Here are the answers to the physics questions:
(a) The period of revolution of the book can be determined from the graph by measuring the time interval between successive peaks or successive troughs. This time interval represents the period.
(b) No, the tangential speed cannot be determined from the information given. The graph shows only the horizontal position vs time. It does not provide any information about the tangential or angular speed.
(c) At the lowest point of the circular path, the forces acting on the book are:
- Weight of the book, downward force from gravity
- Normal force, upward force from the bench supporting the book's weight
- Friction force, horizontal force from the bench on the book opposing its motion
(d) Student 2 is incorrect because kinetic friction acts to oppose motion between two surfaces sliding past each other. At the instant the book is at the lowest point, it is not sliding relative to the bench, so kinetic friction does not apply.
(e) Student 3 is correct. Static friction acts between two surfaces in contact that are not sliding past each other. At its lowest point, the book is in contact with the bench and not sliding, so static friction opposes its horizontal motion.
(f) At its lowest point, the net vertical force on the book is zero. The upward normal force from the bench exactly balances the downward gravitational force. So there is no net vertical force in either direction.
(g) One way the student's derivation is incorrect is that the equation contains the tangential speed vb. However, the tangential speed cannot be determined from the information provided in the question, as explained in (b). So it is invalid to include vb in the derived equation.
(h) The force the bench exerts on the book is equal to the book's weight. As explained in (e) and (f), at the lowest point the net vertical force is zero due to the normal force balancing weight. So the normal force must equal the book's weight.
(i) The book's mechanical energy is greater at the top of the path. As it moves from top to bottom, work is done by friction to reduce its kinetic energy. So it has more kinetic (and thus total mechanical) energy at the top.