Question

A girl presses her physics textbook against a rough vertical wall with her hand. The direction of the frictional force on the book exerted by the wall is:
A. Downwards
B. Upwards.
C. Out from the wall
D. Into the wall

Answer 1

Use the concept of Newton’s second law of motion. Determine all the forces acting on the physics textbook. Draw the free body diagram of the physics textbook and determine what should be the direction of the frictional force for the textbook to be in a steady state.

Complete step by step answer:
We have given that a girl is pressing a book against a vertical rough wall.Since the wall is rough, there must be a frictional force between the surface of the wall and the physics textbook.The frictional force between any two surfaces always acts along the line parallel to the surfaces of the object and the surface in contact with each other.Hence, the frictional force between the rough wall and the textbook cannot act out from the wall or into the wall.Hence, the options C and D are incorrect.Let use draw the free-body diagram of the physics textbook as follows:

The Y-axis shown in the above diagram represents the vertical rough wall and the physics textbook is pressed at point O.The force $F$ is the force applied by the girl on the textbook against the wall in a direction into the wall. The force applied by the girl is balanced by the normal force $N$ exerted by the wall on the textbook along a direction out from the wall.The weight $W$ of the textbook acts in the vertically downward direction. There must be some force balancing the weight of the textbook in the vertically upward direction.This weight of the book is balanced by the frictional force ${F_f}$ on the book exerted by the rough wall.

Therefore, the frictional force must be in the upward direction.Hence, the correct option is B.

Note: One can also determine the direction of the frictional force between the physics textbook and the rough wall by considering that the gravitational force of the Earth pulls the textbook in downward direction. Hence, the frictional fore should be in the upward direction to oppose the gravitational pull. This reduces the effort of drawing the free body diagram of the textbook.