91Ó°ÊÓ

The given data can be listed below as,

The coefficient of friction is the ratio of the force which resist the one surface to slide over another surface to that of normal force is known as coefficient of friction.

Part (a)

We know that static friction is a self-adjustable force and that it will be equal to the applied force until the body starts to move. In the above diagram, part OA is the region of static friction that means the region in which the pull is less than 75N .

The kinetic friction on the other hand, remains constant with time. So, the region of kinetic friction is when pull is greater than 75N .

Part (b)

Expression for the static frictional force can be expressed as,

$F_r={\mathrm{μ}}_{s}R$

Here$F_r$is the frictional force,${\mathrm{μ}}_s$ is the coefficient of static friction, and the normal reaction on the box,$R=W=135N$.

Substitute 75 N for $F_r$ , 135 N for in the above equation.

$$\begin{gathered} 75N={\mathrm{μ}}_s\left(135N\right) \\ =0.55 \end{gathered}$$

Hence, required coefficient of static friction is, 0.55.

Expression for the kinetic frictional force can be expressed as,

$F_r={\mathrm{μ}}_{k}R$

Here ${\mathrm{μ}}_k$ is the coefficient of kinetic friction.

Substitute 50 N for , 135 N for in the above equation.

$$\begin{gathered} 50N={\mathrm{μ}}_s\left(135N\right) \\ =0.37 \end{gathered}$$

Hence, required coefficient of kinetic friction is, 0.37.

Part (c)

When a body is pulled, a sliding tendency develops in it but the body does not move due to friction. As, the pull is increased this sliding tendency goes on increasing but the body still remains stationary. This means that with increase in sliding tendency the frictional force also increased. On further increasing the pull, a certain maximum limit is reached beyond which if the pull is increased, the object will start moving. This is what is shown with the graph slanting upward.

Part (d)

We know the coefficient of friction doesn’t depend upon the weight, but it depends on the roughness of the material.

Hence, the coefficient of friction remain unchanged.