# Textbook Acceleration problem

## 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???????

berkeman
Mentor

## 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 $$\mu_s N$$ (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...

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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