COURSE:COURSE: CE 201 (STATICS)CE 201 (STATICS)

LECTURE NO.:LECTURE NO.: 3737

FACULTY:FACULTY: DR. SHAMSHAD AHMADDR. SHAMSHAD AHMAD

DEPARTMENT:DEPARTMENT: CIVIL ENGINEERINGCIVIL ENGINEERING

UNIVERSITY:UNIVERSITY: KING FAHD UNIVERSITY OF PETROLEUM KING FAHD UNIVERSITY OF PETROLEUM & MINERALS, DHAHRAN, SAUDI ARABIA& MINERALS, DHAHRAN, SAUDI ARABIA

TEXT BOOK:TEXT BOOK: ENGINEERING MECHANICSENGINEERING MECHANICS--STATICS STATICS by R.C. HIBBELER, PRENTICE HALLby R.C. HIBBELER, PRENTICE HALL

LECTURE NO. 37LECTURE NO. 37DRY FRICTIONDRY FRICTION

Objectives:Objectives: To introduce the concept of dry frictionTo introduce the concept of dry friction

DEFINITION OF FRICTIONDEFINITION OF FRICTION

Friction may be defined as a force of resistanceacting on a body, which prevents or retardsslipping of the body relative to a second body orsurface with which it is in contact.

Friction force always acts tangent to the surface of the body in contact to a second body or surface.

TYPES OF FRICTIONTYPES OF FRICTION

Fluid friction exists when the contactingsurfaces are separated by a film of fluid (i.e.,gas or liquid). Fluid friction is studied in fluidmechanics

Dry friction or Coulomb friction occurs between the contacting surfaces of bodies inabsence of a lubricating fluid.

THEORY OF DRY FRICTIONTHEORY OF DRY FRICTIONDevelopment of Frictional Force (F): Let us consider a pulling force P

applied to a block of uniform weight,W, resting on a rough horizontalsurface, as shown in figure below:

Under the effect of the externalforces P and W, two reacting forces(normal force N and frictional force F) are developed, as shown in figure below:

The frictional force, F acts always parallel to the rough surface andthe normal force acts alwaysperpendicular to the rough surface

The frictional force, F always opposes the motion of the body

The frictional force, F increases with increase in applied force P till F reaches to a maximum value,called limiting frictional force Fs.

THEORY OF DRY FRICTIONTHEORY OF DRY FRICTIONLimiting Static Frictional Force (Fs): The limiting friction force Fs is the maximum frictional force

which can develop between a rough surface and a body Experimentally, it has been determined that the limiting frictional

force Fs is directly proportional to the resultant normal reaction N. This may be expressed mathematically as:

sF N s sF N = where the constant of proportionality, s , is called the coefficient of static friction

The coefficient of static friction, s , depends on the contact materials

Typical values of s are given in the following table: Contact materials Coefficient of Static Friction (s)

Metal on ice 0.03 0.05Wood on wood 0.30 0.70Leather on wood 0.20 0.50Leather on metal 0.30 0.60Aluminum on aluminum 1.10 1.70

THEORY OF DRY FRICTIONTHEORY OF DRY FRICTIONAngle of Static Friction s The angle that the resultant Rs of the normal force N and limiting

static frictional force Fs makes with the normal force is called theangle of static friction s , as shown in the following figure:

Referring the above figure, the expression for the angle of static friction s can be obtained in terms of the coefficient of static friction s , as follows:

1 1 1 1tan tan tan tans ss s s sF NN N

= = = =

THEORY OF DRY FRICTIONTHEORY OF DRY FRICTION

Kinetic Frictional Force (Fk): When the applied force P exceeds limiting friction force Fs, the

limiting friction force Fs gets significantly reduced and body startsmoving. The frictional force which acts between the rough surfaceand the body under motion is called kinetic frictional force Fk.

Experiments with sliding blocks indicate that the magnitude of theresultant kinetic frictional force Fk is directly proportional to themagnitude of the resultant normal reaction N This may be expressed mathematically as: kF N k kF N = where the constant of proportionality, k , is called the coefficient of kinetic friction

Typical values of k are approximately taken as 75% of the valuesof s (i.e., 0.75k s = )

THEORY OF DRY FRICTIONTHEORY OF DRY FRICTIONAngle of Kinetic Friction k The angle that the resultant Rk of the normal force N and limiting

kinetic frictional force Fk makes with the normal force is called theangle of kinetic friction k , as shown in the following figure:

Referring the above figure, the expression for the angle of static friction k can be obtained in terms of the coefficient of static friction k , as follows:

1 1 1 1tan tan tan tank kk k k kF NN N

= = = =

THEORY OF DRY FRICTIONTHEORY OF DRY FRICTIONSliding or Tipping: Whether the block will be sliding or tipping (overturning), may be

known by calculating the value of x considering the equilibrium ofthe block, as follows:

0

. . 0 about point OM

W x P hPhxW

= + = =

If x a/2 the block will be sliding If x > a/2 the block will be tipping

(overturning)

THEORY OF DRY FRICTIONTHEORY OF DRY FRICTIONState of the Motion of the Block: When P < Fs, the block will be in

the state of stable equilibrium

When P = Fs, the block will tend toslip, however no motion would takeplace. Such state of the block is called either the state of unstableequilibrium or the state of impendingmotion (i.e., just about to move)

When P > Fs, the block will startmoving after a drop of frictionalforce from Fs to Fk. Such state of the block is called the state of motion.

The state of motion of the block canbe graphically represented as shownin the following figure:

Multiple Choice Problems

1. A block placed on a rough surface is subjected to a force P. If the limiting frictional force between the block and the rough surfaceis Fs, the block will be in state of stable equilibrium when

(a) P < Fs (b) P = Fs (c) P > Fs (d) None of these Ans: (a) Feedback: Friction force, greater than the applied force, will keep the blockin the state of stable equilibrium.