Theory — Buoyancy and Archimedes' Principle
Density
Density is defined as mass per unit volume. It assumes a solid material with no internal voids — any air pockets would change the volume without changing the mass, giving an inaccurate density reading.
Conversion: 1 g/cm³ = 1000 kg/m³
Archimedes' Principle
When an object is submerged in a fluid, the fluid exerts an upward buoyant force equal to the weight of the fluid displaced by the object. This principle applies to all fluids — liquids and gases alike.
F_b = ρ_fluid · V_displaced · g
For water (ρ = 1000 kg/m³ = 1 g/cm³):
F_b = m_displaced_water · g
Section I — Displaced Water Method
Submerge an object in an overflow beaker. Collect and weigh the displaced water. The buoyant force equals the weight of this water. Also measure its volume in a graduated cylinder — confirms that 1 mL = 1 cm³ of water has mass 1 gram.
Section II — Weight in Water Method
Weigh the object in air, then weigh it while fully submerged. The difference in apparent weight IS the buoyant force. This gives a second independent measurement of F_b to compare with Section I.
Calculating Object Density
Once we know the buoyant force and the density of water, we can find the object's density without directly measuring its volume:
ρ_object = m_object / V_object
Combined:
Percent Error
Instructions — Running the Virtual Experiment
Section I — Mass and Volume of Displaced Water
Section II — Weight in Air and Water
Simulation — Buoyancy Experiment
Data Table — All Samples
| Sample | Mass in Air (g) | Mass in Water (g) | F_b (N) | Volume (cm³) | Density (g/cm³) | Reference (g/cm³) | % Error |
|---|---|---|---|---|---|---|---|
| Brass Sample 1 | — | — | — | 8.50 | — | ||
| Brass Sample 2 | — | — | — | 8.50 | — | ||
| Aluminum | — | — | — | 2.70 | — | ||
| Iron/Steel | — | — | — | 7.87 | — | ||
| Copper | — | — | — | 8.96 | — |
Team Questions
Example Lab Report
Sample report demonstrating the expected format and level of detail. Use as a guide for your own submission.
Lab 11 — Archimedes' Principle
Physics 171 | Section: [Your Section] | Date: [Date]
Lab Members: [Names of all members present]
Introduction
This lab tests Archimedes' principle — that the buoyant force on a submerged object equals the weight of fluid displaced. We measure buoyancy using two independent methods: (1) collecting and weighing displaced water, and (2) comparing apparent weight in air versus water. We also determine the density of metal samples and compare to reference values.
Background — Key Equations
Density: ρ = m/V. For water: ρ_water = 1.00 g/cm³ = 1000 kg/m³.
Buoyant force: F_b = ρ_fluid · V_displaced · g = (W_air − W_water)
Object density: ρ_object = (W_air / F_b) · ρ_water
Percent error: |experimental − reference| / reference × 100%
Section I Results — Displaced Water
| Sample | Mass of Displaced Water (g) | Volume (mL) | F_b (N) |
|---|---|---|---|
| Brass Sample 1 | 8.42 | 8.4 | 0.0826 |
| Brass Sample 2 | 6.18 | 6.2 | 0.0606 |
| Aluminum | 9.25 | 9.3 | 0.0907 |
| Iron/Steel | 7.63 | 7.6 | 0.0748 |
| Copper | 5.57 | 5.6 | 0.0546 |
Note: Mass (g) ≈ Volume (mL) for water, confirming ρ_water = 1.00 g/cm³. Small differences due to reading precision.
Section II Results — Weight in Air and Water
| Sample | Mass Air (g) | Mass Water (g) | F_b (N) | Density (g/cm³) | Reference (g/cm³) | % Error |
|---|---|---|---|---|---|---|
| Brass Sample 1 | 71.57 | 63.15 | 0.0826 | 8.51 | 8.50 | 0.12% |
| Brass Sample 2 | 52.53 | 46.35 | 0.0606 | 8.49 | 8.50 | 0.12% |
| Aluminum | 24.98 | 15.73 | 0.0907 | 2.70 | 2.70 | 0.00% |
| Iron/Steel | 60.02 | 52.39 | 0.0748 | 7.87 | 7.87 | 0.00% |
| Copper | 49.93 | 44.36 | 0.0546 | 8.95 | 8.96 | 0.11% |
Sample Calculation — Brass Sample 1
F_b from Section I: F_b = 0.00842 kg × 9.81 m/s² = 0.0826 N
F_b from Section II: F_b = (71.57 − 63.15) g × 0.001 kg/g × 9.81 = 0.0826 N ✓
Object Volume: V = m_water/ρ_water = 8.42 g / 1.00 g/cm³ = 8.42 cm³
Object Density: ρ = 71.57 g / 8.42 cm³ = 8.50 g/cm³
Convert to kg/m³: 8.50 g/cm³ × 1000 = 8500 kg/m³
% Error: |8.51 − 8.50| / 8.50 × 100% = 0.12%
Team Question Answers
Q1: 12 g/cm³ × 1000 = 12,000 kg/m³ (since 1 g/cm³ = 1000 kg/m³)
Q2: Volume displaced = 10 cm³ = 10 × 10⁻⁶ m³. Mass of water = 10 g = 0.010 kg. F_b = 0.010 × 9.81 = 0.0981 N ≈ 0.098 N
Q3: Brass Sample 1 density = 8.51 g/cm³ = 8510 kg/m³. This is within 0.12% of the reference value of 8500 kg/m³.
Q4: % error = |8.51 − 8.50| / 8.50 × 100% = 0.12% (two significant digits)
Discussion
Both measurement methods (displaced water and apparent weight loss) gave identical buoyant force values to three significant figures, strongly confirming Archimedes' principle. The experimental densities agreed with reference values to within 0.12% for all samples. Minor discrepancies are attributed to small amounts of water remaining in the overflow tube between runs and parallax errors in reading the graduated cylinder meniscus.
The plastic cylinder floated rather than sinking — this confirmed that objects with density less than water (ρ_plastic ≈ 0.90 g/cm³ < 1.00 g/cm³) experience a buoyant force greater than their weight, causing them to float until equilibrium is reached at the surface.
Conclusion
The experiment successfully verified Archimedes' principle. The buoyant force measured by two independent methods agreed within experimental uncertainty. Experimental densities for all metal samples matched reference values to within 0.2%, demonstrating that the buoyancy method is an accurate technique for density determination without direct volume measurement.
Practice Questions
Show all work and include units in your answers.