Question

A boy presses a book against the front wall such that the book does not move. What will be the force of friction between the wall and the book?
A. Towards right
B. Towards left
C. Downwards
D. Upwards

Answer 1

Hint:Before we proceed with the problem, it is important to know about the frictional force and the normal force. The frictional force is the force acting in the opposite direction of the motion of an object. The normal force is the force that acts between the objects individually between them. It is a surface force and is normal to the surface of contact of the bodies.

Complete step by step solution:
When you press the book against the wall with some force, the wall is pushing back against the book with an equal and opposite force which is normal in nature. This normal force is the cause of frictional force between the wall and the book. If the book has zero acceleration with respect to the wall, the net force acting on it must be zero.

If we consider gravity to be acting on the book, gravity being a downward force, the magnitude of the frictional force on the book is equal to the gravitational force but in the opposite direction. The frictional force is defined as the product of the coefficient of frictional force and the normal reaction exerted by the surface.
So, \[f = u \times N\]
Here 'u' is a constant for given surfaces in contact.

Now, the Normal reaction or normal force is equal and opposite to the force exerted by an external force on the surface, perpendicular to the surface (or the perpendicular component of the external force). The external force exerted on the surface which is vertical to it, in the given case, is equal to the force that you are applying while you are holding/pressing the book against the wall.

So, at any point in time, frictional force = u X (Force you are applying on the surface, via the book)
\[f = u \times F\]
where,
f is the frictional force
u is the coefficient of friction, and
F perpendicular component of the force exerted by you on the book towards the surface.

Now the direction of frictional force always acts parallel to the surface and in opposite direction to the direction of motion. In absence of friction, the book will fall down, because of gravity acting on it. Hence, friction will try to act in the opposite direction of this motion.So, upwards in this case. Therefore, the force of friction between the wall and the book is upwards.

Hence, option A is the correct answer

Note:The heavier the book, the more frictional force is needed to hold it from falling, and that is why you have to press it harder to hold Heavier books. One can try applying this concept to things you see around.