1. FRICTION

2. Lecture Outline
Definition
Types of friction
Laws of friction
Coefficient of friction
Rough inclined plane
Angle of friction
Angle of repose
Ladder friction
Wedge Friction

3. If force P is so small that it can just move the body, then:
Definition
When two bodies are in contact and have the tendency to move over one another, then resistance to the movement is set up.
This resistance is called Friction or Frictional force.
Frictional force always acts in a direction opposite to the direction of the applied forced or in which contact surface tend to move. Its always parallel to the surface of contact.
If force P is so small that it can just move the body, then:
P=F
R=W

4. Types of friction
Static friction: it is a friction experienced by a body when it is at rest.
P<Fmax.
Dynamic friction: it is the friction experienced by a body when it is in motion. its also called Kinetic friction. It always less than the static friction.
P>Fmax.

5. Types of friction
Sliding friction: it is a friction experienced by a body when it slides over another body
EX: when a piston moves in the cylinder of the engine.
Rolling friction: it is the friction experienced by a body when it rolls over another body.
EX: When the train moves on the railway track

6. Laws of friction
Following are the laws of static Friction:
Force of friction always acts in a direction opposite to that in which the body tends to move.
The force of friction is independent of the area of contact between the two surfaces.
The magnitude of the force of friction is exactly equal to the applied force.
The force of friction depends upon the nature of the surfaces in contact.
The magnitude of the maximum static friction (limiting friction) bears a constant ration to the normal reaction between the two surfaces.
F/R= Constant

7. Laws of friction
Following are the laws of Dynamic or kinetic friction:
Force of friction always acts in a direction opposite to that in which the body is moving
The dynamic friction bears a constant ratio to the normal reation between the two surfaces.
The force of friction remains constant for moderate speed. But it decreases slightly with the increase of speed.

8. Coefficient of friction
Is the ratio of limiting friction to the normal reaction between the surfaces of contact. It is defined by µ .
Let F be the limiting friction and R be the normal reaction acting on a body then:
µ is a unitless quantity. µs µk

9. Rough inclined plane For motion take place down the plane
W . Sinɵ > µ.W. cosɵ
tanɵ>µ

10. Angle of Friction
Is the angle between the resultant (normal reaction and frictional force) and normal reaction.
P= applied force on the block
R= normal reaction
S= resultant of frictional force and normal reaction
F= Frictional force
Ø= angle of friction

11. Angle of repose
Is the maximum angle of inclination of the plane at which a body remains in equilibrium under the action of the friction only. If the angle of inclination is increased gradually, such that the block is just at the point of slide down. At this position the block is in equilibrium under the action of the following forces
Weight of the block, W
Normal reaction, R
Frictional force, F

12. Types of Problems
Data given: all applied forces, coefficient of friction
To find: whether the body will be at rest or in motion (slide).
2. Data given: all applied forces and motion.
To find: coefficient of friction
3. Data given: Coefficient of friction, motion
To find: magnitude and direction of applied force

13. Example 1: A block weighting 800 N , lying on a horizontal floor is just dragged by a force inclined at 35o to the floor. Find:
The value of P

14. Example 2: Find the value of effort P just to move the block weighting 200 N showing in Figure. Coefficient of friction between the block and the surface is 0.4. pulley B is frictionless.

15. Example 3: A body of weight 60 N is resting on a rough inclined plane
Example 3: A body of weight 60 N is resting on a rough inclined plane. A force of 36 N acting parallel to the plane just moves the body up the plane. To move the same body down the plane, a force of 24 N along and up the plane is necessary. Determine the inclination of the plane with the horizontal and coefficient between the body and plane.