Friction
Whenever surface of a body tend to move on or actually moves relative to another surface in contact, an opposing force is generated between the surfaces. This phenomenon is called ‘friction’ and the opposing force is called frictional force.
There are of three types of friction:
- Static Friction.
- Sliding Friction or Kinetic Friction.
- Rolling Friction.
Static Friction
Whenever surface of a body at rest, tend to move on another surface in contact, an opposing force is generated between the surfaces. This phenomenon is called static friction and the opposing force is called force of static friction (fs).
Properties of Static Friction
- Force of static friction is a contact force.
- Force of static frictions is generated tangential to the surfaces in contact and it is in the direction opposite to the direction in which body tend to move.
- Force of static friction is a self adjusting force i.e. it can adjust its value according to the net external force acting on the body up to a maximum limit. This maximum limit up to which the force of static friction can increases its value is known as limiting force of static friction [fsm or fs max]
- The value of fsm doesn’t depend upon the area of contact between the two surfaces.
- Value of fsm is directly proportional to the normal force acting between the two force i.e. fsm ∝ N
Or fsm = μs N ……….………..(1)
Where μs is a constant for the pair of surfaces in contact and it is called ‘coefficient of static friction’.
Static Friction (Video)
In Hindi + English Mix
Example.
A block of mass 5 kg is kept on a rough horizontal surface (ms= 0.4). When a horizontal force of 5N is applied on it. What is the force of static friction on the body.
Solution. N = mg
So, N = 5 x 10 N= 50N
Again, Fsm = μsN = 0.4 x 50 = 20N
Since, the value of the force (which tend to move the body) is lesser than Fsm , it is within the self adjusting range and thereby, fs = F = 5N,
Example.
A vehicle is being moved with some acceleration. A block is kept at rest on the horizontal surface of the vehicle. If coefficient of static friction between the block and the surface is 0.5, determine the maximum possible value acceleration of the vehicle.
Solution.
As the vehicle moves forward with acceleration, there is a pseudo force acting on the block in the opposite direction. The pseudo force is given by Fp= ma0 ………..(1)
But the force of static friction will balance Fp. As acceleration a0 is increased, Fp increases and fs also increase. So, in limiting case Fpmax = fsm
Or, ma0 max = μsN.
Or, maOmax = μsmg
Or, aOmax = μsg
a0max = 5 m/s2
Example.
A block of mass 2 kg is pressed against a rigid vertical wall by a horizontal force of 100N. If co-efficient of static and kinetic friction are each equal to 0.3 then find the magnitude and direction of frictional force on the block.
Solution: Since weight of block is 20 N which is acting downward, it has tendency to move the block downward. Hence the frictional force will be upward. Maximum value of frictional force can be
fs(max) = μFn
Where, Fn is the normal force on the body.
As block is in equilibrium along horizontal
Fn = horizontal external force = 100 N
∴ fs(max) = 0.3 x 100 N = 30 N
Since weight of the block is less than the limiting friction, it will not slide.
Therefore for vertical equilibrium, force of friction is f = 20N. (vertically upwards)
Angle of Friction
The angle subtended by the resultant of the normal force and the limiting force of static friction with the direction of normal force is called angle of friction between the two surfaces
Or tan λ = fsm/N
Or tan λ = μsN/N
Or tan λ = μs ……………(1)
Or λ = tan-1 μs ………….(2)
Since, for a given pair of surface is constant, the angle of friction is also constant for a given pair of surface.
Angle of Repose
Maximum angle of inclination upto which a block kept on the inclined surface can remain at rest is known as angle of repose . Also above this angle the block starts sliding down due to its own weight
Along y –axis:
∑F =may
Or N – mg.cosθc = 0
Or N = mg.cosθc ……………(1)
Along x – axis: ax = 0, ∑Fx = max
Or mgsinθc – Fsm = 0
Or Fsm = mg sinθc
Or, μs N = mg sin θc
Putting the value of N, from Eq.(1)
μsmg.cosθc = mg sin θc
Or, μs = tanθc ………..(2)
Or θc = tan-1μs ………..(3)
Note: Although value of angle of friction is same as that of angle of repose, but there physical significance [physical meaning] is different.
Angle of friction & Angle of Repose (Video)
In Hindi + English Mix
Kinetic Friction Or Sliding Friction
Whenever surface of a body moves on another surface in contact, there appears an opposing force between the surfaces in constant. This force is known a force of sliding friction or force of kinetic friction(fk).
Properties of Force of Kinetic Friction
- Force of kinetic friction (fk) is generated tangential to the surfaces in contact and its direction is opposite to the direction of motion of the surface with respect to other surface.
- The force of kinetic friction does not depend upon the area of contact between the two surfaces.
- The force of kinetic friction between two surfaces is independent of relative speed of surfaces, provided it is too large or too small.
- The magnitude of fk is directly proportional to the normal force that is acting between the two surface.
i.e. fk ∝ N
or fk = μk N ………….(1)
Where of surfaces in constant for the known as coefficient of kinetic friction of the pair of surfaces.
Comparison between fsm and fk
For a given pair of surfaces value of μk is little less than μs.
i.e. μk < μs
or μK N < μsN.
or fk < fsm
i.e. for a given pair of surfaces in contact, the value of liniting force of static friction is a little mire than the value of kinetic friction, provided the normal force acting between the bodies is same in both the cases.
Kinetic Friction (Video)
In Hindi + English Mix
