A student presses a book between his hands. 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 31N. The coefficient of static friction between his hands and the book is 0.40. To keep the book from falling, what is the magnitude of the minimum pressing force that each hand must exert?
2*0.4*F = M g = 31 N
Solve for F, in Newtons
The "2" is there because you are pushing from two sides. There are equal upward friction forces on both covers
39N
To keep the book from falling, the magnitude of the minimum pressing force that each hand must exert is equal to the maximum frictional force that can be generated between the hands and the book. Let's break down the problem step by step to find this force.
1. Identify the forces acting on the book:
- Weight (downward) = 31N
- Normal force (upward) = Equal in magnitude and opposite in direction to the weight (31N)
2. Determine the maximum static frictional force:
The maximum static frictional force can be found using the equation:
F_friction(max) = coefficient of static friction * Normal force
Given that the coefficient of static friction is 0.40 and the normal force is 31N, we can calculate:
F_friction(max) = 0.40 * 31N
Therefore, the maximum static frictional force is 12.4N.
3. Determine the minimum pressing force:
Since the maximum static frictional force is acting horizontally, the student must apply a pressing force on the front and back covers of the book to counterbalance this force.
As the book is pressed between the student's hands, the pressing force on each cover is the same, so we divide the maximum static frictional force by 2:
Minimum pressing force = F_friction(max) / 2 = 12.4N / 2
Therefore, the magnitude of the minimum pressing force that each hand must exert is 6.2N.