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 32 N. The coefficient of static friction between his hands and the book is 0.36. To keep the book from falling, what is the magnitude of the minimum pressing force that each hand must exert?
2*F*mus=weight
2*F*0.36=32N
F=32/(2*0.36)
F=44.4
2 * F * mus = weight
mus = static friction coefficient = 0.36
Solve for F.
The 2 is there because there is friction on both sides.
overall answer is 44.4
To determine the minimum pressing force that each hand must exert to keep the book from falling, we need to consider the balance of forces acting on the book.
In this scenario, there are two forces acting on the book: the weight of the book and the frictional force between the student's hands and the book.
The weight of the book is given as 32 N, which acts vertically downwards.
The frictional force is given by the coefficient of static friction (μ) multiplied by the normal force (N). The normal force is the force exerted by the student's hands perpendicular to the book.
In this case, since the forces exerted by the student's hands are perpendicular to the book and are horizontal (as mentioned in the question), the normal force is equal to the weight of the book (32 N).
Now, we can calculate the frictional force using the formula:
Frictional force = coefficient of static friction * normal force
Frictional force = 0.36 * 32 N
Frictional force = 11.52 N
To keep the book from falling, the pressing force exerted by each hand must be equal to or greater than the frictional force.
Therefore, the minimum pressing force that each hand must exert is 11.52 N.