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Nature of force system

If the body remains at rest under the action of an external force, then the forces on the body are balanced. This means that the forces on the body, including friction, should complete a closed force polygon so that the net force is zero. Let us consider the case of a block of mass “m”, lying on a horizontal surface. There are four forces (i) weight of the block,mg, (ii) normal force, N, (iii) external force (F) and (iv) friction force ( f s ).

A block resting on a plane surface

The forces form a closed vector polygon.

Till the body starts moving, the external force and static friction adjust themselves to complete the closed polygon.

Limiting (maximum) static friction

If we continue to increase the component of external force parallel to the contact surface, then for a particular magnitude, the weld joints at the contact points are broken off and the block starts moving. For any particular pair of surfaces, there is a limiting or maximum static friction ( F s ).

This limiting friction force between two surfaces can not be specified on the basis of the constitution of the material of bodies alone (such as the iron, lead etc), but its value depends on two additional factors (i) the relative smoothness or roughness of the two surfaces in contact and (ii) normal force between the two surfaces. Normal force is responsible to increase numbers of joints between the surfaces and as such affects friction between surfaces. In order to understand this aspect of friction, let us consider that the mass of block is 10 kg and acceleration due to gravity is 10 m / s 2 . From force analysis, we observe that normal force on the body is equal to the weight of the block :

N = mg = 10 X 10 = 100 Newton

A block resting on a plane surface

The free body diagram superimposed on body systems.

Now, let us put another block of mass of 10 kg over the block on the surface. As a result, the normal force increases to 200 N as shown in the figure below.

Two blocks resting on a plane surface

Greater normal force means more joints between surfaces.

As the block is now pressing the underlying surface with greater force, more of the contact points are converted into weld sites. Plainly speaking, the atoms at contact points have moved closure, increasing the inter-atomic forces. For the same pair of surfaces, we would, then, need a bigger maximum force ( F s ) to initiate motion as shown in the figure below.

Friction .vs. external force plot

Greater normal force extends maximum static friction.

Experimentally, it is found that maximum friction force is proportional to normal force on the block.

F s N F s = μ s N

where μ s is called coefficient of static friction, specific to a given pair of the surfaces in contact. It depends on the nature of the surfaces in contact. Importantly, it neither depends on the normal force unlike friction (force) nor it depends on the area in contact. We should also note that coefficient of friction, μ s , being equal to F s N is a ratio of two forces and is, therefore, dimensionless. Further, coefficient of static friction is defined only for the maximum static friction, when body is about to move and not for friction before this stage. What it means that we can not estimate self adjusting static friction, using above relation. The self adjusting friction, as we can remember, is equal to the component of external force parallel to the contact surface.

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