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!
The work done by gravity would be -20.0 J in relation to the work done by Librarian.
*The Librarian lifts the book UPWARD doing 20.0 J of work.
*Gravity pulls the book DOWARD at -20.0 J of work RELATIVE to that of the Librarian's work.
*The book hits the ground with 20.0 J of kinetic energy. WHY? -- Gravity pulled the book DOWNWARD with 20.0 J of work.
(It would be -20.0 J if the question asked for the kinetic energy to be relative to the Librarian's work done).
The situation described is not impossible; instead, it seems to follow the law of conservation of energy. The work done in lifting the book (20.0 J) is converted into potential energy, which is then converted back into kinetic energy as the book falls. Thus, the book hits the ground with 40.0 J of kinetic energy, as stated.
However, in reality, some of the energy is lost due to various factors such as air resistance, friction, and sound. These losses cause the actual kinetic energy of the book when it hits the ground to be less than the calculated value of 40.0 J. The difference accounts for the energy that is dissipated in the form of heat, sound, and other non-conservative forces.
The situation described is impossible because it violates the conservation of energy principle. According to the principle, energy cannot be created or destroyed; it can only be transferred or transformed from one form to another.
To understand why the situation is impossible, let's analyze the steps involved:
1. The librarian lifts the book from the ground to a high shelf, doing 20.0 J of work. This work is done against the force of gravity, and the book gains potential energy equal to the work done in lifting it.
2. When the book falls off the shelf, the force of gravity does work on the book. This work is equivalent to the potential energy the book initially had while on the shelf, which is 20.0 J.
However, the mistake in the given scenario is adding both these works together to claim that the book hits the ground with 40.0 J of kinetic energy. This assumption overlooks the fact that the book's potential energy on the shelf was completely converted into kinetic energy as it fell.
In reality, when the book falls, all its potential energy is converted into kinetic energy as it accelerates towards the ground. Therefore, the book hits the ground with the same amount of energy it had initially, which is 20.0 J. The additional 20.0 J of work done by the librarian in lifting the book does not add to the kinetic energy.
Hence, the correct calculation should be: 20.0 J (initial potential energy on the shelf) = 20.0 J (final kinetic energy when it hits the ground).
This demonstrates the importance of recognizing that energy can only be converted between different forms, rather than being created or destroyed.