5.7:
Mass and Weight
The mass of an object is a measure of the amount of matter it contains and depends on the number of atoms in it.
Its weight is the gravitational force acting on it from a larger object, like the Earth or the Moon, whichever is nearest to it.
As the amount of matter does not change in response to the applied force, the object's mass remains constant.
However, its weight depends on its location. An object on the Earth weighs differently than that on Mars or the Moon, but its mass remains the same. The weight change is due to the difference in acceleration due to gravity acting on it.
Mass can never be zero, but weight becomes zero when gravitational force does not act on it. Using this observation and Newton's second law, an object of mass m weighs m times vector g.
That is to say, the greater the mass of an object, the greater is its weight. Mass is a scalar quantity, but weight is a vector directed towards the Earth's center.
5.7:
Mass and Weight
Mass and weight are often used interchangeably in everyday conversation. For example, medical records often show our weight in kilograms, but never in the correct units of newtons. In physics, however, there is an important distinction. Weight is the pull of the Earth on an object. It depends on the distance from the center of the Earth. Weight dramatically varies if we leave the Earth's surface, unlike mass, which does not vary with location. On the Moon, for example, the acceleration due to gravity is only 1.67 m/s2 compared to 9.8 m/s2 on Earth. Therefore, a 1.0 kg mass has a weight of 9.8 N on the Earth, but only about 1.7 N on the Moon. However, the mass of an object is the same on the Earth's surface, in orbit, or on the surface of the Moon.
When an object is dropped, it accelerates toward the center of the Earth. Newton's second law states that a net force on an object is responsible for its acceleration. If air resistance is considered negligible, the net force acting on a falling object is equal to the gravitational force, commonly known as its weight, or the force due to gravity acting on an object of mass 'm'.
Note that, although they are closely related, weight and mass are different physical quantities. Mass is an intrinsic property of an object; it is a quantity of matter. It is tempting to equate mass to weight because most of our examples take place on the Earth, where the weight of an object varies minimally with the object's location on Earth. In addition, it is difficult to count and identify all of the atoms and molecules in an object, so mass is rarely determined in this manner.
This text is adapted from Openstax, University Physics Volume 1, Section 5.4: Mass and Weight.