PREPARATION SHEET

School name: GBTHS BAMENDA

Teacher: SHU CEDRIC MBOWA

Subject: APPLIED MECHANICSClass: F37 local: FIRST

Time:2HRS 30MIN

Topic to cover: FRICTION

Previous knowledge: resolution of forces, trigonometry

New words: coefficient of friction, cone of friction

Specific objectives: At the end of the lesson, students should be able to

 Define friction

 State the laws of friction and perform calculations

 Know the areas of application of friction.

Evaluation: evaluation will be done by questioning in class and exercises

References: Course Material on Friction by Dr.M.Madhavi,Professor,MED.

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 TOPIC: FRICTION

OBJECTIVES

At the end of this lesson, students should be able to

 Define friction
 State the laws of friction and perform calculations
 Know the areas of application of friction.

1.1 INTRODUCTION

Definition: Friction is defined as the contact resistance exerted by one body upon a second body
when the second body moves or tends to move past the first body. Or friction is a force that
opposes motion. Friction is a retarding force always acting opposite to the direction of motion or
tendency to move.

In some types of machines there is the desire to minimize the retarding effect of friction forces.
Examples: bearings of all types, power screws, gears, flow of fluid in pipes, propulsion of
aircraft, missiles through the atmosphere. Where as in other situations there is the desire to
maximize the effect of friction as in brakes, clutches, belt drives and wedges. Wheeled vehicles
depend on friction for both starting and stopping and ordinary walking depends on friction
between the shoe and ground.

1.2 TYPES OF FRICTION

1. Dry Friction: Dry friction is developed when the unlubricated surface of two solids are in
contact under a condition of sliding or a tendency to slide. This type of friction is also known
as Coulomb friction.
2. Fluid Friction: Fluid friction is developed when adjacent layers in a fluid (liquid or gas) are
moving at different velocities.

1.3 MECHANISM OF FRICTION

Friction exists primarily because of the roughness of the contact surface. Consider a block of
weight w resting on a horizontal surface. The contacting surface possesses a certain amount of

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roughness. Let P be the horizontal force applied which will vary continuously from zero to a
value sufficient to just move the block and then to maintain the motion. The free body diagram
of the block shows active forces as shown below

Frictional force F has the remarkable property of adjusting itself in magnitude equal to the
applied force P till the limiting equilibrium condition.

Block

surface

Figure 1

The above discussion can be represented by a graph with applied force P frictional force F as
shown

Referring the graph we may now recognize three distinct types of problems. Here, we have static
friction, limiting friction and kinetic friction.

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  Static Friction: this occurs when the body is at rest and in this case we can assume
equilibrium P <Fmax = Body is in the static equilibrium condition which means body is
purely at rest. Where P is the applied force.
 Limiting Friction: It is the maximum value of friction force that the surface can exert on
the block and is designated as Fmax.
P = Fmax = Body is in limiting equilibrium condition which means impending motion

Fmax= µSN

Where µs is the coefficient of friction which mainly depends on roughness of the materials of
the surfaces.

 Kinetic Friction: in this case, relative motion is known to exist between the contacting
surfaces. So, the body is in motion and hence
P >Fmax= Body is in motion which means

Fk = µkN

1.4 FRICTION ANGLES

1. Angle of Friction:

It is the angle made by the resultant of the limiting frictional force F max and the normal reaction
N. From figure 1 above,

2. Angle of Repose: It is the minimum angle of inclination of a plane with the horizontal at
which the body kept will just slide down on it without the application of any external
force ( Due to self-weight).

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 Figure 2

Consider the block with weight W is resting on an inclined plane, which makes an angle Θ with
the horizontal as shown in figure 2. When Θ is small the block will rest on the plane. If Θ is
increased gradually a slope is reached at which the block is about to start sliding. This angle Θ is
called angle of repose.

∑ Fx = 0 that is along the plane

µsN-W SinΘ= 0

WSinΘ = µN ------------ (I)

∑ Fy= 0 that is perpendicular to the plane

N-W Cos Θ= 0

WCosΘ = N ------------ (II)

Dividing Eq. (I) by Eq. (II), we get

Tan Θ = µ

In previous discussion, we had Tanø = µs which shows Angle of friction ø = Angle of Repose Θ

The above relation also shows that the angle of repose is independent of weight of the body it
depends on µ.

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1.5 CONE OF FRICTION

Figure 3

When the applied force P is just sufficient to produce the impending motion of given body, angle
of friction ø is obtained which is the angle made by resultant of limiting frictional force with
normal reaction as shown in Fig 3. If the direction of applied force P is gradually changed
through 3600, the resultant R generates a right circular cone with semi vertex angle equal to ø.
This is called Cone of Friction

1.6 LAWS OF FRICTION

1. The frictional force is always tangential to the contact surface and acts in the direction
opposite to that in which the body tends to move.
2. The magnitude of frictional force is self-adjusting to the applied force till the limiting
frictional force is reached and at the limiting frictional force the body will have the
impending motion.
3. Limiting frictional force Fmaxis directly proportional to normal reaction (Fmax = µsN).
4. For a body in motion, kinetic frictional force Fk developed is less than that of limiting
frictional force Fmax and the relation Fk = µkN is applicable.
5. Frictional force depends upon the roughness of the surface and the material in contact. 6
6. Frictional force is independent of the area of contact between the two surfaces.
7. Frictional force is independent of speed of the body.
8. Coefficient of static friction µs.is always greater than coefficient of kinetic friction µk . (µk
may be 25% smaller than µs.in general).

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Note: µs. & µk are dimensionless

9. Coulombs law of friction; It states that the amount of relative surface velocity has no effect
on kinetic friction exerted between the surfaces of two dry objects.

1.7 STEPS IN SOLVING FRICTION PROBLEMS

The first step in solving a friction problem is to identify its type

1. The first type of problem is when the condition of impending motion is known to exist. Here
a body which is in equilibrium is on the verge of slipping or moving, and the friction force
equals the limiting static friction. And hence the laws of equilibrium will be applied.
2. Second if neither the condition of impending motion nor the condition of motion is known to
exist, to determine the actual friction, we first assume static equilibrium and then solve for
the friction force F necessary for equilibrium.
3. Lastly if relative motion is known to exist between the contacting surfaces, the kinetic
coefficient of friction clearly applies.

1.8 APPLICATION EXERCISES

1. Will the 200N block be held in equilibrium by the horizontal force of 300N, if µ=0.3.

SOLUTION

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Since the motion of the block is unpredictable, we assume that 300N force is sufficient to hold
the block from sliding down the plan that is static equilibrium. Let F acts down the plane.

Resolving along the plane,

F + 200 sin30= 300 cos30

F = 300 cos-200sin=160N

For balance to exist, a frictional resistance of F=160kg would be required acting down plane.

Resolving perpendicularly to the plane

-N + 300sin30+ 200cos30 = 0

N=323N

However, the maximum value obtained (limiting friction)

Fi = µN= 0.3 x 323 = 97N

The value of F necessary to hold the block from moving up the plane is 160N. Therefore it
means that the block will move up the plane.

ASSIGNMENT

1. Determine which if any of blocks will move and frictional force acting under each, for A
&C

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1.9 APPLICATION OF FRICTION

1. Wedges: A wedge is one of the simplest and most useful machines. A wedge is used to
produce small adjustments in the position of a body or to apply large forces. Wedges largely
depend on friction to function.
2. Belt Friction: Belt or rope is wrapped around the pulleys to transmit power or effectively
used for braking systems. In order to evaluate the effectiveness of the system, the tensions in
the belt or rope are of important
3. Ladder: Many a times, we come across the uses of ladder for attending the higher heights.
Ladders are used by painters and carpenters who want peg a nail in the wall for mounting a
frame.
Example
1. A uniform ladder weighing 100N and 5 meters long has lower end B resting on the
ground and the upper end A resting against a vertical wall. The inclination of the ladder
with horizontal is 60˚. If the coefficient of friction at all surfaces of contact is 0.25,
determine how much distance up along the ladder a man weighing 600N can ascent
without causing it to slip.