Openai/69297978-d39c-8002-95ab-e03f9037a6a1

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User: When two objects are at rest at each other, say a metallic sphere and the ground sphere earth system, they attract each…

When two objects are at rest at each other, say a metallic sphere and the ground (sphere earth system), they attract each other. The attraction force requires energy, where does this energy come from and where does it goes. Here energy is not changing states, since there is no motion or heat or sound, just two bodies at rest exerting forces.

Assistant: Great question — this one gets to the heart of how potential energy works in classical physics and how “forces without …

Great question — this one gets to the heart of how potential energy works in classical physics and how “forces without motion” fit into energy accounting.

Short answer

When two objects are at rest but exert gravitational (or electrostatic) forces on each other, no energy is being used or spent. A force that does not cause motion does no work, and therefore no energy transfer occurs. The “energy of attraction” is already stored in the gravitational potential energy of the configuration. Nothing is being consumed to maintain the force.

Why a force with no motion consumes no energy

Work is defined as:

W=F⃗⋅d⃗W = \vec{F}\cdot \vec{d}W=F⋅d If the displacement d=0d = 0d=0, then

W=0.W = 0.W=0. So although the sphere and Earth pull on each other, they do not use energy unless one of them actually moves and potential energy decreases.

Analogy:

A compressed spring pushes on your hand. If your hand does not move, the spring stores potential energy, but nothing is spent.

Gravity is similar: the Earth–sphere system has a certain amount of gravitational potential energy based on their separation. If the distance does not change, the energy stays stored.

Where does the “force” come from then? Is energy required to maintain it?

No. Fundamental interactions (gravity, electromagnetism) do not require fuel to keep acting. They are properties of nature encoded in the fields. They don’t continuously expend energy by “keeping the force on”.

Think of the gravitational field like this:

• It can do work if objects move.
• But it doesn’t cost anything to have the field, or to exert a steady force.

This is just like how a magnet pulls on a nail without spending energy — unless the nail moves.

Where is the potential energy located?

In the gravitational field configuration between the two bodies. For a sphere near Earth:

U=mghU = mghU=mgh This is the “stored” energy of separation. If the sphere falls, potential energy converts into kinetic energy and eventually heat/sound when it hits the ground.

If it just sits there, the potential energy is constant and nothing is happening.

But isn’t there tension? Forces? Don’t they require energy?

If the sphere is resting on the ground, the situation is:

• Gravity pulls down.
• The ground pushes up with an equal normal force.
• The sphere doesn’t move.

No net work = no energy transfer.

The forces balance each other but do not consume or release energy.

So the key idea

The presence of a force alone does not imply energy expenditure. Only changes in configuration (motion, deformation, heating, wave emission, etc.) require or release energy.

If you want the deepest answer (GR perspective)

In General Relativity:

• Objects curve spacetime.
• The curvature dictates how objects move.
• No “energy” is spent maintaining curvature.
• Potential energy arises from the geometry of the spacetime configuration.

Again, if objects are static relative to each other, the curvature does not change → no energy change.

Summary

• Two objects at rest can exert forces without any energy being used.
• Energy is only involved if motion or configuration change occurs.
• The “energy of attraction” is potential energy, not a cost of the force.
• Static forces do no work and require no energy input.

If you want, we can go deeper into:

• How this relates to field energy in electromagnetism or GR
• Why magnets don’t “run out of energy”
• How potential energy appears in quantum field theory

Just ask!