Expert: Daniel Mazur - 10/18/2005

Question
I am a biology major and am 19 years old. I had trouble with the following problem:

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 38 N. The coefficient of static friction between his hands and the book is 0.30. To keep the book from falling, what is the magnitude of the minimum pressing force that each hand must exert?  

Answer
Hi Jodi,

The total friction force is a constant given to you (38 N, because it should just compensate the gravity) and you are looking for the pressing forces.

As you are pushing horizontally from two opposite directions and you do NOT cause any horizontal motion, the pushing force of both hands must be of the same magnitude (and opposite orientation, of course).

There are two contacts with the same static friction: Left hand-book and book-right hand. This means the TOTAL friction force is a sum of two partial friction forces. These partial friction forces have the same magnitude and sum up to 38 N, they are therefore 19 N each. Now, each friction force is caused by a pressing force 19 N/0.3 = 63 N and this is the answer to your problem: 63 N for each hand.

Please ask further if you need a more detailed explanation.
Good luck!
Daniel