Question

How do I calculate the coefficient of friction of an object on an incline before the object starts moving? I have measured the angle at 45 degrees and the mass of the object on the incline is 250 g.

Answer 1

Given data:

* The angle of the inclined plane is

$\theta=45^{\circ}$

* The mass of the object is m = 250 g.

Solution:

The diagrammatic representation of the given case is,

The force acting down the inclined plane due to the weight of an object is,

$F=mg\cos (90^{\circ}-\theta)$

where g is the acceleration due to gravity,

Substituting the known values,

$\begin{gathered} F=250\times10^{-3}\times9.8\times\cos (90^{\circ}-45^{\circ}) \\ F=0.25\times9.8\times\cos (45^{\circ}) \\ F=1.73\text{ N} \end{gathered}$

The normal force acting on the object is,

$\begin{gathered} F_N=mg\cos (\theta) \\ F_N=250\times10^{-3}\times9.8\times\cos (45^{\circ}) \\ F_N=0.25\times9.8\times\cos (45^{\circ}) \\ F_N=1.73\text{ N} \end{gathered}$

The frictional force in terms of the normal force is,

$F_s=\mu_sF_N$

where,

$\mu_s\text{ is the static coefficient of friction}$

As the object is in a static state under the action of force, thus, the frictional force is balancing the force acting on the object down the inclined plane (F_s = F)

Substituting the known values,

$\begin{gathered} 1.73=\mu_s\times1.73 \\ \mu_s=\frac{1.73}{1.73} \\ \mu_s=1 \end{gathered}$

Hence, the coefficient of friction of an object on an inclined plane is 1.