- #1
Lost1ne
- 47
- 1
Is there an important difference between total work and external work?
My knowledge would be that total work a.k.a. net work on a system would be equal to the change in kinetic energy of that system and equal to the line integral of the net force on the system dotted with the differential displacement vector over some path that would either track a single particle, if that was our defined system, or a center mass of a system of numerous particles/bodies.
Now please tell me where my thinking goes wrong:
Analyzing the spring image, we can see that the net force (always shorthand for the net external force as all internal forces in a system cancel out by Newton's 3rd Law) would equal zero. Thus, our line integral would result in a value of zero, and thus we may conclude that the spring system does not experience a change in kinetic energy. If this system was at rest before, it is at rest now. I guess I should be specific and say that the center of mass of this spring system had and maintains a non-zero speed. Sure, some of the composing parts of the spring move, but the center of mass of the spring does not accelerate.
But there are two external forces acting on this system, vectors F_1 and F_2, and when examining both of these forces, we can see that they both do positive work on this system according to the book.
Does this mean that if we were to look at the "net work" on this system without using the line-integral approach that we would find that the net work doesn't simply equal the work done by F_1 + the work done by F_2, meaning that "net work" does not necessarily equal "external work" and that there is something else that must be considered? (Internal work?)
(Now after re-examining this, I have another question: how do we define the work done by F_1 and F_2 on the spring? If the spring is our system, composed of many particles, aren't we supposed to examine the center of mass displacements of the spring? If the center of mass doesn't move, how can we claim that these forces "do positive work on the spring as they compress it"?)
I'll also post another example that may also be discussed.
My knowledge would be that total work a.k.a. net work on a system would be equal to the change in kinetic energy of that system and equal to the line integral of the net force on the system dotted with the differential displacement vector over some path that would either track a single particle, if that was our defined system, or a center mass of a system of numerous particles/bodies.
Now please tell me where my thinking goes wrong:
Analyzing the spring image, we can see that the net force (always shorthand for the net external force as all internal forces in a system cancel out by Newton's 3rd Law) would equal zero. Thus, our line integral would result in a value of zero, and thus we may conclude that the spring system does not experience a change in kinetic energy. If this system was at rest before, it is at rest now. I guess I should be specific and say that the center of mass of this spring system had and maintains a non-zero speed. Sure, some of the composing parts of the spring move, but the center of mass of the spring does not accelerate.
But there are two external forces acting on this system, vectors F_1 and F_2, and when examining both of these forces, we can see that they both do positive work on this system according to the book.
Does this mean that if we were to look at the "net work" on this system without using the line-integral approach that we would find that the net work doesn't simply equal the work done by F_1 + the work done by F_2, meaning that "net work" does not necessarily equal "external work" and that there is something else that must be considered? (Internal work?)
(Now after re-examining this, I have another question: how do we define the work done by F_1 and F_2 on the spring? If the spring is our system, composed of many particles, aren't we supposed to examine the center of mass displacements of the spring? If the center of mass doesn't move, how can we claim that these forces "do positive work on the spring as they compress it"?)
I'll also post another example that may also be discussed.