Static And Kinetic Friction :
The force of friction comes into action only when there is a relative motion or there is a tendency of relative motion between the two contact surfaces. When two surfaces are in contact, frictional forces oppose relative motion or impending motion.
The direction of frictional forces are parallel to the surfaces in contact and oppose relative motion between two contact surfaces. Let us consider one situation: a block resting on a rough surface, is there any friction force acting on the block? Answer is ‘no’, because it is not having any motion tendency with respect to surface on which it is placed.
If we try to slide the block and the block is not sliding, then again consider the same question. Is there any frictional force acting? In this case, answer is ‘yes’, because this frictional force is resisting the relative motion of the block. As the box is at rest, the frictional force must exactly balance the pushing force. The nature of friction acting at this stage is called static friction. Once it starts moving kinetic friction comes into picture.
Static And Kinetic Friction
-
The frictional force
between two surfaces before the relative motion actually starts is called static frictional force or static friction, while the frictional force between two surfaces in contact and in relative motion is called kinetic frictional force or kinetic friction. Static friction is a self-adjusting force and it adjusts both in magnitude and direction automatically. Its magnitude is always equal to external effective applied force, tending to cause the relative motion and its direction is always opposite to that of external applied force. So, when a body is not in motion or is in equilibrium, then force of static friction is equal to the component of the applied External force(s) tangential to the surface.
-
Static Friction
exists between the two surfaces when there is tendency of relative motion but no relative motion along the two contact surface. For Example Consider a bed inside a room. When we gently push the bed with a finger, the bed does not move. This means that the bed has a tendency to move in the direction of applied force but does not move as there exists static friction force acting in the direction opposite to the applied force.
-
Kinetic friction
exists between two contact surfaces only when there is relative motion between the two contact surfaces. It stops acting when relative motion between two surfaces ceases. The direction of kinetic friction on an object is opposite to the relative velocity of the object with respect to the other object in contact considered.
Laws Of Friction
In Static Region The maximum force of static friction between any pair of dry unlubricated surfaces follows these two empirical laws.
(a)
It is approximately independent of the area of contact, and
(b)
It is proportional to the normal force
f
∝
N
.
The ratio of the magnitude of the maximum force of static friction to the magnitude of the normal force is called the coefficient of static friction
μ
s
for the surfaces involved. The magnitude of static friction is equal and opposite to the external force exerted, till the object at which force is exerted is at rest. This means it is a variable and self-adjusting force. However it has a maximum value called limiting friction. i.e.
where
The actual force of static friction may be smaller than
and its value depends on other forces acting on the body.
The magnitude of frictional force is equal to that required to keep the body at relative rest. So, we have
The plot of force of friction with the applied force is shown here.
It is observed that
1.
Initially, when there is no applied force, then force of friction is zero.
2.
as the applied force is increased and the body is still at rest, then the force of static friction is equal to the applied force.
3.
for a particular maximum value of the applied force, the body is on the verge of motion or is just about to move. This maximum value of force of static friction is called the force of limiting friction.
4.
when the applied force is increased beyond this maximum value, the body starts moving with respect to the surface on which it is kept and now the friction between the body and the surface is kinetic in nature
In Kinetic Region The force of kinetic friction,
f
k
, between dry unlubricated surfaces follows the same two laws as those of static friction.
(a)
It is approximately independent of the area of contact and
(b)
It is proportional to the normal force.
The force of kinetic friction is also reasonably independent of the relative speed with which the surfaces move over each other (provided it is neither too small, nor too large). The ratio of the magnitude of the force of the kinetic friction to the magnitude of the normal force is called the coefficient of kinetic friction μ
k
. If
f
k
represents the magnitude of the force of kinetic friction,
N
the normal reaction and μ
k
the coefficient of kinetic friction, then
Important Point For Static And Kinetic Friction
1.
Static friction comes into play whenever the surfaces in contact don’t move with respect to each other OR whenever a surface has a tendency to slip on another surface OR whenever force applied on a body kept on a surface tends to move the body and in all these cases the force of friction is opposite to the tendency of motion of the body due to the applied force.
2.
Kinetic friction comes into play whenever there is a relative motion between the two surfaces in contact and then the force of kinetic friction is always directed opposite to the direction of instantaneous relative velocity of the body with respect to the surface on which the body is kept.
Illustration
1.
A block of mass 10 kg is given a velocity of 10 ms
−1
and a force of 100 N in addition to friction force is also acting on the block. Calculate the retardation of the block
Ans.
Since there is relative motion, so the kinetic friction will act to reduce this relative motion.
100 + 10 = 10
a
Direction Of Static Friction Force
The static friction force on an object is opposite to its impending motion relative to the surface or tendency of motion of body w.r.t. the surface. The steps to be followed in determining the direction of static friction force on an object are
:
STEP-1:
Draw the free body diagram with respect to the other object or the surface on which it is kept.
STEP-2:
Also include pseudo force if contact surface is accelerating.
STEP-3:
Find the resultant force.
STEP-4:
Calculate the component of this force tangential to the surfaces in contact i.e. parallel to the contact surfaces.
STEP-5:
The direction of static friction is opposite to the tangential component of resultant contact force. Here once again, we must note that the static friction is involved when there is no relative motion between two surfaces.
Below is explained in tabular form, how the force of friction
f
depends on the applied force
F
.
|
F
|
f
|
F
net
= F – f
|
Static or kinetic friction
|
Relative motion or tendency of relative motion
|
Acceleration of block
|
Diagram
|
|
0
|
0
|
0
|
static
|
Neither tendency nor actual relative motion
|
0
|
|
|
2N
|
2N
|
0
|
static
|
Tendency
|
0
|
|
|
4N
|
4N
|
0
|
static
|
Tendency
|
0
|
|
|
5N
|
5N
|
0
|
static
|
Tendency
|
0
|
|
|
6N
|
4N
|
2N
|
kinetic
|
Actual relative motion
|
2 m/s
2
|
|
|
8N
|
4N
|
4N
|
kinetic
|
Actual relative motion
|
4 m/s
2
|
|
Angle Of Friction (λ):
At a point of rough contact, where slipping is about to occur, the two forces acting on each object are the normal reaction
N
and frictional force µ
N
. The resultant of these two forces is
F
and it makes an angle λ with the normal reaction, where
or
The angle
is called the angle of friction.
