# Gravitational potential energy question -- Ojbect sitting on the Earth

• Vash25
In summary, the object gains kinetic energy when the Earth does work on it through the force of gravity.

#### Vash25

Good day,

If I consider my system to be an object and the earth, and the object is on the surface of the earth, then the system will have gravitational potential energy. Why couldn't I say that only the object (considering it as my system) has gravitational potential energy?

Thanks

Vash25 said:
If I consider my system to be an object and the earth, and the object is on the surface of the earth, then the system will have gravitational potential energy. Why couldn't I say that only the object (considering it as my system) has gravitational potential energy?
We often say this as an short hand, when the object is much less massive than the Earth, so when it's released the potential energy of Earth & object goes almost exclusively into the object's kinetic energy.

Vash25
Vash25 said:
Why couldn't I say that only the object (considering it as my system) has gravitational potential energy?
Leave the object where it is and move the Earth away. The object is unchanged but the potential energy changes. Therefore the potential energy does not belong to the object.

Vash25
Vash25 said:
Why couldn't I say that only the object (considering it as my system) has gravitational potential energy?
If you could say that, then you would be equally justified to say that the Earth (when considered as your system) will have the potential energy and not the object. So which is it that "has" the potential energy, the object or the Earth? The answer is neither, the potential energy belongs to the two-component Earth-object system. When the common potential energy changes, so does the kinetic energy of the system's components. The correct mechanical energy conservation to write in this case is (subscripts o = object and E = Earth) $$\Delta K_{\text{o}}+\Delta K_{\text{E}}+\Delta U_{\text{o+E}}=0.$$It's only because the Earth's vertical speed does not change noticeably over the time that the object falls, that we ignore the Earth's change in kinetic energy as commented by @A.T.

You can separate the two and consider the object as a single-component system, but you have to be careful of what you say and how. If you drop the object when it alone is your system, it does not lose potential energy and gain kinetic energy as sometimes is the claim. The dropped object gains kinetic energy because the Earth does positive work on it through the force of gravity. This positive work is equal to the loss of potential energy of the two-component system. To summarize, you can think of the transfer of energy to the object as taking place internally in the two-component system and externally in the single-component system.

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Vash25, vanhees71 and Dale

## What is gravitational potential energy?

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It is the potential for an object to do work as it moves from a higher position to a lower position in a gravitational field.

## How is gravitational potential energy calculated?

The formula for gravitational potential energy is GPE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object relative to a reference point.

## What is the reference point for gravitational potential energy?

The reference point for gravitational potential energy is often chosen to be the ground or surface on which the object is resting. However, it can also be chosen to be any point in the gravitational field, as long as it is consistent throughout the calculation.

## What happens to gravitational potential energy when an object falls?

As an object falls, its height decreases and its gravitational potential energy decreases as well. This energy is converted into kinetic energy as the object gains speed. When the object reaches the ground, all of its potential energy is converted into kinetic energy.

## Can gravitational potential energy be negative?

Yes, gravitational potential energy can be negative. This occurs when the reference point is chosen to be above the object, resulting in a negative height. However, the overall energy of the system is still conserved, as the negative potential energy is offset by an equal amount of positive kinetic energy.