Archimedes' Principle: Density of a Solid (Floating Sphere)
A mystery sphere floats in water of known density. Read the submerged volume fraction at equilibrium and estimate the sphere’s density from ρ = f·ρ_w, averaged over noisy readings.
Goal
Determine the unknown mass density of a homogeneous solid sphere that floats in fresh water (ρ_w = 1000 kg/m³) using the equilibrium relation ρ/ρ_w = V_submerged / V_total.
Equipment
- Tank of fresh water (ρ_w given)
- Homogeneous mystery sphere
- Scale reading of submerged fraction (simulated)
Theory
For a floating body, weight equals buoyant force: ρ g V = ρ_w g V_sub, hence ρ = ρ_w (V_sub / V). For a uniform sphere, the submerged fraction f = V_sub / V is read from the equilibrium waterline. Random reading error is modelled on f.
Procedure
- The lab uses fresh water with ρ_w = 1000 kg/m³ (shown on the card). The sphere’s density is fixed but hidden from you.
- Inspect the equilibrium: the sphere floats with part of its volume submerged.
- Press “Record reading” to add a row: the simulator estimates the submerged fraction f from the waterline (with small sensor noise).
- Repeat at least 5 times to average out random error.
- The table lists f and ρ = ρ_w·f. Take the sample mean of ρ as your result.
- Compare with the reference density and write the conclusion.
Experiment
Equilibrium float: unknown uniform sphere in fresh water (ρ_w = 1000 kg/m³). The canvas shows the model waterline; each table row uses a noisy reading of f.
Fresh water: ρ_w = 1000 kg/m³
Sphere radius R = 0.12 m (fixed for this lab).
Each reading adds a noisy estimate of the submerged volume fraction f; density is computed as ρ = ρ_w·f. Take ≥5 readings and use the mean.
Measurements
| № | Submerged fraction f | Density estimate ρ kg/m³ | |
|---|---|---|---|
| No measurements yet — take your first reading. | |||
Data processing
Lab report
Opens the system print dialog — choose “Save as PDF” or your printer. Header and footer are hidden when printing.
Archimedes' Principle: Density of a Solid (Floating Sphere)
Generated: 22 Apr 2026, 03:33
Goal
Determine the unknown mass density of a homogeneous solid sphere that floats in fresh water (ρ_w = 1000 kg/m³) using the equilibrium relation ρ/ρ_w = V_submerged / V_total.
Measurement table
| # | Submerged fraction f | Density estimate ρ (kg/m³) |
|---|---|---|
| No measurements yet — take your first reading. | ||
Fit and derived value
Add at least 2 trials to compute the sample mean.
Conclusion
The mean density agrees with the reference value within tolerance. Main uncertainties: reading the submerged fraction, assuming pure fresh water, and treating the sphere as perfectly homogeneous.
PhysSandbox virtual lab — values come from your session; add your own discussion of error sources.
Conclusion
The mean density agrees with the reference value within tolerance. Main uncertainties: reading the submerged fraction, assuming pure fresh water, and treating the sphere as perfectly homogeneous.