# Relationship between Mass and Weight

There is a fundamental relationship between mass and weight. The fundamental property of any object is mass, which is a numerical measure of its inertia. This is a fundamental measure of the matter in an object. The definitions of mass often appear to be circular due to the fact it is hard to explain something when it can be defined in the terms of something else.

Mechanical quantities are termed in three quantities, in terms of mass, length, and time. The symbol for mass is m and the SI unit is in kilograms. Mass is normally considered to be a property which never changes. However, if an object speeds toward the speed of light, relative mass should be taken into consideration.

The weight of an object can be defined as gravitational force on an object, and is calculated as mass time acceleration of gravity. The scientific formula can be written as w=mg. The SI unit is the newton.

Any object in free fall, so that that only the natural force of gravity, expresses weight with regard to Newton’s second law. One question often posed is the question of why you multiply mass times free fall acceleration when the mass is at rest on the table, floor, etc. The ‘g’ value allows you to determine the net result of gravitational force if it were in free fall, and that is another way to define the weight. Weight may also be expressed as a measure of of the intensity of a gravity field in Newtons/kg at your particular location. The weight or the measure of mass in kg times the intensity of the gravity field, which is normally 9.8 Newtons/kg.

On the surface of the earth, where g=9.8 and m=s2, the weight of the mass kg is Newtons, and the weight of mass slugs is pounds.

The SI unit of mass is the kilogram and used universally as a standard mass unit. The SI unit associated with force and weight is the Newton, with 1kg weighing 9.8 Newtons under normal conditions. In the United States, the most used unit is the pound. The mass unit has an inconvenient and large measuring unit known as a “slug.” The use of SI units only and avoidance of a slug is the accepted scientific method,

The weight of a person is determined by mass and the acceleration of gravity. Your perceived weight as standing on the floor or being held up by other weight. If you are in free fall then you are weightless, but your mass, which is often misrepresented as weight is the same.

Sources:

http://www.nyu.edu/pages/mathmol/textbook/weightvmass.html

http://en.wikipedia.org/wiki/Mass_versus_weight

http://www.engineeringtoolbox.com/mass-weight-d_589.html