Discuss friction phenomenon and its effect on motion of body on horizontal and inclined surface

1. Friction
Prepared by
Sandeep Chauhan
Assistant Professor,
Department of Mechanical Department
G. L. Bajaj Institute of Technology & Management,
Greater Noida
Unit 5 of Theory of Machines (RME 602)

2. Contents
What ?
Why ?
during motion of a body on a horizontal surface
during motion of a body on inclined surface
Unit 5 of Theory of Machines (RME 602)

3. Friction: What?
• Friction is defined as phenomenon by which relative motion between
two bodies in contact are resisted.
• Force applied by one body over another body to oppose the relative
motion between them is known as friction force.
• It arises only when one body moves with respect to other or tends to
move.
• It is desirable as well as undesirable.
• Desirable: Belt & rope drive, Friction clutches, Brakes, Walking
• Undesirable: Energy loss at joint
Unit 5 of Theory of Machines (RME 602)

4. Friction: Why?
• All material surfaces, no matter how smooth they are, show many
irregularities in the form of peaks and valleys, which are large when
considered on a molecular scale.
• When these two solid surfaces slide over each other, a real contact
between these surfaces occurs that will cause friction and consequently
the production of heat.
• This friction also causes a lot of wear and tear of the surfaces of the
moving parts.
Unit 5 of Theory of Machines (RME 602)

5. Types of Friction:
On the basis of relative motion, friction is classified into following
groups:
1. Static friction
2. Dynamic or Kinetic friction
a. Sliding friction
b. Rolling friction
c. Pivot friction
Unit 5 of Theory of Machines (RME 602)

6. Types of Friction:
On the basis of condition of surface ,friction is classified into following
groups:
1. Dry Friction :The friction experienced between two dry and
unlubricated surfaces in contact is known as Dry Friction.
2. Greasy Friction or Boundary Friction or Non-viscous Friction: It is
the friction experienced between rubbing surfaces ,when the
surfaces have a skin thin layer of lubricant between them.
3. Film Friction or Viscous Friction : When two contacting surfaces are
completely separated by a thin layer of lubricant and the friction
occurs only due to resistance of the motion of lubricant layers ,
friction is known as film friction.
Unit 5 of Theory of Machines (RME 602)

7. Laws of Static Friction:
1. The force of friction always acts in a direction, opposite to that in which the
body tends to move.
2. The magnitude of the force of friction is exactly equal to the force, which tends
the body to move.
3. The magnitude of the limiting friction (F ) bears a constant ratio to the normal
reaction (Rn ) between the two surfaces.
Mathematically F/Rn = constant
4. The force of friction is independent of the area of contact, between the two
surfaces.
5. The force of friction depends upon the roughness of the surfaces.
Unit 5 of Theory of Machines (RME 602)

8. Law of Kinetic or Dynamic Friction:
1. The force of friction always acts in a
direction, opposite to that in which the
body is moving.
2. The magnitude of the kinetic friction
bears a constant ratio to the normal
reaction between the two surfaces. But this
ratio is slightly less than that in case of
limiting friction.
3. For moderate speeds, the force of
friction remains constant. But it decreases
slightly with the increase of speed.
Unit 5 of Theory of Machines (RME 602)

9. Laws of Solid Friction:
1. The force of friction is directly proportional to the normal load
between the surfaces.
2. The force of friction is independent of the area of the contact surface
for a given normal load.
3. The force of friction depends upon the material of which the contact
surfaces are made.
4. The force of friction is independent of the velocity of sliding of one
body relative to the other body.
Unit 5 of Theory of Machines (RME 602)

10. Limiting Force of Friction or Limiting Friction:
Unit 5 of Theory of Machines (RME 602)

11. Limiting Force of Friction or Limiting Friction:
• The maximum value of frictional force , which comes into play , when
a body just begins to slide over another body , is known as limiting
force of friction.
• When the applied force is less then the limiting force of friction , the
body remains at rest ,and the friction is known as static friction which
may have any value between zero and limiting friction.
Unit 5 of Theory of Machines (RME 602)

12. Coefficient of Friction:
• It is the ratio of Limiting friction force and normal reaction.
Mathematically
Coefficient of friction ( µ ) =
𝐿𝑖𝑚𝑖𝑡𝑖𝑛𝑔 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝐹𝑜𝑟𝑐𝑒
𝑁𝑜𝑟𝑚𝑎𝑙 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠
=
𝐅
Rn
Unit 5 of Theory of Machines (RME 602)

13. Angle of Friction (Ø):
• It is the angle made by resultant of limiting
friction force and normal reaction made with
the normal reaction.
Mathematically, Ø = tan−1 µ
• No movement is possible until the angle
made by resultant with normal reaction
becomes equal to limiting angle of friction.
Unit 5 of Theory of Machines (RME 602)

14. Friction Cone:
• Cone generated when resultant vector (R)
is rotated about normal to relative motion,
is known as friction cone.
• A cone in which the resultant force exerted
by one flat horizontal surface on another
must be located when both surfaces are at
rest, as determined by the coefficient of
static friction.
Unit 5 of Theory of Machines (RME 602)

15. Angle of Repose:
It is the angle made by
inclined plane with
horizontal plane when
body resting on inclined
plane begins to move
down due to its own
weight.
∅ = α
Unit 5 of Theory of Machines (RME 602)

16. Motion of a Body on a Rough Horizontal Plane
Unit 5 of Theory of Machines (RME 602)

17. Motion of a Body on a Rough Inclined Plane
(A) When body moves upward:
Let W = Weight of the body,
α= Angle of inclination of the plane to the horizontal,
φ = Limiting angle of friction for the contact surfaces,
P = Effort applied in a given direction in order to cause the body to slide with
uniform velocity parallel to the plane, considering friction,
P0 = Effort required to move the body up the plane neglecting friction,
θ = Angle which the line of action of P makes with the weight of the body W,
μ = Coefficient of friction between the surfaces of the plane and the body,
RN = Normal reaction, and
R = Resultant reaction.
Unit 5 of Theory of Machines (RME 602)

18. Unit 5 of Theory of Machines (RME 602)

19. Motion of a Body on a Rough Inclined Plane
(A) When body moves downward:
Unit 5 of Theory of Machines (RME 602)