluid
- A substance that flows and has no fixed shape; liquids and gases are fluids.
- Mass m
- Amount of matter measured in kg; weight is the gravitational force mg in N.
- Volume V
- Space occupied, in m³; 1 L=0.001 m³.
- Density ρ (rho)
- Mass per unit volume, ρ=m/V, measured in kg/m³.
- Ideal fluid
- A model with constant density (incompressible) and no viscosity, or internal resistance to flow.
What this picture assumes
Each slider setting is a separate uniform sample, not compression of a fixed amount of incompressible fluid. 1 L=0.001 m³. Reference water density is 1000 kg/m³.
Connect the picture to the physics
Solids, liquids and gases differ because their particles interact and rearrange differently. A solid resists changes of shape. A liquid flows while its volume changes little under ordinary pressure changes. A gas flows and generally compresses readily. Particle spacing alone is not a complete explanation of every material’s density; particle masses matter too.
Density compares mass with volume, not weight with volume. A uniform material sample twice as large has twice the mass and the same density. For a nonuniform or hollow object, total mass divided by overall volume gives an average density.
Incompressible means a fixed amount of the modeled fluid keeps its volume as pressure changes. Zero viscosity means we neglect frictional energy loss within the fluid. Real water and air are not perfect ideal fluids; use the assumptions when they reasonably describe the stated problem.
| State | Shape | Volume/compression |
|---|---|---|
| Solid | Resists shape change | Usually approximately fixed volume |
| Liquid | Takes container shape | Approximately fixed volume; often modeled incompressible |
| Gas | Fills container | Generally compressible; not always an ideal incompressible fluid |
A worked example, step by step
A sample has mass 1.6 kg and volume 2 L. Find its density and compare it with water modeled at 1000 kg/m³.
- Convert volume: 2 L=0.002 m³.
- ρ=m/V=1.6/0.002=800 kg/m³.
- This is 0.8 times the reference water density.
- If another sample of the same uniform material has volume 4 L, its mass is 3.2 kg and its density remains 800 kg/m³.
A larger or heavier object is not automatically denser. Compare mass per equal volume.
Does doubling a uniform sample’s size automatically double its density?
Compare with an explanation
No. If mass and volume both double, their ratio stays fixed.
Predict. Change one thing. Explain.
Compare equal volumes with different masses, then equal masses with different volumes. Finally double both mass and volume. Each setting describes a separate sample; it does not compress one incompressible sample.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Mass=2 kg; volume=2 L=0.002 m³. Density=1000 kg/m³. Changing both mass and volume by the same factor preserves density.
Each slider setting is a separate uniform sample, not compression of a fixed amount of incompressible fluid. 1 L=0.001 m³. Reference water density is 1000 kg/m³.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant force, motion or energy relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA liquid sample has mass 0.6 kg and volume 0.5 L. (a) Convert volume to m³. (b) Calculate density. (c) Predict the mass of 2 L of the same uniform liquid. (d) Explain why the density stays unchanged.
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Compare with the answer and four-point rubric
- 1 point: 0.0005 m³.
- 1 point: ρ=0.6/0.0005=1200 kg/m³.
- 1 point: m=1200(0.002)=2.4 kg.
- 1 point: Mass and volume scale together; their ratio is a material property under the stated conditions.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Density definition?
ρ=m/V.
RECALL 2Are gases fluids?
Yes, though they are often compressible.
RECALL 3What does zero viscosity mean in the ideal model?
Internal frictional resistance and its energy losses are neglected.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Fluids and density: compare equal volumes
- ρ=m/V; m=ρV.
- 1 L=10⁻³ m³; 1 cm³=10⁻⁶ m³.
- Ideal fluid: incompressible and nonviscous.
Remember: A larger or heavier object is not automatically denser. Compare mass per equal volume.
Conditions: Each slider setting is a separate uniform sample, not compression of a fixed amount of incompressible fluid. 1 L=0.001 m³. Reference water density is 1000 kg/m³.
Refresh Kid · Unit 8 · Objectives 8.1.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 8.1, objectives 8.1.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Fall-2026 corrections also checked. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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