UNIT 3
Friction
It is a tangential force developed between the bodies (or two surfaces) which are in contact when one body moves or tends to move over another body (or surface).
Frictional force always acts in the opposite direction of motion or in the opposite direction of impending motion.
- Impending Motion :
It is the state of body in which the body is on the verge of motion i.e. about to move.
Frictional force is denoted by Fs or FK
- Characteristics Frictional Force
- Its reactive and self-adjusting force
- Frictional force increases when external force is increased upto limiting condition.
At the limiting particles try to impend the motion.
When particle is in motion, frictional force decreases with increases in external force.
3. Frictional force always acts in the opposite direction of motion or in the opposite direction of impending motion
4. Upto limiting condition, frictional force is equal in magnitude of external force
- Friction
Friction is defined as the resistive force which acts in the opposite direction of motion of body.
- Classification of Friction:
- Static Friction
- Kinetic Friction A) sliding Friction , B) Rolling Friction
- Static Friction :
Friction experienced by a body when it is at rest condition
- Kinetic Friction :
- Friction experienced by a body when it moves
- When one body slides over another, then friction experienced by a body is sliding friction
- When one body rolls over another, then friction experienced by body is called as Rolling Friction.
- Laws of Friction(Coulombs Law)
- For Static Friction :
1) Frictional force always acts in opposite direction in which body tends to move
2) Frictional force is directly proportional to normal reaction
3) Frictional force is equal to net force acting in the direction in which object tends to move.
4) Frictional force does not depend on the surface area contact.
5) Frictional force depends upon roughness of surface.
Types of friction
Friction is the force that opposes motion between any surfaces that are in contact. There are four types of friction: static, sliding, rolling, and fluid friction. Static, sliding, and rolling friction occur between solid surfaces. Fluid friction occurs in liquids and gases. All four types of friction are described below.
Static Friction
Static friction acts on objects when they are resting on a surface. For example, if you are hiking in the woods, there is static friction between your shoes and the trail each time you put down your foot (see Figure below). Without this static friction, your feet would slip out from under you, making it difficult to walk. In fact, that's exactly what happens if you try to walk on ice. That's because ice is very slippery and offers very little friction.
Sliding Friction
Sliding friction is friction that acts on objects when they are sliding over a surface. Sliding friction is weaker than static friction. That's why it's easier to slide a piece of furniture over the floor after you start it moving than it is to get it moving in the first place. Sliding friction can be useful. For example, you use sliding friction when you write with a pencil. The pencil “lead” slides easily over the paper, but there's just enough friction between the pencil and paper to leave a mark.
Rolling Friction
Rolling friction is friction that acts on objects when they are rolling over a surface. Rolling friction is much weaker than sliding friction or static friction. This explains why most forms of ground transportation use wheels, including bicycles, cars, 4-wheelers, roller skates, scooters, and skateboards. Ball bearings are another use of rolling friction. You can see what they look like in the Figure below. They let parts of a wheel or other machine roll rather than slide over on another.
The ball bearings in this wheel reduce friction between the inner and outer cylinders when they turn.[Figure3]
Fluid Friction
Fluid friction is friction that acts on objects that are moving through a fluid. A fluid is a substance that can flow and take the shape of its container. Fluids include liquids and gases. If you've ever tried to push your open hand through the water in a tub or pool, then you've experienced fluid friction. You can feel the resistance of the water against your hand. Look at the skydiver in the Figure below. He's falling toward Earth with a parachute. Resistance of the air against the parachute slows his descent. The faster or larger a moving object is, the greater is the fluid friction resisting its motion. That's why there is greater air resistance against the parachute than the skydiver's body.
Laws of dry friction:
Dry friction resists relative lateral motion of two solid surfaces in contact. The two regimes of dry friction are 'static friction' ("stiction") between non-moving surfaces, and kinetic friction (sometimes called sliding friction or dynamic friction) between moving surfaces.
Ff ≤μFn
- Ff is the force of friction exerted by each surface on the other. It is parallel to the surface, in a direction opposite to the net applied force.
- μ is the coefficient of friction, which is an empirical property of the contacting materials,
- Fn is the normal force exerted by each surface on the other, directed perpendicular (normal) to the surface.
The Coulomb friction Ff may take any value from zero up to μFn , and the direction
Of the frictional force against a surface is opposite to the motion that surface would experience in the absence of friction. Thus, in the static case, the frictional force is exactly what it must be in order to prevent motion between the surfaces; it balances the net force tending to cause such motion. In this case, rather than providing an estimate of the actual frictional force, the Coulomb approximation provides a threshold value for this force, above which motion would commence. This maximum force is known as traction.
The force of friction is always exerted in a direction that opposes movement (for kinetic friction) or potential movement (for static friction) between the two surfaces. For example, a curling stone sliding along the ice experiences a kinetic force slowing it down. For an example of potential movement, the drive wheels of an accelerating car experience a frictional force pointing forward; if they did not, the wheels would spin, and the rubber would slide backwards along the pavement. Note that it is not the direction of movement of the vehicle they oppose; it is the direction of (potential) sliding between tire and road.
Angle of static Friction (
S) :
For the body at rest, the angle between
Normal reaction and resultant reaction
Is called as angle of static friction (
S)
tan (
S) = 
tan 
S = 
S
S =tan 
Sand
S = tan-1
S
It is the angle made by inclined surface with the horizontal, when the block kept on inclined plane just begins to slide down the plane due to its self-weight.
Angle of friction static and angle of repose are equal.
S = 
tan 
S = 
S
- Coefficient of friction :
- Coefficient of static friction (
) : from Culombs law
Magnitude of frictional force is directly proportional to normal reaction
FS
RN
FS = 
S RN
S = 
B. Coefficient of kinetic friction (
K) :
C. FK
RN
FK = 
K RN
K = 
When two surfaces are sliding past each other, the frictional force between them is usually less than the static friction. The frictional force isFf=μkR where μk, is the coefficient of sliding or dynamic or kinetic friction and , R, is the normal reaction force of the two surfaces.
Figure 1: A block moving across a rough surface.
In Figure 1 the magnitude of the reaction force is R=mg so the magnitude of the dynamic frictional force is Ff=μkR=μkmg.
In Figure 1 there is no force pushing the moving block so this frictional force would cause the block to decelerate.
Unless chemical bonding occursμk<μ. So, once sliding starts under the influence of an applied force, then the resistive effect of the frictional contact between the surfaces is reduced. Typical values of μ are given in table 1.
If a ladder is placed against a rough horizontal floor and a vertical wall (smooth or roughly) then ladder is subjected to non-concurrent force system.
Friction acts along the plane where the two surfaces are touching. For a block on a slope, as shown here, the friction force acts in the plane of the slope. In this case the block is stationary and so the frictional force acts to prevent it sliding down the slope, so the frictional force acts up the slope.
If the block is in equilibrium then the forces on it sum to zero. Resolving perpendicular to the slope gives N=mgcosθ. This means that the maximum frictional force is F=μmgcosθ where μ is the coefficient of friction between the block and the slope.
A wedge is a piece of metal or wood which is usually of a triangular or trapezoidal in cross-section. It is used for either lifting loads through small vertical distances or used for slight adjustments in the position of a body i.e., for tightening fits or keys for shafts.
When lifting a heavy load the wedge is placed below the load and a horizontal force P is applied as shown in Fig. 3.41. If the force P is just sufficient to lift the load, the wedge will move towards left and load will move up. When the wedge moves towards left, the sliding of the surfaces AC and AB will take place. At the same time load moves up and sliding of the load takes place along GD. Thus for the wedge and load shown in Fig.3.41 sliding takes place along surface AB, AC and DG. Hence there will be three normal reactions at AB, AC and DG.
The problems on wedges are generally the problems of equilibrium on inclined planes. Therefore, these problems are solved by equilibrium method or by applying Lami’s Theorem.
Equilibrium Method. In this method, the equilibrium of the load (or the body placed on the wedge) and the equilibrium of the wedge are considered.
Equilibrium of Wedge
Consider the equilibrium of the wedge. The forces acting on the wedge are shown in Fig. 3.42. They are:
(i) The force P applied horizontally on face BC.
(ii) Reaction R1 on the face AC (The reaction R1 is the resultant of the normal reaction N1 on the rubbing face AB and force of friction on surface AC). The reaction R1 will be inclined at an angle θ1 (when θ1 is angle of friction) with the normal.
(iii) Reaction R2 on the face AB (The reaction R2 is the resultant of normal reaction N2 on the rubbing face AB and force of friction on surface AB). The reaction R2 will be inclied at an angle Φ2 with the normal.
When the force P is applied on the wedge, the surface CA will be moving towards left and hence force of friction on this surface will be acting towards right. Similarly, the force of friction on face AB will be acting from A to B. These forces are shown in Fig. 3.42.
Resolving the forces horizontally, we get
Equilibrium of Body placed on the Wedge
The forces acting on the body are shown in Fig.3.44. They are:
(i) The weight W on the body.
(ii)Reaction R3 on the face GD. (The reaction R3 is the resultant of the normal reaction N3 on the rubbing face GD and force of friction on surface GD).
(iii)Reaction R3 on the face GF (The reaction R2 is the resultant of the normal reaction N2 on the rubbing face GF and force of friction on surface GF).
These forces are shown in Fig. 3.44.
Resolving the forces R2, R3 and W horizontally, we get
