Infer liquid density without confusing it with a balance offset

Declare the fluid, reference and evidence

A fluid changes shape under sustained shear rather than supporting a fixed shear deformation like an ideal elastic solid. Liquids and gases both qualify, but an incompressible-liquid approximation treats density as unchanged across the selected pressure range. Density is mass per volume, not weight per volume. A sample can have larger mass without being a denser material.

Build the algebraic model

In this original synthetic packet the true density is 800 kg/m³, equivalent to 0.8 g/cm³. The balance adds a common offset b grams after the assumed container tare. Its reading at volume V cm³ is 0.8V+b. Dividing one reading by volume therefore gives 0.8+b/V g/cm³, which depends on sample size even though the liquid does not change.

Check the original numerical packet

Use two volumes to separate slope and intercept. At 100 cm³ with a +2 g offset the indication is 82 g; at 200 cm³ it is 162 g. Their difference divided by the 100 cm³ volume difference is 0.8 g/cm³, and the inferred offset is 2 g. Retain another volume as a check: 50 cm³ should read 42 g. That check tests this disclosed linear model; it is not independent evidence of an unknown real liquid.

Challenge the assumptions and transfer

Pressure is normal force per area, a different quantity from density. A separate 20 N normal force distributed uniformly over 4 cm² produces 50000 Pa because 4 cm² is 0.0004 m². Halving that area at fixed force doubles pressure; doubling the liquid sample volume does not by itself double its density. A common multiplicative volume calibration error would not cancel from the two-volume slope as the additive mass offset does.

Worked original case

With 150 cm³ and offset −4 g, the indication is 116 g and the one-sample density is 773.333 kg/m³. Comparing with 156 g at 200 cm³ recovers 800 kg/m³.

Bounded investigation

Compare two offsets across three volumes. Save one-sample ratios and two-volume slope estimates, reserve the third volume as a check, and identify which calibration error the method cancels and which it does not.

Changed-case numerical practice

Try the changed case before feedback

A liquid gives indicated masses 66 g at 80 cm³ and 146 g at 180 cm³, with a common additive offset. Find its density in kg/m³.

Numerical result in the requested unitsCompare this result

This practice is public and unsaved. A matching number does not verify understanding. Retain your explanation, assumptions and changed-case evidence in the separate course workspace.

Sources and limits

Original content checked 30 October 2026 against OpenStax College Physics 2e. All records are supplied or generated educational evidence. No pressure rigs, liquid handling, bodily measurements or physical exposure protocols are requested. Virtual admissibility does not certify real equipment safety, practical skill or independent mastery.