What Is the Relationship Between Internal and Conservative Forces?

[fisipavia]

I know that by definition a conservative force is a force that is independent of the path. An internal force is a force within a system. Now, the mechanical energy is conserved only when conservative forces are acting on a particular system. On the other hand some people say that it is conserved when the forces acting on the system are internal forces. From this I would think that internal energy = conservative energy. I was wondering what is the connection between the concepts of internal and conservative forces? What is the relation between the internal/external forces and conservative/non-conservative forces?
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[JohnDubYa]

Now, the mechanical energy is conserved only when conservative forces are acting on a particular system.

Not true. Non-conservative forces can act on the system, but can do no work. When a box slides across a frictionless floor, the normal force acts on the box, but does no work.

On the other hand some people say that it is conserved when the forces acting on the system are internal forces.

Nope. Two objects colliding in an inelastic collision will apply only internal forces against each other (if you define the system as both objects), but the total mechanical energy of the system is not conserved.

 

[JohnDubYa]

On the other hand some people say that it is conserved when the forces acting on the system are internal forces. From this I would think that internal energy = conservative energy. I was wondering what is the connection between the concepts of internal and conservative forces? What is the relation between the internal/external forces and conservative/non-conservative forces?

You have confused momentum with energy.

The MOMENTUM (as opposed to energy) of a system is conserved when no net external force acts on the system.

This is not the same as saying that only internal forces act on the system. Two hockey pucks sliding across a frictionless surface have external forces acting on them (hence, forces other than internal forces). But these external forces vector cancel, leaving no net external force.

The conservation of mechanical energy principle states:

The total mechanical energy of a system is conserved when no non-conservative forces do work on the system.

Make sure you understand the conservation of momentum and energy principles and how they differ.

 

[fisipavia]

Not true. Non-conservative forces can act on the system, but can do no work. When a box slides across a frictionless floor, the normal force acts on the box, but does no work.



Nope. Two objects colliding in an inelastic collision will apply only internal forces against each other (if you define the system as both objects), but the total mechanical energy of the system is not conserved.

Thanks JohnDubYa!
Exactly. Now, that was what I always have been taught. But I began to having doubts when I enter to a site (http://www.glenbrook.k12.il.us/gbssci/phys/Class/energy/u5l2a.html ) that says: " When work is done upon an object by an internal force (for example, gravitational and spring forces), the total mechanical energy (KE + PE) of that object remains constant." I guess that this is correct because it is referring to the system of only one object. Then, in your example the system would be only one object and the force acting on it by the other object would be an external force. My problem was that I was thinking in terms of systems with one or more objects and they where talking of system with only one object (or so I hope ).

 

[arildno]

fisipavia:
Thank you for providing the link.
I must warn you that the author uses the concepts "internal/external forces" in a totally non-standard way
(Basically, he seems to use "internal" to mean "conservative" and "external" to mean "non-conservative")

Now, to provide you with the standard interpretation of "internal/external forces":
These concepts are inimately related to systems of objects and Newtons 3.law of motion
(have you covered Newton's 3.law of motion yet?)

Newton's 3.law states that all forces come in couples; if object 1 imparts a force on object 2, object 2 imparts a force on object 1 of equal magnitude and opposite direction.
(action/reaction couple)

Let us consider a system of objects:
If a given force on some object in that system is imparted on that object by another object inside the system, then the force is called "internal" to the whole system.
(This means, of course, by Newton's 3.law that the reaction force on the other object is also an internal force)

If the source of a given force acting on an object in the system lies outside the system, we call the force an "external force".
Note that the reaction force in this case does not affect any part of the system (it affects some object outside the system (that is, the "original" source mentioned))

To gain some further grip on the conventional meanings, two points are of note:
a)Since the net force acting upon the C.M. of a system of objects is the sum of all forces acting on the objects making up the system, internal forces provide a zero contribution to Newton's 2.law as stated for the C.M. of the system.
In particular, if a system is only under the influence of internal forces, this implies that the momentum of the system is conseved.

b)As JohnDubya clearly stated, internal forces may well do work!
A common way is that internal forces dissipate mechanical energy into heat.

 

[JohnDubYa]

I must warn you that the author uses the concepts "internal/external forces" in a totally non-standard way
(Basically, he seems to use "internal" to mean "conservative" and "external" to mean "non-conservative")

His use of the terms internal and external is not only non-standard, it is simply wrong.

Take two objects and bounce them into each other elastically. (Say, one has a spring attached to it that collides with the other object.)

Now take the same objects and bounce them into each other inelastically. (Substitute the spring for putty.)

The author would be forced to call the spring force in the first example an internal force. But he would have to call the putty force in the second example an external force. This makes zero sense, whatsoever.

 

[fisipavia]

iuff! Thanks to both of you. I was sincerely worried. I thought I have not learn anything. I guess I need to stop doubting on me.

 

[JohnDubYa]

Yes, and start doubting others.