Mass and weight

The mass is an intrinsic (fundamental) property that every object has and is a measure for the amount of matter the object contains. In normal conditions (not relativistic), the mass is constant. Usually it is denoted by m (or M), and the measure (unit) is kilograms.

The weight of an object is a measure of the gravitational force acting on the object. It is defined as w = mg, where m is the mass of the object and g is the gravitational acceleration. Since it is essentially a force, the wight is measured in units of force – newtons (1 N = 1m kg/ s2).

To clarify the difference between mass and weight, let us consider an astronaut who is soon going on a mission to the Moon. While the astronaut is still on Earth, his colleagues measured their mass to be 100 kg. With Earth’s gravity being 9.8 m/s2, the weight of the astronaut will be 980 N.

After landing on the Moon, the astronaut’s mass will still be 100 kg. However, the Moon’s gravitational acceleration is only 1.6 m/s2, so the astronaut’s weight will be 162 N.

Another important difference between mass and weight is that mass is a scalar (it only has numeric value) while weight is a vector (has both numeric value and direction).

Fig. 1: Free fall versus weightlessness

We should also explain two other commonly used, yet not always understood concepts – free fall and weightlessness.

Free fall is the motion of an object SOLELY under the influence of gravity. In free fall there are NO other forces acting upon the object.

Weightlessness can be achieved when an object is not influenced by any gravitational filed. What people really mean when saying weightlessness is in fact the sense of weightlessness and can be experienced during free fall. Because during free fall upon the body acts only the gravitational force and no other forces, the feeling is of a reduced weight. In reality the weight has not changed , but since gravity is a force that can not be felt the same way as all contact forces (normal force, force of friction, force of strain, etc.) are felt, one gets that feeling of weightlessness.

A common mistake is to think that the astronauts at the International Space Station (ISS) are in a state of weightlessness because they either do not feel the Earth’s gravity, or because the gravity there is greatly reduced. Both these assumptions are wrong – the gravity at the space station can be felt just at is felt on the surface of the planet and the gravitational acceleration at the height of the station is only about 10% lower than the average value on the surface.

The real reason to feel weightless at the ISS is that the whole station, together with all instruments and astronauts in it, is in a stat of free fall. Ii falls towards the Earth under the force of gravity but without colliding with it, because the station’s tangential velocity keeps it in orbit while gravity is pulling it towards the Earth.