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The question asked is why the value of limiting friction for any 2 given surfaces is independent of the shape or area of the surface in contact so long as normal reaction remains same.
The surface of bodies is not smooth, it has irregularities on a microscopic level. The frictional force between bodies is due to these irregularities interacting with each other. If one were to determine the actual surface area of two bodies that is in contact, it is much smaller than that of the apparent contact area when they are placed such that they are in contact.
If the normal reaction between the two bodies is increased, the microscopic irregularities are deformed such that there is an increase in the actual area of interaction between the bodies that results in the force of friction. It is this deformation of the surface of bodies due to the normal force that makes the frictional force independent of the shape and apparent area of contact and dependent only on the normal force.
Limiting friction is the maximum value of static friction which operates when a body is just going to start sliding over the surface of another body. It depends upon the nature of the surface but independent of the area of surface, provided the normal reaction remains unaltered.
`rArr F = mu_s*N`
`mu_s` is the coefficient of limiting friction.
This rule of limiting friction can be verified easily through a simple experiment. Consider a wooden block placed on a horizontal surface and attached to a string which passes over a frictionless pulley carrying a scale pan at the free end. Add weights in the scale pan till the wooden block just starts sliding. Repeat the experiment by placing the block on its side and on its base. It will be observed that the weights required to overcome the limiting friction is same in both the cases, though the surface area of contact is clearly different in the two situations.
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