# Internal and external forces

When a person lifts a book while standing on the earth's surface. Why is his force considered external to the book-earth system? Isn't his force internal like the case of the forces that cause the exploson of a bomb. I think the forces the person exerts on both the book and the earth are internal since they are equal but opposite therefore resulting in the position of the centre of mass of the system being maintained and if i'm right is the mechanical energy of the system constant? Am i wrong? Please correct me.

• hint-the categorization of internal/external is dependent on the 'system' taken -in the book -earth system the agency is external and it does some positive work such that the total mechanical energy of the book changes Aug 11 '18 at 22:34

It all depends on what you define the system to be. If your system only consists of the book and the earth, then any force you supply is external. If you include yourself as part of the system, then your force is internal. If your system is just you and the book, then gravity is an external force.

Forces being internal or external has nothing to do with what they physically are and everything to do with how the system is subjectively defined (see drvrm's answer to understand the reasoning one would consider in this subjective decision).

• But does the earth-book system accelerate if the man is excluded from the system? Aug 12 '18 at 7:31
• @Energy No matter what the labels, all forces are still present. If the man lifts the book, both the book and the earth feel a force. They are both pushed away from each other. The book just moves way more than the earth due to its small mass. Aug 12 '18 at 12:38

I think the forces the person exerts on both the book and the earth are internal since they are equal but opposite therefore resulting in the position of the centre of mass of the system being maintained and if I'm right is the mechanical energy of the system constant? Am I wrong? Please correct me.

The importance of categorizing a force as being either internal or external is related to the ability of that type of force to change an object's total mechanical energy when it does work upon an object.

When net work is done upon an object by an external force, the total mechanical energy (KE + PE) of that object is changed.

If the work is positive work, then the object will gain energy. If the work is negative work, then the object will lose energy.

The gain or loss in energy can be in the form of potential energy, kinetic energy, or both. Under such circumstances, the work that is done will be equal to the change in mechanical energy of the object. Because external forces are capable of changing the total mechanical energy of an object, they are sometimes referred to as non-conservative forces.

When the only type of force doing net work upon an object is an internal force (for example, gravitational and spring forces), the total mechanical energy (KE + PE) of that object remains constant. In such cases, the object's energy changes form.

For example, as an object is "forced" from a high elevation to a lower elevation by gravity, some of the potential energy of that object is transformed into kinetic energy. Yet, the sum of the kinetic and potential energies remains constant.

When the only forces doing work are internal forces, energy changes forms - from kinetic to potential (or vice versa); yet the total amount of mechanical energy is conserved. Because internal forces are capable of changing the form of energy without changing the total amount of mechanical energy, they are sometimes referred to as conservative forces.

Another classic example of this is that you cannot grab yourself by the hair and lift yourself up off the ground. That is because your hand is part of your body. So you cannot really create a system where your hand is external to the rest of your body. Of course, you could define the system to be your body minus your hand and say your hand is external to this system.

But when your hand pulls on your hair, your hair will pull back on the hand. And since your whole body is connected, ultimately, there will be no acceleration of the centre of mass of the hand-body system. But someone else could grab you by the hair and pull you up off the ground.

ref.-

• @ drvm: ok, but from your link it says that external forces also cause an acceleration: i am assuming that the accelaration being refered to is that of the system or in other words ; the centre of mass of the system. If we imagine a person lifting the book it seems like the centre of mass of the system does not change position since the person displaces the earth with his feet and the book with his hands there by apply eaual and opposite forces at both ends like an interaction. Therefore the system does not accelerate. Is my reasoning ok or am i lost? Aug 12 '18 at 6:46
• I think if the agency i.e. the man- book-earth all three are taken as a system, then no forces external to the system can be visualized. Aug 12 '18 at 7:13

Your confusion might well arise because of certain (erroneous) simplification which are made when these ideas are introduced in elementary Physics courses.
The system is assumed (although not necessarily stated) to be the book and so the force that your hand is exerting on the book is external to the system.
The work done by that force is then equated to the gain in gravitational potential energy of the book.
This type of analysis provides the “correct” result because the mass of the Earth is so much greater than the mass of the book.
It also ignores the important fact that gravitational potential energy is stored in the book and Earth system.

The mechanical energy of the system is the sum of kinetic energies and potential energies.
Any forces associated with potential energy must be conservative.

An external force originates from outside a system whereas an internal force originates from within a system and must always have a Newton third law pair which is equal in magnitude and opposite in direction.

To simplify the discussion let us assume that the book is going to be raised by an initially compressed, massless (ideal) spring and initially everything is at rest.

Let the system be the book, the spring and the Earth and consider what happens if the spring is allowed to expand.
In such an instance spring potential energy will be converted into kinetic energy of the book and the Earth and gravitational potential energy of the system.
The mechanical energy of the system will remain unchanged as the decrease in spring potential energy will equal the increase in kinetic energy and gravitational potential energy.
All relevant forces are internal and conservative.

If the system is only the book and the Earth then the forces exerted on the book and the Earth by the spring are external forces.
Those external forces do work on the system wrist the spring expands and the mechanical energy of the system increases because the gravitational potential energy (and the kinetic energy) increase.

Now assume that the spring is immersed in treacle ie when the spring expands non-conservative frictional force are acting between the spring and the treacle.

With the book, spring and treacle and Earth as the system there will be a decrease in the mechanical energy of the system as the decrease in spring potential energy will not equal the increase in gravitational potential energy.
There will be a conversion of some of the mechanical energy of the system into heat.

If the system is just the book and the Earth then the mechanical energy of the system increases.

Now this second example with the spring in treacle can be thought of as being equivalent to the bomb that you mentioned with the spring potential energy being replaced by chemical potential energy stored in the explosive (or you lifting the book with chemical potential energy stored in you) and the action of the treacle being mirrored by the production of heat during the chemical reactions.

• All the forces internal to the system come pairwise so the net force is always zero which means that no net work is done internally inside the system and the system's energy stays constant. The mechanical energy (KE+PE) also remains constant. The internal forces can be econservative and nonconservative. I guess the change between PE and KE, while the mechanical energy stays constant, is only possible if the internal forces are conservative. I am not sure how the work done by conservative forces can change PE in KE and vice versa since the net work by conservative forces is zero... Dec 6 '20 at 22:02