Why is the following situation impossible? A librarian lifts a book from the ground to a high shelf, doing 20.0 J of work in the lifting process. As he turns his back, the book falls off the shelf back to the ground. The gravitational force from the Earth on the book does 20.0 J of work on the book while it falls. Because the work done was 20.0 J + 20.0 J = 40.0 J, the book hits the ground with 40.0 J of kinetic energy.
i don't understand why it is impossible. :/ any help appreciated!
20 J of gravitational potential energy is lost as the book falls. Its kinetic energy (KE) as it hits the ground is 20 J.
It has zero KE on the high shelf and regains 20 J on the way back down.
thank you so much!
The situation described is impossible because it violates the principle of conservation of energy. According to this principle, the total amount of energy in a closed system remains constant.
In the scenario provided, the librarian first does 20.0 J of work in lifting the book from the ground to the high shelf. This work done is stored as potential energy in the book when it is on the shelf.
When the book falls off the shelf and returns to the ground, the potential energy that was stored in it is converted into kinetic energy. As the book falls, the force of gravity does 20.0 J of work on the book. This work done by gravity is also converted into kinetic energy.
However, since the librarian did 20.0 J of work to lift the book, this energy should still be accounted for. In other words, the potential energy that the book had while on the shelf should be added to the kinetic energy gained during the fall.
Therefore, the correct calculation would be 20.0 J (potential energy) + 20.0 J (work done by gravity) = 40.0 J (total energy). The book would hit the ground with 40.0 J of kinetic energy, not 80.0 J.
Hence, the scenario described violates the principle of conservation of energy, making it impossible.
The situation described is not impossible, but it is an example of a misconception. It involves a misunderstanding of how work, energy, and gravitational force function.
Firstly, it is important to understand that work is the transfer of energy that occurs when a force is applied to an object and it causes the object to move in the same direction as the force. In the case of lifting the book, the librarian does positive work by applying an upward force on the book, and as a result, the book gains gravitational potential energy.
However, when the book falls off the shelf, it is not the gravitational force that does work on the book. The force of gravity is a conservative force, meaning that it only depends on the initial and final states of the object, not the path it takes. As the book falls, gravity converts its potential energy into kinetic energy. This energy conversion does not involve the force of gravity doing work because the force is perpendicular to the displacement of the book.
Now, let's look at the misconception in the calculation. The total work done on an object is equal to the change in its energy, which is given by the work-energy principle. In the case of the book falling, the work done by gravity is equal to the change in potential energy, not the total energy. The initial potential energy of the book is equal to the work done by the librarian (20.0 J) in lifting it. When the book falls, it loses this potential energy, which is converted into kinetic energy while it is falling. At the moment it reaches the ground, its potential energy is zero, and its kinetic energy is equal to the initial potential energy. Therefore, the book hits the ground with only 20.0 J of kinetic energy, not 40.0 J.
To avoid this misconception, it is essential to understand the concept of work correctly and how energy is transferred and converted.