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Chapter 2: Friction
If we examine the surface of any object, we observe that it is irregular.
It has protrusions and valleys.
When two surfaces are in contact, their irregularities intermesh, and as a result there is a resistance to the sliding or moving of one surface on the other.
This resistance is called friction.
Intergranular fracture in a nickel-chromium alloy, viewed under the scanning electron microscope.
Metal Surface under Microscopic Inspection
The surface of any object when closely examined is seen irregular.
It has protrusions and valleys.
When two surfaces are in contact, their irregularities intermesh, as a result there is a resistance to the sliding or moving of one surface on the other.
This resistance is called friction.
If one surface is to be moved with respect to each other, a force has to be applied to overcome friction.
The direction of a frictional reaction force always opposes the motion.
object moving theof velocity theis where,// vvFf
1. The magnitude of the frictional force depends on the nature of the surfaces; clearly, the rougher the surfaces, the greater is the frictional force. The frictional property of the surfaces is represented by the coefficient of friction μ.
2. The magnitude of the frictional force depends also on the force Fn perpendicular to the surfaces that presses the surfaces together. This force is always referred as the normal force.
nf μFF
1. The kinetic frictional force is the frictional force that acts on a moving object.
2. The static frictional force is the frictional force that acts on a stationary object.
nkf FμF
nsf FμF max,
ks μμ
A rigid sphere rolling on a plane Viscous friction in fluid flows
Other types of frictions
This type of friction is strongly velocity dependent.
Fiction is everywhere around us and is an indispensable factor in the ability of animals to move.
It is the frictional force that dissipates kinetic energy into heat and eventually stops a moving object.
Without friction we could not walk; nor could we balance on an inclined plane.
Sometimes for some mechanical purposes it is desirable to reduce the effect of friction. By introducing lubrication oils the friction can be greatly reduced. This is because the fluid oil fills the irregularities and thereby smoothes out the surfaces.
A natural example of such lubrication occurs in the joints of animals, which are lubricated by a fluid called the synovial fluid.
This lubricant reduces the coefficient of friction by about a factor of 100.
Nature indeed provides very efficient joint lubrication. The coefficient of friction is significantly lower than for steel on ice.
Standing at an Incline Calculate the angle of incline θ of an oak board on which a person of weight W can stand without sliding down.
θWFn cos
θWθWμμFF snf cos6.0cos
θWFp sin
fp FF
pf FF θWθW sincos 6.0
6.0tancos
sin θ
θ
θ
The force Fn normal to the inclined surface is
The static frictional force Ff is
The force parallel to the surface Fp, which tends to cause the sliding, is
The person will fall if
To keep the balance on the oak board
Therefore 31θ
When the joints are in motion, forces acting on the joints are very large. These forces tend to damage the joints unless they are well lubricated.
Frictional wear at the joints is greatly reduced by a smooth cartilage coating at the contact ends of the bone and by synovial fluid which lubricates the contact area.
When a man walks, the full weight of the body rests on one leg through most of each step.
Because the center of gravity is not directly above the joint, the force of the joint is greater than the weight and is about 2.4 times the weight.
The frictional force on the joint is then
)4.2( WμμFF nf
If the joint is not lubricated, the coefficient of friction (μ) would be about 0.3 and so the joint would have experienced a frictional force that is almost 72% of the total body weight.
However when the joint is well lubricated the fractional coefficient is only 0.003 and this will greatly reduce the frictional force down to 0.72% of the total body weight.
A Catfish
Catfish can be rather huge!!
Although in most cases good lubrication of bone-contact surfaces is essential, there are a few cases in nature where bone contacts are purposely unlubricated to increase friction.
Normally the fin is folded flat against the body, but when the fish is attacked, the appropriate muscles pull the bone of the fin into a space provided in the underlying skeleton.
The coefficient of frictional on points B and C must be high in order to lock the fin in the position.
The erect sharp fin discourages predators from eating the catfish.
An example of applying frictional force in nature
An example of applying frictional force in nature
Assume that a dislodging force of 0.1 N is applied at θ= 20° and the angle between the fine bone and the spine is 45°.
After the calculation we may show that the minimum value for the coefficient of friction between the bones to prevent dislodging of the bone is μ = 1.95 which is a large value when compare to a more usual value of ~ 0.5.
