Sorry for the relatively long post! Thank you for reading and let me know if there is anything I can clarify/fix.
My textbooks defines Work in the following way:
- A measure of the amount of energy transferred between two systems.
- Positive work is performed by a system when the force it generates has a component in the direction of the displacement of the point of application"
Let's see if this definition makes sense in a few different examples:
Example 1: A piston
This definition makes a lot of sense in the context of a thermally insulated piston where "System 1" is the molecules inside the piston and "System 2" is the molecules outside the piston. In this example, I will speak from the perspective of the particles in the piston (System 1).
- When the air molecules of the "outside" system push the piston down, "System 1" does negative work. In other words, it absorbs kinetic energy from the "outside" particles.
- When the air molecules inside the piston push it up, "System 1" does positive work. In other words, it transfers its kinetic energy to the "outside" particles.
In both these examples, one system "gained" energy while the other "lost" energy. Though the net change is still 0.
Example 2: A moving ball 'A' colliding elastically with a stationary ball 'B' (in space)
During the collision, ball A (System 1) does positive work, thus transferring its kinetic energy to ball B. Ball B (System 2) does negative work, thus absorbing kinetic energy from ball A.
So far, so good for their definition of work.
Example 3: Thrown ball/Falling ball
I am having a hard time applying this definition of work to a thrown ball for two reasons:
There seems to only be one system here: the earth-ball system. What would the other system be?
There doesn't seem to be any energy transfer occurring. Rather, the kinetic energy of the earth-ball system is being transformed into potential energy. When thrown, gravity is doing negative work on the earth-ball system, transforming their energy. Where is the energy transfer?
Using this 3rd example and my logic, one of the following could be an explanation:
My textbook is limiting the definition of work.
The definition is fine, I'm just not understanding something about the ball example.
EDIT: This was my attempt to reconcile example 3 and the textbook's definition of work:
In example 3, we can treat "System 1" as the Earth, and "System 2" as the ball. Also, I am conceptualizing gravity as an invisible spring between the two.
As the ball is moving up, "System 1" (Earth) is pulling on it, doing negative work (displacement of the ball is in the opposite direction of the force on the ball). This negative work absorbs energy from the ball, decelerating it. "System 2" (the ball) is pulling on Earth, doing positive work (the displacement of the earth is in the direction of the force of the ball). This positive work transfers kinetic energy to the Earth, technically accelerating it.
Unfortunately, once the ball starts falling. It seems both Earth and ball are doing positive work (direction of displacement and force are the same for each), thus breaking conservation of energy.