Final answer:
The work done on a book when lifting it onto a shelf depends on the height of the shelf and the mass of the book, not on the path or time taken. The work against gravity is the product of the book's weight and the shelf's height. Horizontal motion does not affect the work done against gravity.
Step-by-step explanation:
Work Done on a Book
The work you do on a book when you lift it onto a shelf does not depend on the path taken or the time taken. Work is defined as the force exerted on an object times the distance over which the force is applied in the direction of the force. When lifting a book vertically, the work done depends on the height of the shelf and the mass of the book, because the force you must exert equals the gravitational force acting on the book (its weight), and the distance is the height of the shelf. For the example of lifting a 20 N library book 1 meter from the shelf, the work done by gravity would be negative because gravity is acting in the opposite direction of the movement. The work against gravity is positive and equals the weight of the book multiplied by the height (20 N x 1 m = 20 J). Carrying the book horizontally does no work against gravity because there is no vertical displacement.
For the scenario described with the old bookshelf and push applied, the information provided allows for the calculation of the shear modulus of the bookcase, which is a measure of the bookcase's ability to resist shearing forces.
In the case of stacking books with one inch overhangs, the students would need to know the dimensions of the books, specifically the breadth, in order to calculate the maximum number of books that could be stacked before tipping.