1. University Tun Hussein Onn Malaysia (UTHM),
Mechanics of Machines
BDA2033
Lecture #06
By,
Rosli Asmawi
University Tun Hussein Onn Malaysia (UTHM),
Faculty of Mechanical and Manufacturing,
Department of Mechanics

2. CHAPTERS : FRICTION (PART I)
Today’s Objectives:
Students will be able to:
1. understand the characteristics of dry friction
2. solve problems involving dry friction
Learning topics:
• Introduction
• Application
dry friction
angles of friction

3. INTRODUCTION
Friction is defined as a force of resistance acting on a body which prevents or retards slipping of the body relative to a second body.

4. APPLICATION
In designing a brake system for a bicycle, car, or any other vehicle, it is important to understand the frictional forces involved.
For an applied force on the brake pads, how can we determine the magnitude and direction of the resulting friction force?

5. THEORY OF DRY FRICTION
Block of weight W placed on horizontal surface. Forces acting on block are its weight and reaction of surface N.
Small horizontal force P applied to block. For block to remain stationary, in equilibrium, a horizontal component F of the surface reaction is required. F is a static-friction force.
As P increases, the static-friction force F increases as well until it reaches a maximum value Fm.
Further increase in P causes the block to begin to move as F drops to a smaller kinetic-friction force Fk.

6. THEORY OF DRY FRICTION (Cont.’d)
Maximum static-friction force:
Kinetic-friction force:
Maximum static-friction force and kinetic-friction force are:
proportional to normal force
dependent on type and condition of contact surfaces
independent of contact area

7. THEORY OF DRY FRICTION (Cont.’d)
Four situations can occur when a rigid body is in contact with a horizontal surface:
No friction, (Px = 0)
No motion, (Px < Fm)
Motion impending, (Px = Fm)
Motion, (Px > Fm)

8. ANGLE OF FRICTION
Consider block of weight W resting on board with variable inclination angle q.
The value of θ when slip is impending is called the angle of static friction θs ,
and its value when the surfaces are sliding relative to each other is called the
angle of kinetic friction θk.
we can express the angles of static and kinetic friction in terms of the coefficients
of friction.
tan θs = μs , tan θk = μk
In some situations it is more convenient to express the reaction in terms of its
magnitude R and angle of friction θ between the reaction and the normal to
surface.
Motion impending
No motion
Motion
No friction

9. PROBLEM INVOLVING DRY FRICTION
Coefficient of static friction is known
Motion is impending
Determine magnitude or direction of one of the applied forces
All applied forces known
Motion is impending
Determine value of coefficient of static friction.
All applied forces known
Coefficient of static friction is known
Determine whether body will remain at rest or slide

10. EXAMPLE
SOLUTION:
Determine values of friction force and normal reaction force from plane required to maintain equilibrium.
Calculate maximum friction force and compare with friction force required for equilibrium. If it is greater, block will not slide.
If maximum friction force is less than friction force required for equilibrium, block will slide. Calculate kinetic-friction force.
A 450 N force acts as shown on a 1350 N block placed on an inclined plane. The coefficients of friction between the block and plane are ms = 0.25 and mk = Determine whether the block is in equilibrium and find the value of the friction force.

11. SOLUTION
SOLUTION:
Determine values of friction force and normal reaction force from plane required to maintain equilibrium.
Calculate maximum friction force and compare with friction force required for equilibrium. If it is greater, block will not slide.
The block will slide down the plane.

12. SOLUTION (Cont.’d)
If maximum friction force is less than friction force required for equilibrium, block will slide. Calculate kinetic-friction force.

13. IN CLASS TUTORIAL
The arrangement in figure above exerts a horizontal force on the stationary 180 N
crate. The coefficient of static friction between the crate and the ramp is μs = 0.4.
If the rope exerts a 90N force on the crate, what is the friction force exerted on the crate by the ramp? [ans : f = N]
What is the largest force the rope can exert on the crate without causing it to slide up the ramp? [ans : T = 161 N]

14. IN CLASS TUTORIAL

15. End of Lecture