# Weights

Physical size
Surname Specific weight
Formula symbol ${\ displaystyle \ gamma}$
Size and
unit system
unit dimension
SI N · m -3  = kg · m -2 · s -2 M · L −2 · T −2

The weight of a physical body , also called specific weight , formula symbol (Greek gamma ), is the ratio of its weight to its volume and therefore a related quantity . ${\ displaystyle \ gamma}$

The  DIN recommended since 1938 in the German Standards to abandon the term "specific gravity" in favor of "gravity". From 1971 to 1984 weight was also avoided in DIN 1306 . The weight is hardly used in physics today, but it is still widely used in technology, especially in geotechnology . The density of a body, from which the specific gravity can be derived, is preferred .

## definition

The weight of a material is its weight in relation to its volume : ${\ displaystyle F _ {\ text {G}}}$${\ displaystyle V}$

${\ displaystyle \ gamma = {\ frac {F _ {\ mathrm {G}}} {V}} = {\ frac {m \, g} {V}} = \ rho \, g}$

With

• the crowd ${\ displaystyle m}$
• the acceleration due to gravity ${\ displaystyle g}$
• the density .${\ displaystyle \ rho}$

The unit of the weights is:

${\ displaystyle [\ gamma] = {\ frac {\ mathrm {N}} {\ mathrm {m} ^ {3}}} = {\ frac {\ mathrm {kg} \ cdot \ mathrm {m}} {\ mathrm {m} ^ {3} \ cdot \ mathrm {s} ^ {2}}} = {\ frac {\ mathrm {kg}} {\ mathrm {m} ^ {2} \ cdot \ mathrm {s} ^ {2}}}}$

## Dependencies

The weight acting on a body of mass is proportional to the gravitational acceleration : ${\ displaystyle m}$${\ displaystyle g}$

${\ displaystyle F_ {G} = m \ cdot g}$

Thus the value of the specific gravity of a material depends on the strength of gravity , e.g. B. the value of the specific gravity on the moon is only about 1/6 as large as on the earth's surface . On earth, too, gravity differs depending on the location: the acceleration due to gravity at the North Pole is half a percent greater than at the equator due to the flattening of gravity , and it is also smaller on a mountain than at sea ​​level .

The value of the weight depends not only on the type of material, but also on the location. This is in contrast to density , which only depends on the mass and volume of the body under consideration: ${\ displaystyle \ rho}$

${\ displaystyle \ rho = {\ frac {m} {V}} = {\ frac {\ gamma} {g}}}$

The temperature and the ambient pressure of a sample also have an influence on the value of the specific gravity, as the volume of the sample changes due to thermal expansion or pressure increase. This is also the case with density.

In order to obtain a clear value for the specific gravity of a material despite these dependencies, it is common practice to relate its value to standard conditions for acceleration due to gravity, pressure and temperature.