You are reshelving books in a library. you lift a book from the floor to the top shelf. the kinetic energy of the book on the floor was zero and the kinetic energy of the book on the top shelf is zero, so no change occurs in the kinetic energy, yet you did some work in lifting the book. is the work–kinetic energy theorem violated?

No, the theorem is not violated

Explanation:

No, it is not violated because the work done by gravitational force must also be taken into account. The force to lift the book at constant speed is the same as the gravitational force, i.e. the work done by the gravitational force (weight) is equal in magnitude but negative to the work done by the person to lift the book. (The work done by gravity is negative because displacement and weight have opposite directions).

So if we apply the theorem the work and kinetic energy, we have that the total work done in the book (work of the person plus the gravitational work) is equal to zero, and it is equal to the change of the kinetic energy. The theorem is fulfilled

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