Question

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.

Short answer

This situation impossible because it is not including the internal and external work.

Step-by-step solution

Defining internal and external work  

When one part of the system does the work on another part of the same system, then the work is called internal work. If a force is exerted on the system and does work on the system, then it is called external work.

Evaluating the situation 

We need to be very careful in identifying internal and external work on the book-Earth system. The first 20 J, done by the librarian on the system, is external work, so the system now contains an additional 20 J compared to the initial configuration. When the book falls and the system return to the initial configuration, the 20 J of work done by the gravitational force from the Earth is internal work. This work only transforms the gravitational potential energy of the system into kinetic energy. It does not add more energy to the system. Therefore, the book hits the ground with 20 J of kinetic energy. The book-Earth system now has zero gravitational potential energy, for the total energy of 20 J, which is the energy put into the system by the librarian.