What is mass, and how is it different from weight?

Mass belongs to the load, not the location

Mass characterizes a body’s inertia: how difficult it is to change its velocity with a given force. Other conditions being equal, a more massive load is harder to speed up or stop. Moving the closed case to the Moon does not remove this property. If its composition and state have not changed, we should not assign it a new mass merely because it is somewhere else. NIST: mass and weight.

We denote mass by $m$m. Its SI unit is the kilogram, symbol kg. A load with a mass of 60 kg, for instance, remains a 60 kg load on the Moon. Lifting it against local gravity is easier, but the net force needed for the same change in velocity has not become six times smaller.

“Easier to hold up” and “less mass” are therefore different conclusions. The former concerns the surrounding field and the support; the latter concerns a property of the load itself.

Gravity, the support force and the support load differ

Put the suitcase on a horizontal platform. The gravitational force, usually called weight in English, acts on the case downwards. The normal reaction is the force with which the platform acts on the case upwards. We denote its magnitude by $N$N. This support prevents the case from starting to fall.

We also need the force in the opposite direction: the case pushes down on the platform. Denote the magnitude of this support load by $P$P. The platform pushes up on the case. These two contact forces have equal magnitudes but act on different bodies. The load’s magnitude corresponds to the apparent weight indicated by an ideal force scale. Ukrainian school physics uses the word for weight specifically for the action on a support or suspension; our symbols keep the physical distinction explicit. Physics textbook, §12, pp.75–76.

The support load is not an extra force pulling the case down alongside gravity. $P$P acts on the platform, whereas gravity acts on the case. Adding them as two forces on the suitcase would be a mistake. The first two drawings below separate these questions.

The Moon changes how much support is needed

When the suitcase rests on a horizontal support, the normal reaction balances gravity. The support load equals them in magnitude. In a simple local model, we write $P=mg$P = mg, where $g$g is the acceleration gravity would produce here without the support.

For our comparison, the reference values of $g$g are 9.82 m/s² for Earth, 1.62 m/s² for the Moon and 3.73 m/s² for Mars. These are rounded mean surface gravity values from NASA’s individual factsheets. They correspond to a model without rotation, rather than exact values for every city, mountain or latitude. We also neglect air buoyancy and other additional forces. NASA: Earth, Moon, Mars, parameter definitions.

On the Moon, the force needed to support the same load is about one sixth of Earth’s. The mass entry, however, must remain the same in all three places. Change the mass in the comparison and follow which numbers change with it.

Why does a household scale display kilograms?

In a force-based scale, the load compresses an elastic element or sensor. The instrument detects a contact force, while its dial or electronics can present the result as mass using a calibration for Earth conditions. A “kg” label does not turn mass into force. It means the instrument converts the measured force signal into an estimate of mass. NIST: everyday weighing and mass, OpenStax: what force scales read.

Move such an instrument to the Moon while retaining its Earth calibration, and the lower load may produce a smaller “kg” number. The suitcase has not lost material: the assumptions used to infer mass from force no longer match the conditions. Our comparison therefore shows force in newtons separately from unchanged mass. Measurement Canada: moving scales between locations.

This does not describe every way of weighing. An equal-arm balance, for example, compares a load with reference masses in the same field. Ask how the particular instrument works before interpreting the number on its scale.

Zero support load does not mean zero mass

The equality $P=mg$P = mg has conditions. If the support accelerates the object upwards, it must push harder than merely to hold it up, and the contact reading increases. During downward acceleration, the reading can decrease. Moving up or down at constant velocity does not cause this effect: the change in velocity matters. OpenStax: an elevator example.

In ideal free fall without contact support, the object and instrument fall together. The object does not press on the support, and the contact reading is zero. Its mass remains and gravity still acts. Weightlessness should therefore not be explained as the disappearance of mass or gravity. NASA: free fall and weightlessness.

Return to the suitcase: if its force reading on the Moon becomes about six times smaller, has its mass become six times smaller? No. The support force changed in a different field. A zero reading in free fall represents yet another change of conditions, rather than an emptied case.

To read a number correctly, establish three things: which quantity is measured, in which units, and under which conditions. Compare Earth and the Moon on the Solar System map. Next in the course, we will examine how forces change motion.