## Weight

Weight and mass are often taken to be synonymous. In fact they are very different concepts, but people are easily confused because although weight is actually a force measured in newtons and mass is the amount of matter measured in kg, people often say their weight measured in kg.

Mass is a measure of the amount of matter in an object. It is measured in kg, and is the same everywhere for a particular object wherever it is in the Universe. The weight of an object is equal to the gravitational force exerted on it. The strength of gravity varies from place to place, being dependent on the distribution of matter, so the weight of a particular object will also vary from place to place.

The weight and mass of an object are related via the strength of the gravitational field. If the strength of the gravitational field at a particular field is g, then

whereis the weight of the object at that point

is the mass of the object

is the gravitational field strength, equal to the gravitational force per unit mass. If the force of gravity between two objects of massandis given bywhereand r is the distance between the masses then the gravitational field strength at the position of massdue the the presence of massis given by

Sometimes weight is described as the force due to an acceleration. Someone on the Earth accelerating downwards under the force of gravity would have zero weight by this definition, but it must be realised that weight in this sense is the weight experienced by the body. A person falling freely under gravity would feel themselves weightless, but in fact their weight would be the force of gravity exerted on them. Similarly, a person in a lift accelerating upwards would experience an increase in weight in the sense above, in the sense that the force on their feet would increase by the amount needed for the upwards acceleration. The person in the lift illustrated below has weightfeels their own weight as the reaction of the lifton their feet.

Applying Newton's second law gives R-mg=ma rightarrow R=mg+ma.