Mass, weight and density

An astronaut does not lose matter merely by travelling to a world with weaker gravity. A gravitational force sensor would show a different reading there because it responds to force. Everyday speech often uses weight for a mass in kilograms, but an exam calculation needs the quantities and their units separated.

The value of g is force per kilogram when used in W = mg. Convert the mass to kilograms before multiplying by g in N/kg. A zero support-force reading during free fall also does not prove that gravity has disappeared: the object can still have gravitational weight while no surface is supporting it.

The cylinder's final reading contains both the original water volume and the newly displaced volume. Using that final reading directly would overestimate the object's volume and underestimate density. Lower the object gently, keep all of it below the surface and avoid losing water over the cylinder's edge.

Select a different approach if immersion changes the sample. A porous material can absorb liquid, a soluble solid can disappear into it, and a floating object displaces only part of its own external volume when left freely at the surface. State the suitability conditions instead of describing displacement as a universal method for every irregular object.

Freezing water forms a structure that occupies a larger volume for approximately the same mass. Dividing that mass by a larger volume gives a smaller density. The individual water molecules have not become larger, and the change should not be explained as water acquiring extra mass on freezing.

If a piece of ice is pushed farther below the surface and released, it displaces more water than required for balance and experiences an upward resultant force. It rises until enough of its volume is above water for the forces to balance again. The density comparison must always identify the surrounding liquid, since changing that liquid can change whether an object floats.

Density contains a mass unit above a volume unit, so both must be converted. Converting only grams would make the numerical value smaller and give the wrong unit combination. The much larger number of cubic centimetres inside one cubic metre more than offsets the mass conversion.

You can often leave a calculation in g/cm³ until the final step if both mass and volume were measured in those units. Converting every input first is valid too, but creates more powers of ten to track. Water near room temperature is about 1 g/cm³ or 1000 kg/m³, giving a useful check on the direction of conversion.

A balance's tare function can perform this subtraction before the liquid is added. Place the empty, dry container on the balance, zero the reading and then add the sample. If the container changes between the empty and filled measurements, the subtraction no longer represents just the liquid you intended to measure.

Keep liquid on the outside of the container out of the measurement: it adds mass but is not included in the cylinder's internal volume reading. Read the meniscus correctly and make sure the mass and volume refer to the same quantity of liquid, rather than weighing one portion and reading the volume of another.

A compact steel block has little external volume for its mass. Even when fully submerged, the buoyant force from the displaced water may be smaller than its weight, so it sinks. Forming steel into a hollow watertight hull changes the volume available to displace water without requiring a proportional increase in mass.

Adding cargo makes the vessel sit lower because more displaced water is needed to balance the larger weight. Flooding can fill the previously air-filled volume with water and remove the benefit of that hollow space. The explanation depends on a watertight shape and adequate displaced volume; it does not mean every metal object with an air pocket must float safely.