Question

Question #40c12

Answer 1

You do positive work to increase the potential energy of the system that consists of the Earth and the book.

Explanation:

The definition of work is

`W=vecF@vecd`

which is a vector dot product. The magnitude of this product is usually written as

`W=Fdcostheta`

To make this formula work, both `F` and `d` are taken as positive values, and the sign of the work is based on the sign of the `costheta` term.

In simpler terms, if `vecF` and `vecd` are in the same direction (or even have a component in the same direction), the `costheta` term is positive, and positive work has been done. If `vecF` and `vecd` are in opposite directions, (the force opposes the motion) the work done is negative.

In this problem, if you lift the book, you are doing positive work on the book. At the same time, the force of gravity is doing negative work on the book.

If there is no overall change in the kinetic energy of the book (if the does not change speed as you raise it), then all the work you do in raising the book becomes potential energy because you have lifted the book against the force of gravity.

Strictly, it is not correct to say that the book has potential energy. Rather, you should say that potential energy has been stored in the system of Earth + book, because you relocated the book in the presence of the force of gravity.

In the end, the potential energy of the system has been increased by exactly the amount of work you did when you lifted it. This is given by:

`W=mgh` where `mg` is the weight of the book (also the force of gravity) and `h` is the vertical distance you raised it.