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Direction of friction is opposite to the component of net external force parallel to the contact surface. It is the criteria to decide the direction of friction. There are, however, situations in which external force may not be obvious. In the illustration of the above section, there is no external force on the upper block "B". What would be the direction of friction on block "B"? As a matter of fact, it is the only force (we do not consider vertical normal force as it perpendicular to motion) on block acting parallel to contact surface. Clearly, we can not apply the criteria for determining direction in this case.
We actually analyze the forces on the underneath block "A". The net external force parallel to interface is acting towards right. It, then, follows that the friction on "A" is towards left. Taking cue from this revelation and using Newton’s third law of motion , we decide that the direction of friction on block "B" should be towards right as shown in the figure below.
Alternatively, we can consider relative motion between bodies in contact. In the illustration, we see that block “A” has relative velocity (or tendency to have one) towards right with respect to block “B”. It means that the block “B” has relative velocity (or tendency to have one) towards left with respect to block “A”. Hence, friction force on block “B” is towards right i.e. opposite to relative velocity of “B” with respect to block “A”.
We can formulate a directional rule about the direction of friction as :
“The direction of friction on a body is opposite to the relative velocity of the body (or the tendency to have one) with respect to the body, which is applying friction on it.”
There are two types of contact forces that we encounter when two bodies interact. The contact forces are normal and friction forces. The normal force is a reaction of a body against any attempt (force) to deform it. The ability of a body to resist deformation also has electromagnetic origin operating at the surface as in the case of friction.
The two contact forces, therefore, can be considered to be manifestation of same inter – atomic forces that apply at the contact interface. The resultant electromagnetic force acts in a direction inclined to the surface. Its component perpendicular to surface is the normal force and component parallel to the surface is friction.
The resultant or net electromagnetic contact force is the vector sum of the two components and is given by :
$$\begin{array}{l}{F}_{C}=\sqrt{({{F}_{N}}^{2}+{{F}_{F}}^{2})}\end{array}$$
Where :
${F}_{C}$ : Resultant contact force
${F}_{N}$ : Normal force, also represented simply as "N"
${F}_{F}$ : Friction force, which can be ${f}_{s}$ (static friction) , ${F}_{s}$ (maximum static friction) or ${F}_{k}$ (kinetic friction)
For the maximum static friction ( ${F}_{s}$ ) and a given normal force (N), the magnitude of resultant contact force is :
$$\begin{array}{l}{F}_{C}=\sqrt{({{F}_{N}}^{2}+{{F}_{F}}^{2})}=\sqrt{({N}^{2}+{{F}_{s}}^{2})}\\ \Rightarrow {F}_{C}=\sqrt{({N}^{2}+{{\mu}_{s}}^{2}{N}^{2})}\\ \Rightarrow {F}_{C}=N\sqrt{(1+{{\mu}_{s}}^{2})}\end{array}$$
This expression represents the maximum contact force between a pair of surfaces.
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