Engineering Mathematics


Friction is the contact resistance exerted by one body when the second body moves or tends to move past the first body. Friction is a retarding force that always acts opposite to the motion or to the tendency to move.

Types of Friction
Dry Friction
Dry friction, also called Coulomb friction, occurs when unlubricated surfaces of two solids are in contact and slide or tend to slide from each other. If lubricant separates these two surfaces, the friction created is called lubricated friction. This section will deal only with dry friction.

Fluid Friction
Fluid friction occurs when layers of two viscous fluids moves at different velocities. The relative velocity between layers causes frictional forces between fluid elements, thus, no fluid friction occurs when there is no relative velocity.

Skin friction
Skin friction also called friction drag is a component of the force resisting the motion of a solid body through a fluid.

Internal Friction
Internal friction is associated with shear deformation of the solid materials subjected to cyclical loading. As deformation undergo during loading, internal friction may accompany this deformation.

Elements of Dry Friction
$N$ = Total reaction perpendicular to the contact surface
$f$ = Friction force
$\mu$ = Coefficient of friction
$R$ = Resultant of f and N
$\phi$ = angle of friction

Dry friction between the block and the floor


Formulas for dry friction

$f = \mu N$

$\tan \phi = \dfrac{f}{N}$

$\tan \phi = \mu$


000-friction-inclined-plane.gifConsider the block shown to the right that weighs   $W$.   It is placed upon a plane that inclined at an angle   $\theta$   with the horizontal.

  • If   $\phi \lt \theta$   the maximum available friction force   $f$   is less than   $W_x$   thus, the block will slide down the plane.
  • If   $\phi = \theta$   the friction force   $f$   will just equate to   $W_x$   thus, the block is in impending motion down the plane.
  • If   $\phi > \theta$ the maximum available frictional resistance   $f$   is greater than   $W_x$   thus, the block is stationary.

We can therefore conclude that the maximum angle   $\theta$   that a plane may be inclined without causing the body to slide down is equal to the angle of friction   $\phi$.