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 A 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.

16. Example 4: The 300 N crate with mass center at G is supported on the horizontal surfaces by a skid at A and a roller at B. if a force P of 60 N is required to initiate motion of the crate, determine the coefficient of static friction at A.

17. Example 5: The strut AB of negligible mass is hinged to the horizontal surface at A and to the uniform 25-Kg wheel at B. Determine the minimum couple moment M applied to the wheel which will cause it to slip if the coefficient of static friction between the wheel and the surface is 0.40.

18. Ladder Friction
let us consider a ladder AB of length l and weight W resting on a wall and floor making an angle ∂ with the floor.
Let µa and µB are the coefficients of friction of wall and ladder, and floor and ladder respectively.
When the lower end of ladder tends to slip away
from the wall, then the direction of frictional
force FB will be towards the wall.
When the upper end of the ladder moves
Downward, the frictional force FA will act upward.
RA & RB are the normal reactions at A and B respectively.

19. Ladder Friction
The ladder is in equilibrium under the action of the following forces:
a) Weight of the ladder
b) Normal reaction RA at A
c) Frictional force FA at A
d) Normal reaction RB at B
e) Frictional force FB at B

20. Example 6: A ladder of weight 390 N and 6 m long placed against a vertical wall at an angle of 30o as shown below. The coefficient of friction between the ladder and the wall is 0.25 and that between the ladder and floor is find how high a man of weight 1170 N can ascend before the ladder begins to slip.

21. Example 7: A ladder rests along vertical wall
Example 7: A ladder rests along vertical wall. The coefficient of friction between the floor and the ladder is 0.4 and between wall and ladder is the weight of ladder is 200 N and may be considered as concentrated at CG. The ladder also support a vertical load of 900 N at 1m along the length of ladder from top. Determine the least value of inclination of ladder at which the ladder may be placed without slipping.

22. Example 8: The 700-N force is applied to the 100-Kg block, which is stationary before the force is applied. Determine the magnitude and direction of the friction force F exerted by horizontal surface on the block.

23. Example 9: The magnitude of force P slowly increased
Example 9: The magnitude of force P slowly increased. Does the homogeneous box of mass m slip or tip first? State the value of p which would cause each occurrence.

24. Example 10: The system of two blocks, cable, and fixed pully is initially at the rest. Determine the horizontal force P necessary to cause motion when (a) P is applied to the 5-Kg block and (b) P is applied to the 10-Kg block. Determine the corresponding tension in cable T for each case.

25. Example 11
A block of 140 kg weight placed on an inclined surface as shown in Fig. Determine the required force (P) to move the body upward if the coefficient of friction between the block and the surface is μs = 0.25.

26. Example 12
The uniform beam as shown in Fig. is supported by the rope which is attached to the end of the beam, wraps over a smooth peg, and is then connected to the 50 kg block. If the coefficient of static friction between the beam and the block is µs=0.4, determine the maximum distance that the block can be placed from A (d) and still remain in equilibrium. Assume the block will not tip and neglect the weight of the beam.

27. Example 13

28. Example 14
A body of weight 4900 N is lying on an inclined wooden plane as shown in Fig. 1. The coefficient of friction is 0.3. answer the following:
State if the body will rest on the plane, moving up or moving down.
If the body is moving, what force is parallel to the plane is necessary to apply on the body to hold it?