ARCHIMEDES' PRINCIPLE

BUOYANCY & DISPLACED FLUID EXPERIMENT

Experiment Mode:

ARCHIMEDES' PRINCIPLE

READY (ABOVE TANK)
Weight (W = mg)
Buoyant Force (FB = ρfVsubg)
Spring Scale Tension (T)
BUOYANT FORCE (FB) 0.00 N
WEIGHT (W) 0.00 N
ℹ Place and release object to verify Archimedes' Principle.

Experiment Presets

Physical Parameters

Mode 1: Vary Mass
kg
0.1 kg 5.0 kg 10.0 kg
m³ (4.0 L)
0.001 m³ (1 L) 0.005 m³ (5 L) 0.010 m³ (10 L)
Calculated Object Density (ρobj = m/V): 500.0 kg/m³ Lighter than fluid (Floats)
kg/m³
500 (Oil) 1000 (Water) 1500 kg/m³
m/s²

Live Telemetry Measurements

LIVE
Object Mass (m)
2.00 kg
Object Volume (V)
0.0040 m³
4.00 L
Object Density (ρobj)
500.0 kg/m³
Fluid Density (ρfluid)
1000.0 kg/m³
Displaced Volume (Vdisp)
0.0020 m³
2.00 L
Submerged Fraction
50.0 %
Weight (W = mg)
19.62 N
Buoyant Force (FB)
19.62 N
Net Force (Fnet = FB - W)
0.00 N
Equilibrium State
FLOATING

Experimental Observation Table

Record and analyze experimental trials across different mass, volume, and fluid densities.

# Mode Mass (kg) Volume (m³) ρobj (kg/m³) ρfluid (kg/m³) Vdisplaced (L) Weight (N) Buoyant Force (N) Net Force (N) State Action
No readings recorded yet. Click "Add Current Reading" after releasing an object into fluid.

Guided Laboratory Procedure

  1. Select Experiment Mode: Choose Mode 1 (Vary Mass), Mode 2 (Vary Volume), or Mode 3 (Vary Fluid Density).
  2. Choose Presets or Custom Values: Select a material (e.g. Wood, Plastic, Aluminum) or fluid preset (Water, Oil, Seawater).
  3. Adjust Physical Parameters: Fine-tune mass (m), volume (V), and fluid density (ρfluid) using the sliders.
  4. Observe Object Density: Check ρobj = m / V. Predict whether ρobj < ρfluid (Floats), ρobj = ρfluid (Neutrally Buoyant), or ρobj > ρfluid (Sinks).
  5. Place Object: Click Place Above Tank to attach object to the suspended digital hoist scale.
  6. Release Object: Click Release Object to submerge it into the liquid.
  7. Observe Liquid Displacement: Watch the main tank fluid level rise and overflow into the adjacent graduated measuring cylinder.
  8. Analyze Forces: Observe the force vectors (Weight W ↓ vs Buoyant Force FB ↑).
  9. Verify Archimedes' Principle: Confirm that the weight of the displaced fluid equals the buoyant force (FB = ρfluid · Vdisp · g).
  10. Record Data: Click Add Current Reading to log trial metrics in your observation table.

Working Principle & Mathematical Formulation

1. Archimedes' Principle

"Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object."

FB = mdisplaced fluid · g = ρfluid · Vsubmerged · g

2. Conditions of Equilibrium

  • Floating (ρobj < ρfluid): Object settles at partial submerged volume fraction:
    Vsubmerged / Vtotal = ρobj / ρfluid
    Here FB = W, and net vertical force is zero.
  • Neutral Buoyancy (ρobj = ρfluid): Object stays suspended at any depth since FB = W when fully submerged.
  • Sinking (ρobj > ρfluid): Weight exceeds maximum possible buoyant force (W > FB,max). The object sinks to the bottom where normal force N = W - FB establishes equilibrium.

3. Apparent Weight in Fluid

When an object is immersed, its apparent weight measured by a submerged scale or hanging tension is:

Wapparent = W - FB = (mobj - ρfluid Vsub) · g

4. Real-World Applications

🚢 Cargo Ships & Hull Design ⚓ Submarines (Ballast Tanks) 🧪 Hydrometers (Fluid Density Testing) 🎈 Hot Air Balloons 🧊 Icebergs (10% Above Water)