Key Concepts: Density, Volume, Energy, and Error Analysis

Density ρ = m / V; density is a property of a substance; for water, ρ_water is constant under given conditions.
If mass changes for a fixed density, volume changes proportionally to keep ρ constant: ρ = m / V remains the same as m and V vary.
If ρobject > ρwater, the object sinks; if ρobject < ρwater, it floats.
1 cm³ = 1 mL (cm³ and mL are equivalent for volume).

Regular-shaped object: V = L × W × H; units in cm³ or m³ as appropriate.
Irregular-shaped object: use displacement method; Vdisplaced = Vfinal − Vinitial; ρ = m / Vdisplaced.
Do not rely on dissolution or non-displacement methods for volume measurement of irregular shapes.

Work: $W = F \cdot d$ .
Energy transfer during a fall: potential energy converts to kinetic energy as the object moves downward.
Kinetic energy: $KE = \tfrac{1}{2} m v^2$ ; Potential energy: $PE = m g h$ .

KE is energy of motion; PE is energy of position; they are related during motion but are distinct forms.

Accuracy: closeness of a measurement to the true value.
Percent error: \%
Error = \left| \frac{E{exp} - E{true}}{E_{true}} \right| \times 100\%.
Precision: reproducibility of measurements; assessed by standard deviation.
Standard deviation (population): $\sigma = \sqrt{\frac{1}{n} \sum<em>{i=1}^n (x</em>i - \bar{x})^2}$ .
Note: some contexts use denominator (n−1) for sample SD; here, division by n reflects the teaching approach.
Errors can be systematic (instrument bias, calibration issues) or random (fluctuations); uncalibrated instruments yield reproducible but biased results.
In lab discussions, identify whether errors are more systematic or random; report percent error and SD; discuss implications for precision and accuracy.

Discuss sources of error in the conclusion section; assess impact on results and overall data quality.
Ensure consistent units and appropriate significant figures in reported results.