Question

A student presses a book between his hands, as the drawing indicates. The forces that he exerts on the front and back covers of the book are perpendicular to the book and are horizontal. The book weighs 34 N. The coefficient of static friction between his hands and the book is 0.34. To keep the book from falling, what is the magnitude of the minimum pressing force that each hand must exert?

Answer 1

If the force exert is perpendicular to the surface of the book, then the pressing force is rather not that important as long as the hand is always in contact with the book. For example, suppose you have a smooth hand surface, no matter how much force you exert onto an object, it will still drop from your hand.

Answer 2

W represent the weight of the book, H1 and H2 the pressure by the hands and N1 and N2 the resulting friction force.
You know that N1=0.34*H1 and N2 =0.34*H2 (See definition of friction force)

You do no want the book to fall so the acceleration = 0.
If you apply the second Law of Newton, you have : 0=N1 + N2 - W
which gives us: W= N1 + N2 => W=0.34 (H1+H2)

Obviously you want the book to also stay in the same place horizontally so H1=H2=H

Now you have W= 0.34 * 2 * H => H=34/(0.34*2) = 5 N

So each hand hast to apply a force of 5 N.

I hope this was conclusive :)