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 30.8 N. The coefficient of static friction between his hands and the book is 0.424. To keep the book from falling, what is the magnitude of the minimum pressing force that each hand must exert?
34 N
Well, it seems like the student is in quite a bind trying to keep that book from falling! But fear not, dear student, for I, Clown Bot, am here to help with a humorous twist.
To find the minimum pressing force required, we need to consider the static friction between the student's hands and the book. Let's dive into the physics of it, shall we?
We can start by finding the maximum frictional force that can be exerted on each side of the book. We know that the coefficient of static friction is 0.424, and the weight of the book is 30.8 N. So, multiplying these values gives us a maximum frictional force of... (wait for it)...
30.8 N * 0.424 = 13.0592 N (approximately).
Hmm, that's quite a mouthful, isn't it? But it's just a number! Now, since the student wants to keep the book from falling, the minimum pressing force that each hand must exert is equal to the weight of the book PLUS the maximum frictional force.
So, adding the weight of the book (30.8 N) to the maximum frictional force, we get...
30.8 N + 13.0592 N = 43.8592 N (approximately).
Ta-da! The student needs to exert a minimum pressing force of approximately 43.8592 N with each hand to keep the book from falling.
Remember, dear student, don't let the weight of the situation get you down. Just keep pressing forward (or in this case, outward)!
To keep the book from falling, the maximum frictional force between the student's hands and the book should be equal to or greater than the weight of the book.
The formula for frictional force is:
Frictional force = coefficient of friction * normal force
In this case, the normal force is equal to the weight of the book, because the hands are pressing the book vertically:
Normal force = Weight = 30.8 N
Therefore, the maximum frictional force is:
Maximum frictional force = coefficient of friction * normal force
= 0.424 * 30.8 N
= 13.0592 N
So, the magnitude of the minimum pressing force that each hand must exert is 13.0592 N.
To determine the minimum pressing force that each hand must exert, we need to consider the equilibrium conditions.
In this case, there are two forces acting on the book: the weight of the book (acting downwards) and the frictional force (acting upwards). Since the student wants to keep the book from falling, the magnitude of the minimum pressing force should be equal to or greater than the combined weight and frictional force.
Let's calculate the weight of the book first. The weight is given as 30.8 N.
Next, we need to determine the frictional force. The coefficient of static friction between the student's hands and the book is 0.424. The frictional force can be calculated using the formula:
Frictional force = coefficient of static friction × normal force
In this case, the normal force is equal to the weight of the book. Therefore, the frictional force can be calculated as:
Frictional force = 0.424 × 30.8 N
Now, add the weight and frictional force to find the minimum pressing force:
Minimum pressing force = weight of the book + frictional force
Therefore, the magnitude of the minimum pressing force that each hand must exert is equal to the weight of the book plus the frictional force.