A person holds a book at rest a few feet above a table. The person then lowers the book at a slow constant speed and places it on the table. Which of the following accurately describes the change in the mechanical energy of the earth-book system?

A. the total mechanical energy is unchanged, because there is no change in the book's kinetic energy as it is lowered to the table.

B. the total mechanical energy is unchanged, because no work is done on the earth-book system while the book is lowered.

C. the total mechanical energy decreases, because the person does positive work on the book by exerting a force that opposes the gravitational force.

D. The total mechanical energy decreases, because the person does negative work on the book by exerting a force on the book in the direction opposite to its displacement.

The person moved the book from rest to opposite side of displacement ie he moved it down from rest up above the table at a steady speed till it is on the table.

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snehashish65 snehashish65 · Answer 2 · 2021-11-30T18:56:42+01:00

The total mechanical energy decreases, because the person does negative work on the book by exerting a force on the book in the direction opposite to its displacement. Hence, option (D) is correct.

The given problem is based on the concept of mechanical energy. The mechanical energy is the energy of any object by virtue of its position or motion. And mathematically, it is expressed as the sum of kinetic energy and potential energy.

And the expression for the work done is given as,

W = Fd

here,

W is the work done.

F is the applied force and d is the displacement.

In the given problem, the person then lowers the book at a slow constant speed. This means some work has been done by applying force in downward direction. This work will be negative, because it is opposite to the displacement. So, work done is negative.

And according to work energy concept,

Work done = Change in kinetic energy

Negative work accounts for negative value of kinetic energy. Which means kinetic energy is decreasing continuously. And if kinetic energy decreases, then ultimately, the mechanical energy also decreases.

Thus, we can conclude that the total mechanical energy decreases, because the person does negative work on the book by exerting a force on the book in the direction opposite to its displacement. Hence, option (D) is correct.

Learn more about the mechanical energy here:

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