A 0.60-kg book slides on a horizontal table. The kinetic friction force on the book has magnitude 1.8 N. (a) How much work is done on the book by friction during a displacement of 3.0 m to the left? (b) The book now slides 3.0 m to the right, returning to its starting point. During this second 3.0-m displacement, how much work is done on the book by friction? (c) What is the total work done on the book by friction during the complete round trip? (d) On the basis of your answer to part (c), would you say that the friction force is conservative or non-conservative? Explain.

The magnitude of the kinetic friction force is f = 1.8 N

The mass of the book is m = 0.60 kg

The displacement of the book is x = 3 m

The opposing effect on an object between object and surface is called friction. Its direction is always opposite to the direction of motion of the object.

The work done on book y kinetic force for left displacement is given as:

$W_i=-f\cdot x\cos \theta$

Here, g is the gravitational acceleration and its value is $9.8m/s^2$, $\theta$ is the angle with the direction of movement of the book from kinetic friction and its value is $0°$

Substitute all the values in the above equation and we get,

$$\begin{gathered} {\mathrm{W}}_{\mathrm{l}}=-\left(1.8\mathrm{N}\right)\left(3\mathrm{m}\right)\left(\cos 0°\right) \\ {\mathrm{W}}_{\mathrm{l}}=5.4\mathrm{J} \end{gathered}$$

Therefore, the work done on the book for left movement is - 5.4 J .

The work done in the book for right movement is given as:

$W_r=f\cdot x\cos \alpha$

Here, g is the gravitational acceleration and its value is $9.8m/s^2$, $\theta$ is the angle with the direction of movement of the roofer and its value is $180°$

Substitute all the values in the above equation and we get,

$$\begin{gathered} {\mathrm{W}}_r=\left(1.8\mathrm{N}\right)\left(3\mathrm{m}\right)\left(\cos 180°\right) \\ {\mathrm{W}}_r=-5.4\mathrm{J} \end{gathered}$$

Therefore, the work done on the book for the right move is - 5.4 J .

The total work done by kinetic friction force on the book is given as:

$W=W_l+W_r$

Substitute all the values in the above equation.

W = 5.4 J - 5.4 J

W = - 10.8 J

Thus, the total work done by kinetic friction force on the book is - 10.8 J .

The non-conservative force is the force whose work done is dependent on the path and depends on the path for the movement of the object.

The initial and final position of the book is the same but the total work is not zero so kinetic friction force is a non-conservative force.