# Forces and Energy

Which is more fundamental in physics? The concept of energy, or the concept of force?
I know the word "axiom" is reserved for mathematics, but what are the "axioms of classical physics", for the lack of a better word?
While both concepts are mathematically equivalent, it seems to me that the concept of force is usually taught in introductory physics classes before the concept of energy. Is this because the notion of "force" is more intuitive than that of "energy" (an easier transition from basic kinematics perhaps)?

A.T.
Which is more fundamental in physics? The concept of energy, or the concept of force?
Energy is more general.

Drakkith
Staff Emeritus
While both concepts are mathematically equivalent, it seems to me that the concept of force is usually taught in introductory physics classes before the concept of energy. Is this because the notion of "force" is more intuitive than that of "energy" (an easier transition from basic kinematics perhaps)?

I think force is typically easier to understand. Everyone intuitively understands that you need to apply a force on something to make it move and objects don't just move by themselves for no reason. Most people have no idea what energy really is though. It's more of an abstract idea, but one that can be used in a lot of different areas, including places where force can't or where it is simply too hard to calculate the end result using forces.

• PFuser1232
Andrew Mason
Homework Helper
Which is more fundamental in physics? The concept of energy, or the concept of force?
I know the word "axiom" is reserved for mathematics, but what are the "axioms of classical physics", for the lack of a better word?
While both concepts are mathematically equivalent, it seems to me that the concept of force is usually taught in introductory physics classes before the concept of energy. Is this because the notion of "force" is more intuitive than that of "energy" (an easier transition from basic kinematics perhaps)?
In the evolution of physics, the concept of "force" preceded the concept of energy by at least 200 years. Furthermore, energy is defined as the ability to do work and "work" is defined as the application of a force through a distance. Physicists speak about the four fundamental "forces" of nature, not the fundamental energies of nature. So for those reasons one could argue that "force" is the more fundamental concept.

However, when you are dealing with quantum physics and the interactions of photons and matter particles, the concept of force is more difficult. The concept of "force" requires "mass". Since photons lack mass, it is difficult to apply the concept of force in interactions of matter with photons. But one can speak of the energy (and momentum) of any kind of particle, including those that lack mass.

So, I would say that the answer to your question depends on the level at which you are studying or applying physical concepts.

AM

A.T.
In the evolution of physics, the concept of "force" preceded the concept of energy by at least 200 years.
Which would suggest that energy is more fundamental. Usually we discover some specific laws, and then strive to unite them based on some more fundamental law.

Physicists speak about the four fundamental "forces" of nature
That merely means that these four are the most fundamental among all forces. It says nothing about whether they are more fundamental than enegy.

However, when you are dealing with quantum physics...
Even classical mechanics can be done using the Lagrangian formalism, which is not based on forces, like Newtonian mechanics, but still involves energy as a key element. This also suggests that energy is more general.

• Apoorv3012
Andrew Mason
Homework Helper
Which would suggest that energy is more fundamental. Usually we discover some specific laws, and then strive to unite them based on some more fundamental law.

That merely means that these four are the most fundamental among all forces. It says nothing about whether they are more fundamental than enegy.

Even classical mechanics can be done using the Lagrangian formalism, which is not based on forces, like Newtonian mechanics, but still involves energy as a key element. This also suggests that energy is more general.

These are all fair points. My point is that there is no definitive answer to this question.

AM

A.T.
My point is that there is no definitive answer to this question.
I agree with that point.

energy is a function of state of any system. When there is a change in state of the system, its energy changes. We attribute this change in energy to a physical quantity---force. Force is much easier to understand obviously, but in harder problems, it gets too tedious to work with vector components and stuff. That's when we actually realise the use of energy as a parameter to solve the system. Energy is more fundamental.

I agree with that point.
I agree with you mate. If we stop talking about what is taught first but what is more fundamental then the answer is very clearly energy.

The idea of force is actually very absurd (in a way) and it actually is an extention of energy. Let me point out a contradiction.
The terms "work" and "energy" both are used to describe each other, while work is basically nothing but energy. We use force just because it can be easily measured, force is produced when we are spending the energy of a system.
I personally view force as my energy spent, unrelating the concept of force from kinetics and Newton's law of motion. This gives a kind of relation between force and energy.
Also swallowing of the definition of "work" has been always a little bitter for me, all it tells us is multiply force and displacement w/o any physical interpretation.

Actually some of my ideas on force and energy vanished out of my mind and not able to recall, I pondered over it a week ago. Please add someting to my POV. Thank you.

Andrew Mason
Homework Helper
The idea of force is actually very absurd (in a way) and it actually is an extention of energy. Let me point out a contradiction.
The terms "work" and "energy" both are used to describe each other, while work is basically nothing but energy.
Work, or the application of a force through a displacement, is a dynamic process by which energy is transferred from one body to another. A body can possess energy (potential or kinetic). But if it transfers that energy to another body, work must be done.

We use force just because it can be easily measured, force is produced when we are spending the energy of a system.

I personally view force as my energy spent, unrelating the concept of force from kinetics and Newton's law of motion. This gives a kind of relation between force and energy.
Are you sure about that? Do you exert a force on your bed when you sleep? Do you expend energy applying this force?
Also swallowing of the definition of "work" has been always a little bitter for me, all it tells us is multiply force and displacement w/o any physical interpretation.
Work is the application of a force over a distance. How does that not, in itself, provide a physical interpretation of what work is?

AM

• Apoorv3012
Work, or the application of a force through a displacement, is a dynamic process by which energy is transferred from one body to another. A body can possess energy (potential or kinetic). But if it transfers that energy to another body, work must be done.

Are you sure about that? Do you exert a force on your bed when you sleep? Do you expend energy applying this force?
Work is the application of a force over a distance. How does that not, in itself, provide a physical interpretation of what work is?

AM
Actually I read multiple threads over this and I leaned that you are right, when a system reaches a state of energy (like me on bed) then it doesn't need any energy for any exerted force (normal force and gravitational pull), but if a system's energy is to change then expenditure or gain of energy is required which is done by doing work on that system. Thank you for reply.

gmax137
... Also swallowing of the definition of "work" has been always a little bitter for me, all it tells us is multiply force and displacement w/o any physical interpretation

If you carry a load of bricks from the street up to the roof, the "work" you do on the bricks depends on
(1) how heavy the bricks are (force) and
(2) how high up is the roof (distance).

That's pretty "intuitive," at least to me.

If you carry a load of bricks from the street up to the roof, the "work" you do on the bricks depends on
(1) how heavy the bricks are (force) and
(2) how high up is the roof (distance).

That's pretty "intuitive," at least to me.
Yes now I get the intuition but it was given very bluntly in my book, but why do we give it a fancy name as work although we can substitute it with gain in energy or expenditure of energy.

Andrew Mason
Homework Helper
Yes now I get the intuition but it was given very bluntly in my book, but why do we give it a fancy name as work although we can substitute it with gain in energy or expenditure of energy.
"Work" is easier to use than "gain or expenditure of energy". Besides, work is not exactly "gain or expenditure of energy". Rather the gain or expenditure of energy of a body is equal to the work done on or by the body.

The difference between work and energy is subtle but important. Energy is a quantity that is always conserved in interactions between bodies, which is to say that it is the same, in total, before and after a process occurs. Work is the measure of the flow of mechanical energy between bodies during the interaction. Unlike energy, work is NOT an attribute of a body.

The first law of thermodynamics expresses the conservation of energy by relating the change in energy of a system resulting from a thermodynamic process to the energy flows during the process:

##\Delta U = Q + W##

##\Delta U## is the difference in Energy of the system ie. energy after the process completed - energy before process began. Q the non-mechanical work done on or by the system at the molecular level during the process (referred to as heat flow). W is the useful mechanical work done on or by the system during the process.

AM

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• Apoorv3012
Even classical mechanics can be done using the Lagrangian formalism, which is not based on forces, like Newtonian mechanics, but still involves energy as a key element. This also suggests that energy is more general.

Please someone correct me if I'm wrong, but there are forces that just can't have any lagrangian formulation associated to them.