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Consider a block of mass being dragged over a horizontal
surface, whose coefficient of friction is
, by a horizontal
force
. See Fig. 32. The weight
of the block
acts vertically downwards, giving rise to a reaction
acting
vertically upwards. The magnitude of the frictional force
, which
impedes the motion of the block, is simply
times the
normal reaction
. Hence,
. The acceleration of
the block is, therefore,
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Consider a block of mass sliding down a rough incline (coefficient of
friction
)
which subtends an angle
to the horizontal, as shown in Fig 33.
The weight
of the block can be resolved into components
, acting
normal to the incline, and
,
acting parallel to the incline. The reaction of the incline
to the weight of the block acts normally outwards from the incline, and is
of magnitude
.
Parallel to the incline,
the block is subject
to the downward gravitational force
,
and the upward frictional force
(which acts to prevent the block sliding down the
incline). In order for the block to move, the magnitude of the former force must
exceed the maximum value of the latter, which is
time the magnitude
of the normal reaction, or
. Hence, the condition
for the weight of the block to overcome friction, and, thus, to cause the block
to slide down the incline, is
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Up to now, we have implicitly suggested that the coefficient of friction between an
object and a surface is the same whether the object remains stationary or slides over the surface.
In fact, this is generally not the case. Usually, the coefficient of friction
when the object is stationary is slightly larger than the coefficient when the object is sliding. We call the former coefficient the
coefficient of static friction, , whereas the latter coefficient
is usually termed the coefficient of kinetic (or dynamical) friction,
.
The fact that
simply implies that objects have a
tendency to ``stick'' to rough surfaces when placed upon them. The force required to
unstick a given object, and, thereby, set it in motion, is
times the
normal reaction at the surface. Once the object has been set in motion,
the frictional force acting to impede this motion falls somewhat to
times
the normal reaction.