Experiment 5: Water Displacement — Density of Irregular Objects

How do you measure the volume of a stone? No ruler formula fits its lumps — but Archimedes' bathtub trick does: a submerged object pushes aside exactly its own volume of water. In this experiment you will use displacement to find volumes, combine them with mass to get density = mass ÷ volume, and discover why density — not weight, not size — decides whether something floats.

The physics behind the practical

Density measures how tightly matter is packed: ρ = m/V, in g/cm³ when mass is in grams and volume in millilitres (1 mL = 1 cm³). Water's density is 1.00 g/cm³, and that number is the floating referee: an object with average density below 1.00 floats, above it sinks. A steel ship floats because its average density — steel plus the air in its hull — is below water's; a steel bolt, solid all through at 7.8 g/cm³, goes straight to the bottom.

Displacement works because water is effectively incompressible and must go somewhere: lower an object in and the level rises by exactly the object's volume (for a floating object, by the volume of the submerged part — which is why the sim's floating oak block is the subtle case). Reading the level correctly matters: read the bottom of the meniscus, at eye level, before and after.

Variables and controls

In the virtual lab

Select Granite rock — 270 g and press Lower object in. The readouts show the water rise: Volume = 100 cm³, and Density = 2.70 g/cm³ with the verdict "sinks", because 2.70 > 1.00. Refill with the Refill tank button and try the Oak block — 75 g: same 100 cm³ volume, but the verdict is "floats" — density 0.75 g/cm³ — and only part of it submerges. The Steel bolt — 390 g is the extreme: it displaces only 50 cm³, so its density is 7.80 g/cm³. The Data Visualization chart plots each density against water's dashed line at 1.00 g/cm³ — everything above the line sinks, everything below floats. Log mass, volume, density and verdict for all three objects.

Hands-on: your own irregular objects

Weigh the dry object. Part-fill a graduated cylinder, read the level at the meniscus bottom, then lower the object gently on a thread — tilting the cylinder or lowering slowly so nothing splashes out. Read the new level; the difference is the volume. Repeat for each object, and dry objects before weighing so clinging water does not inflate the mass.

A worked investigation

Virtual-lab results first:

Step 1 — A hands-on stone. Mass 132 g. Water rises from 200 mL to 255 mL, so V = 255 − 200 = 55 cm³.

Step 2 — Density. ρ = 132 ÷ 55 = 2.4 g/cm³ — squarely in the stone range (2–3 g/cm³), denser than water, so it sinks; it would also sink in oil (0.9 g/cm³), which floats only objects below 0.9.

Step 3 — Uncertainty. Each jug reading is good to about ±2 mL, so the difference carries up to ±4 mL: V = 55 ± 4 cm³. Density then lies between 132 ÷ 59 = 2.24 and 132 ÷ 51 = 2.59, so report ρ = 2.4 ± 0.2 g/cm³. A narrow graduated cylinder beats a wide jug precisely because the same volume rise is a bigger, more readable level change.

Step 4 — Identification. 2.4 g/cm³ suggests common rock (granite 2.7, sandstone ~2.3) rather than metal (aluminium 2.7 is close, but its look and feel differ) — a reminder that density narrows the field; it rarely proves identity alone.

Conclusion and evaluation

Displacement gave consistent volumes and the float/sink verdicts matched density vs 1.00 g/cm³ in every case. The largest error source is reading the levels (meniscus and parallax), followed by bubbles clinging to rough objects, which add false volume, and splashing on entry, which loses water and shrinks the apparent volume. Lowering on a thread and tapping bubbles free fixes most of both. One hard limit: objects that dissolve or react with water (sugar, bath bombs) cannot be measured this way — you would need a liquid they ignore, such as oil.

Safety

Mop spills immediately — wet floors are the main hazard. Handle glass cylinders with dry hands, and never use objects that react with water or are needed sharp or electrical.

Common mistakes

• Reading the top of the meniscus, or reading from above (parallax) — both bias every volume the same way.
• Dropping the object in so water splashes out: the rise then under-measures the volume.
• Air bubbles clinging to a rough object counted as part of its volume.
• Weighing the object wet after a first dunk — clinging water inflates mass and density.
• Confusing mass with density — the 390 g bolt sinks and the 75 g block floats because density, not heaviness, decides.

Exam Experience

Question 1 — calculation [4 marks]. An irregular object has a mass of 84 g. Lowered into a cylinder, it raises the water level from 150 mL to 180 mL. Calculate its volume and density, and state whether it would float in oil of density 0.90 g/cm³.

Scoring guide:

• Volume = 180 − 150 = 30 mL = 30 cm³ [1]
• Density = 84 ÷ 30 = 2.8 g/cm³ [1]
• 2.8 > 0.90, so it is denser than the oil [1]
• It sinks in the oil (and in water) [1]

Question 2 — evaluation and design [4 marks]. A cork floats, so it cannot simply be lowered into the water to measure its volume by displacement. Describe a method to find the cork's volume (and hence its density), and identify one source of error in your method.

Scoring guide:

• Attach the cork to a dense sinker of known/measured volume, or push it fully under with a thin pin [1]
• Measure the combined displaced volume with both fully submerged [1]
• Subtract the sinker's own volume (measured separately, or negligible pin volume) to get the cork's volume; density = mass ÷ volume [1]
• Error source: air trapped under the cork, the pin's submerged length varying, or the thread absorbing water [1]

Multiple choice 1. When reading a graduated cylinder, the correct technique is to read:

• A. The top of the meniscus, from above
• B. The bottom of the meniscus, at eye level
• C. Either edge — the difference is negligible
• D. The level only after the object is removed

Answer: B. The bottom of the meniscus at eye level avoids the systematic parallax and meniscus errors that bias every reading the same way.

Multiple choice 2. A steel ship floats even though steel has density 7.8 g/cm³ because:

• A. Steel becomes less dense when shaped into a hull
• B. The ship's average density, including the air inside the hull, is less than water's
• C. Water's density increases under a large ship
• D. Ships are held up by their engines

Answer: B. Floating is decided by average density: hull steel plus enclosed air averages below 1.00 g/cm³, so the ship displaces its weight of water before it is fully submerged.

Going deeper: density at work

Density earns its keep far beyond this tank. A hydrometer — a weighted float — puts Archimedes to work measuring liquid densities (battery acid, brewing wort, aquarium salt water): it sinks until it displaces its own weight, and the scale reads higher on the stem in thinner liquids. Floating fractions are the same law in disguise: a floating object submerges exactly the fraction ρ_object/ρ_fluid of its volume. Your oak block (0.75 g/cm³) floats with 75% of its volume underwater and 25% showing; an iceberg at 0.92 g/cm³ in seawater (about 1.03 g/cm³) hides 0.92/1.03 ≈ 89% of itself below the surface — the literal tip-of-the-iceberg ratio that ships respect.

Try the displacement method once more, detective-style: a metal key of mass 68 g raises the cylinder level from 60 mL to 68 mL, so its volume is 8 cm³ and its density is 68 ÷ 8 = 8.5 g/cm³ — a match for brass, and a clean exclusion of aluminium (2.7) and steel (7.8). Two cautions before you trust such identifications. First, the two meniscus readings each carry ±1 mL, so the 8 cm³ difference carries about ±2 cm³ — a 25% uncertainty that makes 8.5 "consistent with brass" rather than a proof; a bigger sample tightens it. Second, a hollow object defeats the method cheerfully: displacement measures the *outside* volume, so a sealed empty shell reports the density of shell-plus-air. Archaeologists, assayers and scrap dealers have all been fooled by exactly that — measure, but know what your measurement actually measured.

One more angle: floating in other liquids

The floating-fraction rule (fraction submerged = ρ_object ÷ ρ_fluid) travels to any liquid. A block of density 0.85 g/cm³ floats in water with 85% submerged; floated in cooking oil (0.90 g/cm³) it rides lower — 0.85 ÷ 0.90 = 94% submerged, nearly awash — and in a dense brine (1.20 g/cm³) it bobs high with only 71% under. Same block, three freeboards: that is the whole principle of the hydrometer and of loading marks on ships' hulls (the Plimsoll line exists because a ship floats deeper in fresh water than in salty). Your tank, a block and three liquids reproduce a law that maritime safety is built on.