Environmental Engineering Reference
In-Depth Information
surface area and increasing the compression causes this fraction to increase by
deformation of the points of contact. The parallel component of the force is called
friction; it clearly acts to resist any motion if we attempt to drag one surface across
the other. Already we can guess that as the normal force increases so will the
friction because of the more intimate contact between the two surfaces.
F
m s N
m k N
F = A
A
Figure 2.19
The magnitude of friction F plotted against the applied force A .
Now consider a simple experiment. A wooden block rests on a table. A force
A is applied to the block in some direction parallel to the plane of the table.
As the magnitude of A is increased from zero the following is observed. For
small values of A the block remains stationary. The fact that the block does not
accelerate as A is increased implies that friction must be equal in magnitude
but opposite in direction to the applied force. This is represented by the linear
portion of the graph of F against A in Figure 2.19. At some value of A the block
begins to move indicating that there must be a maximum value of friction, F max ,
acting between the block and the table. It is found experimentally that F max is
proportional to the normal force. This is hardly surprising since the two forces
have a similar origin, and both are dependent on the actual contact area between
the surfaces. This connection is expressed via
F max =
µ s N,
(2.29)
where the constant µ s is known as the coefficient of static friction and is
dependent on the nature of the surfaces. µ s is typically found to lie in the range
0 . 1
0 . 9 for everyday objects, although it is possible to manufacture materials
that have µ s considerably greater than unity. When the applied force exceeds
F max the object will start to move and the magnitude of friction will decrease
slightly to a roughly constant value of µ k N where µ k is the coefficient of kinetic
friction. Although µ k does have a weak and complicated dependence on velocity,
for simplicity of calculation we will treat it as a constant, dependent only on the
nature of the surfaces in contact. Certain fluids can have a dramatic effect on the
friction between two surfaces. When oil is used to coat surfaces it acts as a buffer
between the ridges and drastically reduces the value of µ s . Note that Eq. (2.29) is
not a vector equation. It expresses the relationship between the magnitudes of two
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