Suppose you are reshelving books in a library. As you lift a book from the floor and place it on the top shelf, two forces act on the book: your upward lifting force and the downward gravity force. Is the mechanical work done by your lifting force positive, negative, or zero? Is the work done by the gravity force positive, zero or negative? Is the sum of the works done by both forces positive, negative or zero?

Sum of works done is zero as both W_you and W_gravity is equal and opposite.

Explanation:

Mechanical work done by you will be positive as the force applied and displacement covered, both will be in same direction.

⇒Work done, W = F. D = Fd cosΘ

so, here, Θ = 0° = w_you = Fd

↑F mech

Book ↑displacement

↓F gravity

⇒Work done by gravity is negative

[AS Θ = 180 ]

sum of works done is zero as both W_you and W_gravity is equal and opposite.