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 30.0 N. The coefficient of static friction between his hands and the book is 0.435. To keep the book from falling, what is the magnitude of the minimum pressing force that each hand must exert?
Each hand applies a maximum friction force
(0.435 F),
where F is the pressing force
Twice that force must equal or exceed the weight, M g
0.87 F > M g
Fmin = M*g/0.87 newtons
To find the magnitude of the minimum pressing force that each hand must exert to keep the book from falling, we need to consider the forces acting on the book.
Given information:
Weight of the book (force due to gravity) = 30.0 N
Coefficient of static friction between hands and book = 0.435
The forces acting on the book are:
1. Weight of the book, which acts downward.
2. Normal force exerted by the hands on the book, which acts upward and perpendicular to the book.
3. Frictional force between the hands and the book, which acts horizontally.
To keep the book from falling, the normal force exerted by the hands on the book must balance the weight of the book. This means the magnitude of the normal force should be equal to the weight of the book (30.0 N).
Now, let's calculate the frictional force between the hands and the book using the equation:
Frictional force = Coefficient of static friction * Normal force
Frictional force = 0.435 * 30.0 N
Frictional force = 13.05 N
Since the frictional force acts in the opposite direction of the pressing force, the magnitude of the minimum pressing force that each hand must exert to counteract the friction and keep the book from falling will be:
Pressing force = Frictional force
Pressing force = 13.05 N
Therefore, the magnitude of the minimum pressing force that each hand must exert is 13.05 N.