Question

Briefly explain the origin of friction. Show that in an inclined plane, the angle of friction is equal to the angle of repose.

Answer 1

If a very gentle force in the horizontal direction is given to an object at rest on the table it does not move. It is because of the opposing force exerted by the surface on the object which resists its motion. This force is called the frictional force. During the time of Newton and Galileo, a frictional force was considered as one of the natural forces like a gravitational force. But in the twentieth century, the understanding of atoms, electrons, and protons has changed the perspective.

The frictional force is actually the electromagnetic force between the atoms on the two surfaces. Even well-polished surfaces have irregularities on the surface at the microscopic level. The component of force parallel to the inclined plane (mg sin θ) tries to move the object down. The component of force perpendicular to the inclined plane (mg cos θ) is balanced by the Normal force (N).
N = mg cos θ ………(1)

When the object just begins to move, the static friction attains its maximum value

`f_s = f_s^"max" = mu_sN`

This friction also satisfies the relation

`f_s^"max"` = µ_s mg sin θ ……….(2)

Equating the right-hand side of equations (1) and (2),

`(f_s^"max")"/"N = sintheta/costheta`

From the definition of angle of friction, we also know that

tan θ = µ_s ………..(3)

in which θ is the angle of friction.

Thus the angle of repose is the same as the angle of friction. But the difference is that the angle of repose refers to inclined surfaces and the angle of friction is applicable to any type of surface.