Acceleration of a Textbook on a Flat Surface

In summary, on a level, flat, horizontal surface, a textbook at rest has coefficients of static and kinetic friction of 0.750 and 0.250 respectively. When a horizontal force is gradually applied, the book begins to move with an acceleration of 4.9 m/s^2. This is due to the excess force after the book breaks loose from the static friction.
  • #1
frostking
21
0

Homework Statement


A textbook is at rest on a level, flat, horizontal surface. The coefficients of static and kinetic friction along the surface of contact are 0.750 and 0.250 respectively. A horizontal force is applied to the book. Its magnitude is increased from zero very slowly and gradually until the book begins to move. What is the acceleration of the textbook during the first instant that it moves?


Homework Equations


Force of kinetic friction = coefficent of kinetic friction times Force normal
Force of static friction = coefficent of static friction times force normal
For the book to move the static friction force has been overcome by the push.
We are interested in the movement in the x direction only.

The Attempt at a Solution



Force of friction is equal to kinetic coefficient times force normal the instant the book starts to move. I am trying to figure out how to use a kinematic equation but since I do not know the time or the velocity final I am stumped. We do know that initial velocity is 0. Thinking about it, would the force of kinetic friction equal the force of static friction at the exact moment of movement? If so since the mass is the same in either case if we set these two equations equal and then solve

0.750 m a = 0.250 m acceleration??
 
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  • #2
frostking said:

Homework Statement


A textbook is at rest on a level, flat, horizontal surface. The coefficients of static and kinetic friction along the surface of contact are 0.750 and 0.250 respectively. A horizontal force is applied to the book. Its magnitude is increased from zero very slowly and gradually until the book begins to move. What is the acceleration of the textbook during the first instant that it moves?


Homework Equations


Force of kinetic friction = coefficent of kinetic friction times Force normal
Force of static friction = coefficent of static friction times force normal
For the book to move the static friction force has been overcome by the push.
We are interested in the movement in the x direction only.

The Attempt at a Solution



Force of friction is equal to kinetic coefficient times force normal the instant the book starts to move. I am trying to figure out how to use a kinematic equation but since I do not know the time or the velocity final I am stumped. We do know that initial velocity is 0. Thinking about it, would the force of kinetic friction equal the force of static friction at the exact moment of movement? If so since the mass is the same in either case if we set these two equations equal and then solve

0.750 m a = 0.250 m acceleration??

Welcome to the PF. Before the book breaks free and starts to move, the force opposing the motion is [tex]\mu_s N[/tex] (static coefficient of friction). After it breaks loose, the friction force opposing the pushing force is what?

So there is an excess of force right after the book breaks loose. That excess force does what to the motion of the book?

Now write the equations out, and look to see if you have a nice solution to the problem...
 
Last edited:
  • #3
Thanks very much for the welcome and the push!

The answer is 4.9 m/s^2! I am studying for a midterm and this one was posted on an old test. THanks much for your time and effort. Frostking
 

1. What is the textbook acceleration problem?

The textbook acceleration problem is a common issue in physics textbooks where the acceleration values given in the examples and problems do not match the actual acceleration of the objects in the real world. This can lead to confusion and incorrect understanding of the concepts.

2. Why does the textbook acceleration problem occur?

The textbook acceleration problem occurs because most physics textbooks use simplified examples and problems to make the concepts easier to understand. These simplified examples do not take into account real-world factors such as air resistance and friction, which can affect the acceleration of objects.

3. How does the textbook acceleration problem affect students?

The textbook acceleration problem can affect students by causing confusion and incorrect understanding of the concepts. It can also lead to frustration and lack of interest in the subject if students continually get incorrect answers to problems.

4. What can be done to address the textbook acceleration problem?

To address the textbook acceleration problem, teachers can supplement textbook examples with real-world examples that take into account factors such as air resistance and friction. They can also encourage students to think critically and question the given values in the textbook.

5. Is the textbook acceleration problem a significant issue in the field of physics?

The textbook acceleration problem is a common issue in physics textbooks but it may not be considered a significant issue in the field. However, it is important for educators to be aware of this problem and take steps to address it in order to promote a better understanding of physics concepts among students.

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