Question About Potential Energy

[Metovich]

I have two simple examples of potential energy and kinetic energy.

First example: Imagine a book on the ground and I want to lift it.At first I apply a force just a little more than the gravitational force of the Earth so that it has some velocity. After the book gets that velocity, I keep my force same with the gravitational force of the Earth so the kinetic energy stays constant along the path. As I know, the potential energy of the system of BOOK+EARTH increases (I always thought that the potential of the book increases), as I lift the book. When we look at the systems for that example;

System: Book alone
External forces on the system: My force + Gravitational force by the Earth
Internal forces of the system: ---
Result: The kinetic energy of the system stays constant. There is not net work done on the book.

System:Earth alone
External forces on the system: Gravitational force by the book
Internal forces of the of the system: ---
Result: The kinetic energy of the system should increase. There is some net work done on the Earth.

System: Book+Earth
External forces on the system: My force
Internal forces of the system: Gravitational force by the Earth on the book and gravitational force by the book on the Earth but they cancel each other because the internal force is conservative for a system
Result: The potential energy of the system increases. There is some net work done on the book+earth system by me.

Second example: Imagine that I let the book go from some height. Looking at the systems for that example;

System: Book alone
External forces on the system: Gravitational force by the Earth
Internal forces of the system: ---
Result: The kinetic energy of the book increases. There is some net work done on the book. The increase in kinetic energy of the SYSTEM: BOOK ALONE is greater that the increase in kinetic energy of the SYSTEM: EARTH ALONE.

System: Earth alone
External forces on the system: Gravitational force by the book
Internal forces of the system: ---
Result: The kinetic energy of the Earth increases. There is net work done on the Earth.

System: Book+Earth
External forces on the system: ---
Internal forces of the system: Gravitational force by the Earth on the book and gravitational force by the book on the Earth but they cancel each other because the internal force is conservative for a system.
Result: There is no net work done on the system, so the total energy of the system doesn't change. The kinetic energy of the book and the Earth increases and potential energy of the system decreases with an equal amount.

I would like to know whether the information that I provided here is true or not. Also it seems there can be a kinetic energy of one thing ( Earth or book) but there can't be a potential energy of one thing. The system should consist of at least two things for the potential energy to exist which seems weird to me. Also my other deduction from those examples is that if we don't do any external work on systems like Book+Earth (second example) , they just tend to lose their potential energy and gain kinetic energy.

 

[mfb]

As I know, the potential energy of the system of BOOK+EARTH increases

Right.

System:Earth alone
External forces on the system: Gravitational force by the book
Internal forces of the of the system: ---
Result: The kinetic energy of the system should increase. There is some net work done on the Earth.

There is also a force from the book acting on "You+Earth". If you don't want to consider yourself part of Earth, you should introduce you as part of the system.
I assume you stand on Earth.

The system should consist of at least two things for the potential energy to exist which seems weird to me.

Often it is sufficient to consider Earth as external force. It won't move notably if you move books around. In that case you can assign potential energy to individual objects, like a book.

 

[CWatters]

There are some errors in your analysis. Perhaps consider a spring between two identical objects so the situation is symmetrical. Then look back over your analysis.

 

[Khashishi]

The system should consist of at least two things for the potential energy to exist which seems weird to me.

Right. The potential energy is due to the interaction between two or more objects (or two or more parts of a compound object like a spring). It's basically the same concept as "binding energy", except that binding energy is generally inverted in sign (so that a positive binding energy is actually referring to a negative potential energy).

they just tend to lose their potential energy and gain kinetic energy.

It can go in either direction. I don't think there's any tendency to go one way.