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Friction
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Contact forces − A contact force on an object arises due to contact with some other
object − solid or fluid.
Example− force of friction
Friction − Friction is the property due to which force is set up at the surface of contact
of the two bodies preventing any relative motion between them.
It has been observed that if we cut off the engine of a moving car, it comes to rest after
covering some distance. According to Newton's first law, the motion could only be
destroyed by an external force. This means some external force is there, which opposes the
motion.
The emergence of this external force is due to a phenomenon called friction.
Friction is the phenomenon by virtue of which an opposition comes in to play between
two surfaces when one tends to slide/roll over the other.
The opposing force which comes into play is known as force of friction.
Force of friction is the force, which comes in to play between two surfaces when one
tends to slide/roll over the other.
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Cause of friction − No solid surface is perfectly smooth. Thus, when a body B is placed
over another body A, the irregularities of the two surfaces get interlocked and when
one body moves or tends to move over the other, there is always a force which
opposes the motion. Such resistance to motion is called friction.
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Friction always acts in a direction opposite to that of motion.
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Sliding friction − Whenever a body slides or tends to slide over the surface of another
body, the friction that comes into play is called sliding friction. It is of two types:
o Static friction − It is that opposing force which comes into play when a body
tends to slide over the surface of another body.
Dynamic friction − It is that opposing force which comes into play when a body
is actually sliding over the surface of another body. Dynamic friction is also
called the kinetic friction.
The maximum value of static friction which comes into play when the body is just on
the point of sliding is called the limiting friction.
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LAWS OF LIMITING FRICTION Statements about factors upon which the force of limiting friction between two surface
depends, are termed as laws of limiting friction. They are stated below:
(i) The direction of force of friction is always opposite to the direction of motion.
(ii) The force of limiting friction depends upon the nature and state of polish of the
surfaces in contact and acts tangentially to the interface between the two surfaces.
(iii) The magnitude of limiting friction 'F' is directly proponional to the magnitude of the
normal reaction R between the two surfaces in contact, i.e.,
Fα R
(iv) The magnitude of the limiting friction between two surfaces is independent of the
area and shape of the surfaces in contact so long as the normal reaction remains the same.
CO-EFFICIENT OF FRICTION
Co-efficient of friction of a pair of surfaces in contact is defined as the ratio between the
limiting
friction F to the normal reaction R. It is denoted µ.
µ = F /R
Since F depends upon the nature and state of polish of the surfaces in contact, µ also
depends upon these factors.
Angle of Friction: Let a block of mass 'm', placed over another surface, be pulled towards
right with a force P. When it is just on the point of sliding,
force
of limiting friction F acts in opposite direction. Let, 'OA'
be the
resultant of F and normal reaction R, making angle e with
R. 'θ' is
called the angle of friction.
Angle of friction is the angle which the resultant of limiting friction and normal reaction
makes with the normal reaction.
In triangle OAR
AB
OC
F
tanθ= =
µ ……(1) = = OB
R
OB
F
µ ( Co − efficient of friction ) =
R
Thus, co-efficient of friction is the tangent of angle of friction
Angle of Repose:
Consider a body of mass 'm' placed over an inclined plane
Weight mg of the body can be resolved into two components.
[Fig.].
(i) mg sin α along the plane
(ii) mg cos α, perpendicular to the plane.
If we increase the angle of inclination of the plane, component mg sin α keeps on
increasing. A stage comes when this component increases beyond limiting friction and the
body begins to slide. Such an angle of inclined plane is called the angle of repose.
Angle of repose is the angle which an inclined plane makes with the horizontal so that a
body placed over it just begins to slide of its own accord.
When the body is on the verge of sliding
mg sinα = F
Dividing
or
and
mg cosα = R
mgsinα
F
= mgcosα
R
tanα = F
=µ
R
tan α = µ ………..(2)
from (1) and (2)
α = θ
Thus angle of friction and the angle of repose are equal in magnitude.
Advantages and Disadvantages of Friction or "FRICTION, A NECESSARY Evil".
Advantages. There are so many advantages of friction, that it is impossible to imagine our
routine without friction. While writing, we are able to hold our pen in our hands, it is due to
the frictional force between pen and hand. While reading, we hold our book in our hands.
This is due to friction. We are able to walk on earth due to friction. We are able to stop a
moving automobile by the application of brakes. This is again due to friction. Hence friction
is a necessity.
Disadvantages. Due to friction we have, constantly, to do work to maintain the speed of a
machine. Had it not been there, a cycle once given push would roll for ever. So work done
against it is mere wastage of energy. Secondly, due to friction there is wear and tear of the
different parts of the machine. Thus friction is an evil.
From advantages and disadvantages of friction it is clear that friction is necessary and at the
same time it is an evil. Hence friction is a necessary evil.
Friction can be reduced if we try to remove the cause of friction.
(i) By rubbing and polishing. By rubbing, the irregularities of the surface are smoothened,
thus
avoiding the chance of getting the irregularities interlocked. This reduces the friction
between them.
(ii) By lubricants. A lubricant is an oil or grease which when spread over the surfaces fills the
irregularities and forms a thin layer between them, thus avoiding their interlockings. The
sliding now takes place between upper surface and the layer of lubricant. This friction is
much lesser than that between two surfaces.
(iii) By converting sliding into rolling friction. If we slide a heavy object on the floor we
require a big force. On the other hand, if we put it on wheels (a trolly) we can move it easily.
This is due to the reason that rolling friction is much lesser than the sliding friction. Sliding
friction can be converted into rolling friction by means of a system known as ball bearing
system. A number of steel balls are inserted between the axle and wheel, which reduces the
force of friction by considerable amount
(iv) By streamlining. As a body is driven through fluid, fluid friction depends upon the shape
of body. It is minimum for a shape known as streamlined shape. This shape is a pin-pointed
one. That is why all high speed bodies, aeroplanes, rockets etc. have pin pointed shapes.
CIRCULAR MOTION
Centripetal force:
Where,
M = Mass of the body
v = Velocity of the body
R = Radius of the circular path
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Motion of a car on a level road:
If R1 and R2 are the normal reactions of the ground on the two tyres of a car of weight Mg,
going around on a circular turn of radius r, with velocity v, on a level road, then
F1 = µR1
and F2 = µR2
Where, µ is the coefficient of friction between the tyres and the road
The total force of friction provides the necessary centripetal force, i.e.,
The total normal reaction balances the weight of the car, i.e.,
From equations (i) and (ii), we have
The above equation gives the maximum velocity with which the car can take a turn of radius
rs, when the coefficient of friction between the tyres and the road is equal to r.
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Motion of a car on a banked road:
For the vehicle to go round the curved track at a reasonable speed without skidding, the
greater centripetal force is managed for it by raising the outer edge of the track a little
above the inner edge. It is called banking of circular tracks.
Consider a vehicle of weight Mg, moving round a curved path of radius r, with a speed v, on
a road banked through angleθ.
The vehicle is under the action of the following forces:
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The weight Mg acting vertically downwards
The reaction R of the ground to the vehicle, acting along the normal to the banked
road OA in the upward direction
The vertical component R cos θ of the normal reaction R will balance the weight of the
vehicle and the horizontal component R sin θ will provide the necessary centripetal force to
the vehicle. Thus,
R cos θ = Mg …(i)
R sin θ =
…(ii)
On dividing equation (ii) by equation (i), we get
As the vehicle moves along the circular banked road OA, the force of friction between the
road and the tyres of the vehicle, F = μR, acts in the direction AO.
The frictional force can be resolved into two components:
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μ R sin θ in the downward direction
μ R cos θ in the inward direction
Since there is no motion along the vertical,
R cos θ = Mg + μ R sin θ ……. (iii)
Let vmax be the maximum permissible speed of the vehicle. The centripetal force is now
provided by the components R sin θ and μ Mg cos θ, i.e.,
R sin θ + μ R cos θ =
…….. (iv)
From equation(iii),we have
Mg = R cos θ (1−μ tan θ)…(v)
Again from equation (iv), we have
= R cosθ (μ + tanθ) …(vi)
On dividing equation (iv) by (v), we have