mass and weight
mass
mass is a measure of the quantity of matter in an object at rest relative to the observer. it is measured in kilograms (kg). mass does not change with location – an object has the same mass on earth as on the moon.
weight
weight is a gravitational force on an object that has mass. it is measured in newtons (n). weight depends on the gravitational field strength at that location – an object weighs less on the moon than on earth.
gravitational field strength
gravitational field strength (g) is defined as the gravitational force per unit mass. use the equation:
g = W / m
where g is gravitational field strength (n/kg or m/s²), w is weight (n), and m is mass (kg).
connection to acceleration
gravitational field strength is equivalent to the acceleration of free fall. on earth, g ≈ 9.8 n/kg, which means a freely falling object accelerates at 9.8 m/s².
varying gravitational field strength
on the moon, g ≈ 1.6 n/kg. this is why objects weigh about 1/6 of their earth weight on the moon, even though their mass stays the same.
calculating weight
rearranging the equation gives:
W = mg
this shows that weight is mass multiplied by gravitational field strength. on earth, a 1 kg object weighs about 9.8 n.
comparing mass and weight
a balance compares masses by balancing an object against standard masses. it works because both sides experience the same gravitational field. this means you can use a balance to compare masses anywhere, even on the moon.
a note on terminology
in everyday language, people often use "weight" to mean mass (e.g., "i weigh 60 kg"). in physics, this is incorrect. mass is measured in kg, weight is measured in n.
key equations
g = W / m(gravitational field strength)W = mg(weight)
weight as a gravitational field effect (supplement)
weight is the effect of a gravitational field on a mass. any mass creates a gravitational field around it. the strength of that field depends on the size of the mass and the distance from it. when you stand on earth, you feel your weight because earth's gravitational field pulls you toward its center.