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An example of an internal force is the tension in the spring of a harmonic oscillator. An example of an external force is the gravity on a pendulum.

Are there any forces that are both internal and external? Are the fields generated by a force field internal, external, or (if they exist) internal-external?

EDIT: My question is different from the "suggested" post because I'm asking for whether there exists a third category, while the suggested post is asking for an explanation of the difference between internal and external forces.

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    $\begingroup$ Possible duplicate of Internal and external forces $\endgroup$
    – BioPhysicist
    Commented Jan 12, 2019 at 3:16
  • $\begingroup$ If the generated force field depends on matter both inside and outside the system, is that what you mean? (I.e. the application point is dont-care) $\endgroup$
    – Emil
    Commented Jan 12, 2019 at 7:55
  • $\begingroup$ See the following link upon which my answer below was based:physicsclassroom.com/class/energy/Lesson-2/… $\endgroup$
    – Bob D
    Commented Jan 12, 2019 at 18:41
  • $\begingroup$ See ADDENDUM to my answer. $\endgroup$
    – Bob D
    Commented Jan 12, 2019 at 20:12

2 Answers 2

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Forces are forces. Whether they are “internal” or “external” has nothing to do with the type of force they are. It has only to do with where you draw the completely arbitrary boundary of “the system” being studied. If they cross that boundary, they are “external”; if they don’t, they are “internal”. A force either crosses the boundary or it doesn’t, so there are no “internal-external” forces.

The main thing to understand is that you make this distinction as part of your analysis. Nature does not.

For example, if you include the Earth in the pendulum system, the force the Earth exerts on the pendulum is an internal force and the pendulum exerts an equal and opposite force on the Earth. The effect of the pendulum on the Earth’s motion is tiny, so the Earth is usually considered “external” to the pendulum. This is simply an excellent approximation. In reality, the causally connected part of our universe is one big system.

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  • $\begingroup$ I've noticed a lot of questions regrading "reaction" forces. Is that a new pedagogical tool? Don't remember ever hearing about them. I'm in the forces are forces camp. $\endgroup$
    – JEB
    Commented Jan 12, 2019 at 3:08
  • $\begingroup$ Forces can be analyzed as internal/external but velocity cannot. Why? Can momentum be analyzed as internal/external? Why or why not? $\endgroup$
    – Fomalhaut
    Commented Jan 12, 2019 at 3:10
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    $\begingroup$ Forces are between particles. If one particle is “inside the system” and one is “outside the system”, then the force crosses the system boundary and is “external”. Velocity and momentum are properties of individual particles, not pairs of particles. They can’t cross a boundary. $\endgroup$
    – G. Smith
    Commented Jan 12, 2019 at 3:14
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    $\begingroup$ @JEB To my mind, “reaction force” is an intuitive but potentially misleading concept related to our notions of cause and effect. When you fire a gun, you feel the “reaction force” or recoil. But of course at a fundamental level this reaction force is just interatomic forces explainable using electromagnetism and quantum mechanics. $\endgroup$
    – G. Smith
    Commented Jan 12, 2019 at 3:26
  • $\begingroup$ "The main thing to understand is that youmake this distinction as part of your analysis. Nature does not." Wrong. Causal closure is the thesis that all forces are internal forces. "Forces are between particles." Wrong. A hypothetical force that changed a fundamental particle of one type into another type is not between a pair of particles. And it would be an internal force. $\endgroup$
    – Fomalhaut
    Commented Jan 12, 2019 at 4:40
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Forces can be categorized in a number of ways, external versus internal is one of the ways. One way to describe the difference between external and internal forces is the way in which the force is able to change the total mechanical energy (kinetic plus potential) of an object.

The net work done by an external force on an object can change the sum of the objects kinetic and potential energy. Positive work increases that total whereas negative work reduces the total. Examples of external forces are contact (applied) forces, tension, normal forces, and friction forces. These forces are sometimes referred to as non-conservative forces.

If the only type of force doing work on an object is an internal force, the sum of the kinetic and potential energies will be constant. Examples of internal forces are the force of gravity, spring forces, magnetic and electrical forces. These forces are sometimes referred to as conservative forces.

ADDENDUM:

First, I wish to make it clear that the above distinctions between internal vs. external forces are only one possible way to distinguish them. I completely agree with the following statement made by G. Smith:

“The main thing to understand is that you make this distinction as part of your analysis. Nature does not.”

However, if you choose to make the distinction in the way I have, the following are a couple of examples of the application of this distinction.

Gravity-

A rock of mass $m$ sits on the ground. I lift the rock to a height $h$ above the surface. The rock has acquired gravitational potential energy ($mgh$). Since I have increased its mechanical energy, the force I applied would be considered external by virtue of the distinction given. By my doing work I have transferred energy from my body to the rock.

I now let the rock go. It falls due to the force of gravity. When it reaches the ground it loses its gravitational potential energy but gains an equal amount of kinetic energy. Its total mechanical energy is unchanged. By virtue of the distinction given above, the force of gravity is an internal force.

Spring-

An ideal coil spring attached to a vertical wall has a mass attached to its free end sitting on a frictionless surface in mechanical equilibrium. I pull the mass increasing the length of the spring by $x$ from its equilibrium position. I have given the mass a potential energy of $\frac{kx^2}{2}$ by virtue of its new position on the spring relative to its original position. I have transferred energy from my body to the mass. The force I applied is external. I have increased the masses mechanical energy.

I release the mass. The mass loses its potential energy but gains an equal amount of kinetic energy so that $\frac{mv^2}{2}=\frac{kx^2}{2}$ as it passes through its original equilibrium position. There is no net change in the mechanical energy of the mass. The spring force is internal. (Of course the mass will continue to oscillate converting between kinetic and potential energy.)

Hope this further helps.

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    $\begingroup$ Any force, including conservative ones, can be considered an external force. Consider a rock falling under the influence of gravity without other forces. If the system is defined as the rock particles only, gravitational force does work on the system and changes the mechanical energy (there is nogravitational potential energy because gravity is an external force and PE belongs to a system). As @GSmith answers, internal and external are defined based on the users system definition, not on whether they have a potential energy associated with them. $\endgroup$
    – Bill N
    Commented Jan 12, 2019 at 17:49
  • $\begingroup$ @BillN Not sure I agree. If the system is defined as the rock particles only, then from the frame of reference of the rock there is no change in its mechanical (kinetic or potential) energy as it falls. There is only a change in its kinetic energy as it falls with respect to an external frame of reference, say the ground. But with respect to that frame of reference there is also a change in its potential energy and the one equals the other, i.e., no change in the total mechanical energy. $\endgroup$
    – Bob D
    Commented Jan 12, 2019 at 18:37
  • $\begingroup$ @BillN Just to conclude, I never said the characterization in my answer is the only way to forces. But I think it is a good introduction and is based on the following link: physicsclassroom.com/class/energy/Lesson-2/… $\endgroup$
    – Bob D
    Commented Jan 12, 2019 at 18:38
  • $\begingroup$ The choice of a reference frame doesn't define the size or content of a system. And the choice to use potential energy changes versus work done by conservative force interactions is independent of the reference frame. If you use work done by gravity, you don't use gravitational potential energy. $\endgroup$
    – Bill N
    Commented Jan 12, 2019 at 20:13
  • $\begingroup$ This answer and the article on physicsclassrom.com are just confused. Force being internal has nothing to do with the force being conservative. There are situations where internal forces are not conservative, such as mutual friction forces between two sliding surfaces, or electric forces between accelerating charged bodies. G. Smith's answer explains the concept of internal/external force well. $\endgroup$
    – Ján Lalinský
    Commented Jan 12, 2019 at 22:15

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