# Weight force

The force of gravity, and weight is caused by the effect of a gravitational field caused power to a body . In the rotating reference system of a celestial body (such as that of the earth), this gravitational field is made up of a gravitational component and a small centrifugal component. The gravitational force is perpendicular to the bottom directed what in the gravitational field of the earth almost, but not exactly the direction to the center of the Earth corresponds.

Usually or is used as a symbol . The SI unit for weight is the Newton  (N). ${\ displaystyle {\ vec {F}} _ {\ text {G}}}$${\ displaystyle {\ vec {G}}}$

## Amount, direction and point of attack

The weight force can be calculated as the product of the mass with the gravitational acceleration : ${\ displaystyle {\ vec {F}} _ {\ text {G}}}$ ${\ displaystyle m}$ ${\ displaystyle {\ vec {g}}}$

${\ displaystyle {\ vec {F}} _ {\ text {G}} = m \, {\ vec {g}}}$

Apart from minor irregularities, the weight of a body is always directed towards the center of the celestial body on which it is located, since the gravitational field is a radial field as a good approximation . In most applications, however, sufficient accuracy can be achieved if the gravitational field is viewed as a homogeneous field , namely when all dimensions are much smaller than the radius of the celestial body. In this case the weight has the same direction and strength at every location.

The trajectory of a moving rigid body runs exactly as if the entire weight force was attacking the center of gravity (center of gravity) of the body. This also applies to the movement of the center of gravity of a system of several bodies. In a homogeneous gravitational field, the center of gravity coincides with the center of mass . If the weight is the only force acting, the body or the multi-body system is in a state of free fall . Since the inertia of a body depends on the mass in the same way as the weight, the accelerations of all freely falling bodies are the same. The acceleration due to gravity does not depend on the mass or other properties of the body, but at most on its location.

## Weight on earth

The approximate value can be used for the acceleration due to gravity on the earth's surface . ${\ displaystyle g = 9 {,} 81 \, \ mathrm {\ tfrac {m} {s ^ {2}}}}$

However, if you want to determine the weight on the earth more precisely, the location dependency of the gravitational acceleration ( at the equator or at the poles) must be taken into account using gravity formulas, for example the Somigliana formula . There are various causes for this location dependency: ${\ displaystyle g = 9 {,} 78 \, \ mathrm {\ tfrac {m} {s ^ {2}}}}$${\ displaystyle 9 {,} 83 \, \ mathrm {\ tfrac {m} {s ^ {2}}}}$

1. the centrifugal acceleration caused by the rotation of the earth ,
2. the different strength of gravity due to the flattening of the earth ,
3. local gravitational anomalies .

On the earth's surface, the first two effects depend on the geographical latitude : the first, because the latitude determines the distance of the location from the earth's axis; the second, because the latitude determines the distance from the center of the earth and the exact distribution of the earth's mass in relation to the location. In addition, there is a dependence on the height of the location above the earth's surface.

## Weight and mass

In everyday language , the weight of a body is spoken of without distinguishing whether it is its mass or its weight. However, the physical terms are very different:

• The mass is a measure of how strongly a body is generally influenced by gravitational fields and how much it resists accelerations ( inertia ).
• The weight, on the other hand, indicates how strongly a body is specifically attracted to the earth or the celestial body on which it is located.

The mass is therefore an inherent property of the body, while the weight force is the result of an external influence on the body.

As a result, the mass of a body is always the same , regardless of where it is (earth, moon , weightlessness , ...), while the weight acting on it depends on the acceleration of gravity. (On the moon the weight is only about one sixth of that on earth. A body with a mass of 6 kg is therefore only as heavy on the moon as a body with a mass of 1 kg on earth)

Until 1960 it was customary to give the force in the unit kilopond  (kp). This was defined in such a way that the weight on earth, measured in kiloponds, had the same measure as the mass in kilograms ( ). After that, the kilopond in the SI system of units was replaced by the unit Newton (1 kp = 9.80665 N ≈ 1  daN ). Since then, the mass and the weight force have dimensions that are approximately around the above. Differentiating factor . ${\ displaystyle 1 \, \ mathrm {kp} = g \ cdot 1 \, \ mathrm {kg}}$${\ displaystyle 9 {,} 81}$

## Measurement

Measuring devices for the direct determination of a weight force are force gauges , for example spring balances . However, the static buoyancy falsifies the result, which is particularly noticeable with bodies of low density .

The weight force can also be determined indirectly by weighing and then converting the weight value . If you take a closer look at the functionality of a balance, you will find that the actual directly recorded measured variable is the weight force falsified by the buoyancy, even if a mass is displayed as the weighing value. For example, B. a simple beam balance the forces that the two masses exert on their respective pan.

## literature

Weight force is explained in many books that introduce mechanics. Examples are:

## Individual evidence

1. James H. Allen: Statics for mechanical engineers for dummies . John Wiley & Sons , 2012, ISBN 978-3-527-70761-4 , pp. 158 ( Google Books ).
2. Eberhard Brommundt, Gottfried Sachs , Delf Sachau: Technical Mechanics: An Introduction . 4th edition. Oldenbourg Verlag , Munich 2007, ISBN 978-3-486-58111-9 , p. 70 ( Google Books ).
3. Karlheinz Kabus: Mechanics and strength theory . 8th edition. Carl Hanser Verlag, Munich 2017, ISBN 978-3-446-45320-3 , pp. 121 ( Google Books ).