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magnitude of any forces acting on the objects that tend to induce lateral
relative motion, up to this maximum. Once this maximum is exceeded, the
static friction ceases to operate, and kinetic friction takes over.
The other factor in Equation (12.5) is the magnitude of the normal
force, which is the force acting perpendicular to the surfaces that prevent
them from penetrating each other. One common situation occurs when an
object (such as a bowl of petunias) is resting on top of another object (such
as a table). The normal force in this case is simply the force required to
counteract gravity. To be more precise, it is the force required to counteract
the component of gravity that acts perpendicular to the surfaces and wants
to smash them together. If the table is at an incline, then we can separate
gravity into a normal component and a lateral component, as shown in
Figure 12.4. (Inside a computer, we'd probably describe the orientation of
the table with a normal vector, and use the dot product to separate gravity
into the relative and normal components, as we described in Section 2.11.2.)
Since the bowl and the table do not accelerate relative to each other, we
know that the normal force of the table pushing against the bowl must be
exactly equal to the normal component of the force of gravity pulling the
bowl towards the table.
Figure 12.4. Free-body diagrams of a bowl of petunias on a table at various angles of
inclination.
Figure 12.4 shows several free-body diagrams of identical bowls of petu-
nias resting on tables at various angles of inclination. Notice that in each
figure, the force of gravity acting on the bowl, labeled g , is the same. The
normal and lateral components of gravity have been broken out in blue.
The actual force of static friction is the black vector labeled f s . On the
left, the maximum amount of friction available is labeled “max f s ,” in the
middle and right-hand images the maximum amount of friction is being
applied.
 
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