# What has no potential energy

## Potential energy: ability to do work!

There are different forms of potential energy. A body has potential energy precisely when it is in a so-called Force field is located. This can for example be a electric field or Gravitational field be.

Examples of force fields

Gravitational field our earth is a possible force field that has an impact on mass-afflicted Body has. You can tell that, for example, a ball falls to the ground and does not just float in the air. Whether the ball is electrically charged has no effect on the strength of the gravitational Attraction.

Electric field along an electrical conductor causes the electrical charges (electrons) to migrate through the conductor and make your lamp glow.

### Potential energy in the gravitational field

To get a feel for how big the gravitational potential energy a body has in the gravitational field, let's take an apple as an example. Leave out the apple 10 meters high falling into a pile of sand. Then look at the depth of the impact hole. Then throw out the apple 20 meters Height and then out 50 meters. You will find that the impact hole even more deeper is, the greater the starting height from which you threw the apple. It is intuitively clear that the apple that fell from a great height initially possessed the greatest potential energy. For example, we can describe the height above the ground briefly and easily with \ (h \). The unit of height is \ (\ text {m} \) (meter).

Another ingredient for the size of the potential energy is that Dimensions \ (m \) (stands for English word "mass"). You could do the same experiment with the apple, but always throw down a thicker apple (ie with more mass). Of course, you should always throw apples of different weights from the same height to see whether the mass has an effect You will find that the depth of the hole does not matter whether you use double the height or double the mass.

What would happen if you did the experiment with the apple on the moon? So that you can answer this question, you have to know which other physical quantities influence the potential energy in the gravitational field. From the example above it is clear that the height and the Dimensions of the body influences its potential energy, because a higher lying apple or a heavier apple does more work and thus causes a deeper hole.

They know that the gravitational force \ (F _ {\ text g} \), i.e. the force that acts on a body in the gravitational field, is the product of its mass \ (m \) and the gravitational acceleration \ (g \): where a Body above our mother earth experiences an acceleration of \ (9.8 \, \ frac {\ text m} {\ text {s} ^ 2} \). That means: Within a second, the speed of the falling body increases by a whopping \ (9.8 \, \ frac {\ text m} {\ text s} \)! On the moon, the gravitational field is weaker, which is why the bodies there are not accelerated as much. There the gravitational acceleration is just \ (1.6 \, \ frac {\ text m} {\ text {s} ^ 2} \).

How much job a body has now performed depends on the distance over which the gravitational force has acted. In the above case, the force of gravity acted on the apple over a distance of 10 meters, then 20 meters and at the end even 50 meters. The work done is "force multiplied by the distance covered", where in our case the distance is the height above the ground:

But if the apple not yet released, but kept at the height \ (h \), he has not yet been able to do any work. BUT, he could do it if he was let go! That is why we denote the formula in this case with potential energy. The apple thus has a "potential" to do the work given:

Potential energy of a body in the gravitational field

You can also read from the formula which physical unit the potential energy has: In order not to have to write this long unit for energy after every result, it is simply abbreviated with a capital \ (\ text {J} \). This letter stands for "Joule", in honor of a clever physicist.

Example: mountaineering

You drank a 0.5 liter coke bottle. On the bottle label you can read that there is \ (836 \, \ text {kJ} \) energy in this amount of cola. You would now like to do sports in order to 'burn' this absorbed energy again. Since you have just acquired the knowledge about the potential energy, you decide to go mountain climbing. So you're wondering how high do you have to climb to the top until you've 'burned' the \ (836 \, \ text {kJ} \). To do this, you use the formula for potential energy and rearrange it according to the height \ (h \):

The energy to be burned is \ (W _ {\ text {pot}} = 836 \, \ text {kJ} = 836 \ cdot 10 ^ 3 \, \ text {J} \). You also know your mass: \ (m = 60 \, \ text {kg} \). You also know the gravitational acceleration \ (g \) on earth: \ (g = 9.8 \, \ frac {\ text m} {\ text {s} ^ 2} \). Inserting the values ​​in gives the necessary amount \ (h \) to get rid of the energy of the cola you drink:

Have fun climbing!