Question

Does the work you do on a book when you lift it onto a shelf depend on the path taken? On the time taken? On the height of the shelf? On the mass of the book?

Short answer

The work done on a book when it is lifted onto a shelf doesn’t depend on the path and on the time taken, but it depends on the height of the shelf and the mass of the book.

Step-by-step solution

Step 1: Definition of Concept

Potential energy: The work done on the object to displace it against the conservative gravitational force is stored in the form of potential energy which is given as,

$$\begin{gathered} \mathbf{W}\mathbf{=}\mathbf{P}\mathbf{.}\mathbf{E}\mathbf{.} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{mg}\left(h_2-h_1\right) \end{gathered}$$

(1.1)

Here, m is the mass of an object, g is the acceleration due to gravity, ${\mathbf{h}}_{\mathbf{2}}$is the final height of the object, and ${\mathbf{h}}_{\mathbf{1}}$is the initial height of the object.

Explain the work done on a book when it is lifted

From equation (1.1), it is clear that the work done on a book when it is lifted onto a shelf depends on the height of the self and on the mass of the book and is independent of the path and the time taken.