I have a question regarding work energy value being positive and negative. When an object is raised vertically, the formula is: Work = displacement * force. The force is calculated with the gravitational acceleration. However, does it matter with what acceleration the object is being raised? Work energy of the object being raised = potential energy of the object at the height where the object is raised to. Based on the conservation of energy, the object's potential energy will be: the mass of the object * distance (height) * gravity. So, it appears that the acceleration with whcih the object is raised doesn't count in this case because of the gravitational field. I researched on the Google, and found a great explanation to share this point with my student. The Earth and the object being raised is part of one system. These two objects are connected by gravity. Please let me know if there is any better way to explain this point. Also, I understand that the person raising the object is creating positive work energy while the gravity is producing negative work energy.
The key is that gravitational potential energy is a property of a system of two or more objects. In this case, as you stated, the system is the book and the earth. Many times (most?), people say the book has a potential energy because it is at a height above the earth, but it is more correctly said as the book-earth system has a potential energy. It's easier to say the book has the potential energy as it moves and the earth doesn't, but that's incorrect.
Consider the person lifting the book - that is an external force - not part of the system we defined. The force is in the up direction, the displacement is in the up direction, so the work done by the force on the system is positive and the energy of the system is increased. Since the book's KE was zero in the beginning and zero at the end, there is no change in KE; this new energy of position is called "potential energy" as it has the potential to turn into KE when released. By lifting the book at a constant velocity, a FBD shows that the external force = mg, which gives
W = mgh when raised to a height, h.
But, the gravitational field also does internal work on the book - and it's negative as the book moves up and the gravitational force is down. The work is equal and opposite to the work done by the external force as we consider the book moving at a constant velocity, so the acceleration is zero (except of course at the beginning and end of the movement, but that is assume to be of short duration, so it is ignored).
Summarizing:
1. Positive Work done by an external force on the book-earth system causes an increase in gravitational potential energy. The book is moving up from the earth.
2. Positive Work done by an internal force (the gravitational field force) on the book earth system causes a decrease in gravitational potential energy. That would be the case when the object moves down towards the earth.
John
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