# Every object has gravity

## Force, weight and gravity

### Gravitational force

When you hang a weight on a spring scale, it will be attracted to the earth. This pull towards the center of the earth is called gravitational force or simply gravitation.

Even particle physicists still don't know exactly what causes gravity, but here are some of its most important features:

• All masses attract each other.
• The larger the mass, the stronger the attraction.
• The closer the masses are, the stronger the attraction.

The gravity between small masses is extremely weak. It's less than \$ \ mathrm {10 ^ {- 7} \ N} \$ between you and a cat on your lap! But the earth is so massive that its gravitational pull is strong enough to keep most things firmly on the ground.

### Weight

Weight is another name for the earth's gravitational force on an object. Like other forces, weight is given in Newtons (N).

Near the earth's surface, an object with a mass of 1 kg has a weight of around 9.81 N - but that depends on the location of the measurement. For many everyday calculations one usually uses 10 N, also on this homepage. Larger masses have greater weights. Here are some examples:

### Gravitational field strength, g

The earth has a Gravitational fieldthat exerts a force on every mass in and on it. One works near the surface of the earth Gravitational force from 10 Newtons to every kilogram of mass: The gravitational field strength of the earth is thus 10 Newtons per kilogram (\$ \ mathrm {\ frac {N} {kg}} \$).

The gravitational field strength is represented by the symbol \$ g \$.
So: Weight = mass \$ \ cdot \$ g

Notation in symbols:

\$ W \ = \ m \ \ cdot \ g \$

Symbols and units:

• \$ W \$ = weight in Newtons (\$ \ mathrm N \$)
• \$ m \$ = mass in kilograms (\$ \ mathrm {kg} \$)
• \$ g \$ = gravitational field strength, \$ \ mathrm {10 \ \ frac {N} {kg}} \$ near the earth's surface

In everyday language we often use the word "weight" when it should actually mean "mass". Even scales that actually measure weight are usually divided into units of mass. But the two parachutists above "weigh" Not 100 kilograms, but have a mass of 100 kilograms and a weight of 1000 Newtons.

Example:

What is the acceleration of the rocket pictured?

To determine the rocket's acceleration, you need to know the resulting force. And to find out, you have to know how much the rocket weighs.

Weight = \$ mg \ = \ \ mathrm {200 \ kg \ \ cdot \ 10 \ \ frac {N} {kg} \ = 2000 \ N} \$

It follows:

resulting force (upwards) = \$ \ mathrm {3000 \ N \ - \ 2000 \ N \ = \ 1000 \ N} \$

But:

resulting force = mass \$ \ cdot \$ acceleration

So:

\$ \ mathrm {1000 \ N \ = \ 200 \ kg \ \ cdot \ acceleration} \$

The rearranged equation gives:

Acceleration of the rocket = \$ \ mathrm {5 \ \ frac {m} {s ^ 2}} \$

### Variable weight, constant mass

On the moon, your weight (in Newtons) would be much less than on earth because the moon's gravitational field is weaker.

On earth, too, your weight can vary slightly from place to place, because the gravitational field strength of the earth is not the same everywhere. As you move away from the earth, your weight decreases. If you were to fly deep into space and you were free from any gravitational pull, your weight would be zero.

Whether on earth, on the moon or deep in space, your body always has the same resistance to a change in movement. So your mass (\$ \ mathrm {kg} \$) does not change - at least not under normal circumstances. But...

According to Einstein's theory of relativity, the mass can also change. For example, it increases when an object accelerates. However, the change is far too small to be noticeable at speeds well below the speed of light. So for all practical purposes we can assume that mass is constant.

### Two meanings for g

The acceleration of every object can be determined with the help of the equation force = mass x acceleration (picture at the top). For example, a force of 20 N acts on the mass of 2 kg, so its acceleration is \$ \ mathrm {10 \ \ frac {m} {s ^ 2}} \$.

The result also applies to all other objects in the picture, including the two parachutists. The acceleration is always \$ \ mathrm {10 \ \ frac {m} {s ^ 2}} \$ or \$ g \$ (where \$ g \$ is the gravitational field strength of the earth, \$ \ mathrm {10 \ \ frac {N} {kg }} \$), is.

So the symbol \$ g \$ has two meanings:

• \$ g \$ is the gravitational field strength (\$ \ mathrm {10 \ \ frac {N} {kg}} \$).
• \$ g \$ is the acceleration in free fall (\$ \ mathrm {10 \ \ frac {m} {s ^ 2}} \$).