Derive an algebraic equation for the vertical force that the bench exerts on the book at the lowest point of the circular path in terms of the book’s mass mb , tangential speed vb , radius R of the path, and physical constants, as appropriate. Do not substitute any numerical values for variables or physical constants.

(a) i. Determine the period of revolution of the book.
ii. Calculate the tangential speed vb (not the angular speed) of the book.

(b) i. On the dot below, which represents the book, draw and label the forces (not components) that act on the book at the lowest point of its circular path. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot. ii. At the lowest point of the circular path, the book is moving only in the horizontal direction.

In what direction, if any, is the net vertical force on the book? Up _No Down direction, since the net vertical force is equal to zero Without deriving any equations, briefly explain your reasoning in terms of the book's motion

(c) Derive an algebraic equation for the vertical force that the bench exerts on the book at the lowest point of the circular path in terms of the book's mass mb, tangential speed vh, radius R of the path, and physical constants, as appropriate. Do not substitute any numerical values for variables or physical constants.

(d) At the lowest point of the circular path, is the force that the bench exerts on the book greater than, less than, or equal to the weight of the book? - Less Than Greater Than Equal to Briefly explain how your answers in (b)ii and (c) support your selection.