Potential energy of gravity

In summary: Gaining muscle requires energy to be expended and the energy needed to do this is typically supplied by an external force. In the case of gravity, the external force is the person's muscles working against the force of gravity.
  • #1
Antiphon
1,686
4
Frankly, I think gravity should be repulsive force on the basis of a simple energy argument which I will now make. I request anyone with insight to find the flaw in my argument. (there has to be one since I think we'd all agree that gravity is an attractive force.)

One way to compute forces is to take a differential of a field energy along some spatial displacement. The force will point in the direction that decreases the energy of the field. Simple example: two electrons near one another. If you integrate the energy of the electrostatic fields through space 1/2*epsilon*E^2 in MKS units, you'll find that there is less energy in the field if the electrons are further apart. Therefore the force they experience is repulsive.

Why is this not the case for gravity? By this reasoning, masses should repel one another.

What am I missing?
 
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  • #2
What is the energy density of the gravitational field?
 
  • #3
DaleSpam said:
What is the energy density of the gravitational field?

Good question. But there has to be one otherwise lifting weights at the gym wouldn't build muscles, right?
 
  • #4
Using a field argument to claim that a force should be opposite to what is observed seems backwards. Isn't a field essentially a mathematical construct for describing the force that a body would feel at every point in a space?
 
  • #5
johng23 said:
Using a field argument to claim that a force should be opposite to what is observed seems backwards. Isn't a field essentially a mathematical construct for describing the force that a body would feel at every point in a space?

Yes.

I found a thread with a good review of the question at https://www.physicsforums.com/showthread.php?t=316784&page=3

I'm comfortable with a negative energy density in the gravitational field as the origin of it.
 
  • #6
Antiphon said:
Good question. But there has to be one otherwise lifting weights at the gym wouldn't build muscles, right?
Building muscles requires a force, not necessarily a conservative force that would be associated with an energy density and a conserved energy.
 

1. What is potential energy of gravity?

Potential energy of gravity is the energy possessed by an object due to its position in a gravitational field. It is the energy that an object has the potential to convert into other forms of energy, such as kinetic energy, if it were to fall or move in the direction of the gravitational force.

2. How is potential energy of gravity calculated?

The potential energy of gravity is calculated by multiplying the mass of an object by the acceleration due to gravity (9.8 m/s²) and the height of the object above the ground. The equation is PE = mgh, where PE is potential energy, m is mass, g is acceleration due to gravity, and h is height.

3. Can potential energy of gravity be negative?

Yes, potential energy of gravity can be negative. This occurs when an object has a negative height or is in a position where it has less potential energy than its zero position, such as when it is in a hole or below ground level.

4. How does potential energy of gravity affect an object?

The potential energy of gravity affects an object by determining how much energy it has stored due to its position in a gravitational field. This energy can be converted into other forms of energy, such as kinetic energy, when the object moves or falls. The higher the potential energy of gravity, the greater the force of gravity acting on the object.

5. What is the relationship between potential energy of gravity and mass/height?

The potential energy of gravity is directly proportional to both the mass and the height of an object. This means that the greater the mass or height of an object, the greater its potential energy of gravity. For example, a heavier object at the same height will have more potential energy of gravity than a lighter object.

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