Mass, Weight & Density

These ideas explain how “how much stuff” an object has, how strongly gravity pulls it, and how tightly that stuff is packed.

Mass and Weight

Mass is the amount of matter in an object. It does not change if you move the object from Earth to the Moon. It is a scalar.

Weight is the force of gravity on a mass. It can change if the gravitational field changes. It is a vector.

• Mass (m): measured in kilograms (kg). Measured with a balance (compares mass).
• Weight (W): measured in newtons (N). Measured with a spring balance/force meter.
• Relationship: \, $$W = mg$$ where g is gravitational field strength in N/kg.

Gravitational Field Strength, g

Gravitational field strength is force per kilogram: $$g = \frac{W}{m}$$ On Earth, $g \approx 9.8\,\text{N/kg}$ (often taken as 10 N/kg). It is also the acceleration of free fall.

Density

Density tells us how tightly matter is packed: $$\rho = \frac{m}{V}$$ where $\rho$ is density, $m$ is mass, and $V$ is volume.

• Units: kg/m³ or g/cm³. Conversion: $1\,\text{g/cm}^3 = 1000\,\text{kg/m}^3$.
• Analogy: A suitcase packed tightly has higher density than a loosely packed one of the same size.

Measuring Density

• Regular solid (e.g., cube): measure dimensions with a ruler to find $V$, measure mass with a balance, then use $\rho = m/V$.
• Irregular solid (sinks): put it in a measuring cylinder of water; volume rises by its volume (displacement). Find mass with a balance. Then $\rho = m/V$.
• Liquid: measure volume with a measuring cylinder. Find mass by weighing the filled container and subtracting the empty container’s mass.

Floating and Sinking

• An object floats in a liquid if its average density is less than the liquid’s density; it sinks if greater.
• One liquid floats on another if it has lower density and they do not mix (e.g., oil floats on water).

Common Misconceptions

• “Mass changes on the Moon.” False: mass stays the same; weight changes.
• “Weight is measured in kg.” False: weight is a force, measured in newtons (N).
• “Bigger objects are always denser.” False: density depends on material and packing, not size.