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Friction between solids
Life as we know it would he very strange without friction. Friction is useful in brakes - indeed,
without the frictional force between our feet and the ground we could not walk! Frictional
forces play a large part in the losses of energy from machinery and in this area great efforts
have been made to reduce them. Guillaume Amontons first established that there existed a
proportional relationship between friction force and the force between the bodies in contact.
Amontons' paper ‘De la résistance causée dans les machines’ was published in 1699 in
Memoires de l'Académie des Sciences.
To move one body over another which is at rest requires a force. This is needed both to
change the momentum of the first body and also to overcome the frictional force between
the two surfaces. The force needed to overcome the frictional force when the bodies are at
rest is called the limiting friction.
By experiment it has been found that the limiting frictional force between two surfaces
depends on
(a) the nature of the two surfaces, and
(b) the normal reaction between them. This can be expressed as an equation as
frictional force (F) = coefficient of friction () x normal reaction (R) (Figure 1)
normal reaction (R)
R
force (F)
Figure 1
The coefficient of friction depends on both surfaces.
When the object is moving the friction between the two surfaces is usually less than the
Iimiting friction. It is known as the coefficient of kinetic friction and is almost independent of
the relative velocities of the two surfaces.
Coefficients of friction:
Materials
Steel on steel
Aluminium on steel
Copper on steel
Brass on steel
Zinc on cast iron
Copper on cast iron
Glass on glass
Copper on glass
Teflon on Teflon
Teflon on steel
Steel on air
Rubber on concrete
Steel on ice
Tendon and sheath
Lubricated bone joint
Wood on wood
Waxed wood on dry snow
Static
0.74
0.61
0.53
0.51
0.85
0.94
0.68
0.04
0.04
0.001
1.0
0.03
0.013
0.001
0.3
Kinetic
0.57
0.47
0.36
0.44
0.21
0.29
0.4
0.53
0.04
0.04
0.001
0.8
0.003
0.04
1
You will see later that it is very simple to calculate the coefficient of friction from the slope
down which an object will slide. Remember that a frictional force always acts to oppose the
motion.
The frictional forces between glass fibres and the resins in which they are embedded (fibreglass) are vital factors in the strength of these materials.
Careful study of friction has shown that the frictional force between two surfaces is
independent of the area of contact. This can be explained as follows.
Think of two surfaces of steel which have been polished. When they are placed together we
think that they are in contact over their whole surface area but this is not the case.
In fact, they only touch at something like one ten-thousandth of their actual area as shown in
Figure 2.
F
F
Figure 2
cold weld
At the points of contact the surfaces are actually cold-welded’ together and it requires
energy to break the welds.
The motion of the top surface over the other is a stick-slip movement: the small projections
have to be broken as the object moves.
The friction between a rubber tyre and the surface of a road is of considerable importance in
safety. In normal use the tyres have a tread to allow the passage of water but in dry racingcar tyres, the so-called ‘slicks’, the tyre is perfectly smooth and relies on the heat generated
due to friction to melt a little of the tyre and so increase the road-holding ability.
Measurement of the coefficient of friction between two solid surfaces
(i) Direct method
A mass A is pulled across a horizontal surface by a Newton-meter and the force required is
recorded. If the weight of the object is known, the coefficient of friction may be determined.
(ii) Using a slope
The object is placed on a slope as shown in Figure 3 and the tilt of the slope () is slowly
increased until the object begins to slide down. At the moment of slip the forces on the
object are given by:
along the plane:
perpendicular to the plane:
F = mg sin 
R = mg cos 
R = mgcos 
F = R = mgsin 
Figure 3
Therefore:
Coefficient of friction () = F/R = tan
mg

2