Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

A filing cabinet weighing 556 N rests on the floor. The coefficient of static friction between it and the floor is 0.68 , and the coefficient of kinetic friction is 0.56 . In four different attempts to move it, it is pushed with horizontal forces of magnitudes (a) 222 N , (b) 334 N , (c) 445 N , and (d) 556 N . For each attempt, calculate the magnitude of the frictional force on it from the floor. (The cabinet is initially at rest.) (e) In which of the attempts does the cabinet move?

(a) The magnitude of the frictional force is f = 222 N .

(b) The magnitude of the frictional force is f = 334 N .

(d) The magnitude of the frictional force is f = 311 N .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data:

Weight of the cabinet, W = 556 N

Coefficient of static friction between the cabinet and the floor, $μ_{s} = 0.68$

Coefficient of kinetic friction, $μ_{k} = 0.56$

Step 2: Understanding the concept:

In order to move a filing cabinet, the force applied must be able to overcome

the frictional force.

Apply Newton’s second law

$F_{push} - f = F_{net} = ma$

If you find the applied force $F_{p u s h}$ to be less than $f_{s, \max}$ , the maximum static frictional force, our conclusion would then be “no, the cabinet does not move” (which means is actually zero and the frictional force is simply $f = F_{p u s h}$ ). On the other hand, if you obtain a > 0 then the cabinet moves (so $f = f_{k}$ ).

For $f_{s, m a x}$ and $f_{k}$ use Eq. 6-1 and Eq. 6-2 (respectively), and in those formulas set the magnitude of the normal force to the weight of the cabinet.

Step 3: Calculate the maximum static friction and kinetic friction:

The maximum static frictional force is,

$f_{s, \max} = μ_{s} F_{N}$

Here, the weight of the cabinet will be balanced by the normal force. Therefore,

$f_{s, \max} = μ_{s} W$

And the kinetic frictional force is,

$f_{k} = μ_{k} f_{k} = μ_{k} W = (0.56) (556 N) = 311 N$

Step 4: (a) Define the magnitude of the frictional force with horizontal force of magnitude 222 N :

Calculate the magnitude of the frictional force on the cabinet from the floor when it is pushed with horizontal force of magnitudes, which is,

. $F_{p u s h} = 222 N$

Here, the magnitude of the horizontal pushing force is less than the maximum static force. Therefore,

$F_{p u s h} < f_{s, m a x} 222 N < 378 N$

Hence, the cabinet does not move. So, acceleration of the cabinet will be zero.

$a = 0 m / s^{2}$

The frictional force is,

$F_{p u s h} - f = m a = m (0 m / s^{2}) = 0 f = F_{p u s h} = 222 N$

Here, the magnitude of the frictional force between the carbonate and the floor is f = 222N .

Step 5: (b) Determine the magnitude of the frictional force with horizontal force of magnitude 334 N :

Calculate the magnitude of the frictional force on the cabinet from the floor when it is pushed with horizontal force of magnitudes, which is

$F_{p u s h} = 334 N$

Here, the magnitude of the horizontal pushing force is less than the maximum static force. Thus,

$F_{p u s h} < f_{s, m a x} 334 N < 378 N$

Hence, the cabinet does not move. So, acceleration of the cabinet will be zero.

$a = 0 m / s^{2}$

The frictional force is,

$F_{p u s h} - f = m a = 0 f = F_{p u s h} = 334 N$

Step 6: (c) Define the magnitude of the frictional force with horizontal force 445 N :

Calculate the magnitude of the frictional force on the cabinet from the floor when it is pushed with horizontal force of magnitudes, which is,

$F_{p u s h} = 445 N$ .

Here, the magnitude of the horizontal pushing force is less than the maximum static force. Thus,

$F_{p u s h} > f_{s, m a x} 445 N > 378 N$

Hence, the cabinet will move. So, the frictional force will be he kinetic friction. Hence, the friction force in this case between the cabinet and the floor is,

$f = F_{k} = 311 N$

Step 7: (d) The magnitude of the frictional force with horizontal force 556 N :

Calculate the magnitude of the frictional force on it from the floor when it is pushed with horizontal force of magnitudes, which is,

$F_{p u s h} = 556 N$ .

Again, you have

$F_{p u s h} > f_{s, m a x} 556 N > 378 N$

Which means the cabinet moves.

Hence, the cabinet will move. So, the frictional force will be he kinetic friction. Hence, the friction force in this case between the cabinet and the floor is,

$f = f_{k} = 311 N$

Step 8: (e) Find out in which of the attempts does the cabinet move:

As in part (c) and (d) you have $F_{p u s h} > f_{s, m a x}$ which means the cabinet moves.

Hence, the cabinet moves in (c) and (d).

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given data:

Step 2: Understanding the concept:

Step 3: Calculate the maximum static friction and kinetic friction:

Step 4: (a) Define the magnitude of the frictional force with horizontal force of magnitude 222 N :

Step 5: (b) Determine the magnitude of the frictional force with horizontal force of magnitude 334 N :

Step 6: (c) Define the magnitude of the frictional force with horizontal force 445 N :

Step 7: (d) The magnitude of the frictional force with horizontal force 556 N :

Step 8: (e) Find out in which of the attempts does the cabinet move:

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given data:

Step 2: Understanding the concept:

Step 3: Calculate the maximum static friction and kinetic friction:

Step 4: (a) Define the magnitude of the frictional force with horizontal force of magnitude 222 N :

Step 5: (b) Determine the magnitude of the frictional force with horizontal force of magnitude 334 N :

Step 6: (c) Define the magnitude of the frictional force with horizontal force 445 N :

Step 7: (d) The magnitude of the frictional force with horizontal force 556 N :

Step 8: (e) Find out in which of the attempts does the cabinet move:

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Famous Physicists

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics