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0593_C06_fm Page 181 Monday, May 6, 2002 2:28 PM

Forces and Force Systems 181

When the contact forces are replaced by a nearly equivalent single force, it is often
convenient to divide this single force into components: one normal to the contact surface
and the other tangent to the contacting surface. The component tangent to the contacting
surface is called the friction force. If there is sliding between the bodies, this friction force
may often be regarded as proportional to the normal force, but with lesser magnitude
than the normal force and directed opposite to the direction of sliding. That is, when there
is sliding, the friction force is like a drag force and is represented by:

≤
F = µ with 0 ≤ µ 1 (6.7.11)
N
where µ is called the coefficient of friction or drag factor. When µ is zero, the friction force
is zero, and the contacting surfaces (or at least one of the contacting surfaces) are said to
be smooth.

6.7.4 Action–Reaction
Forces exerted by one body on another (say, A or B) are responded to by forces exerted
from the second body onto the first (B on A). These reaction forces are equal in magnitude,
but are directed opposite to the original forces. To see this, consider two bodies A and B
exerting forces on each other as in Figure 6.7.7. Also, consider free-body diagrams of A
and B as in Figure 6.7.8. In the diagram for A, let S and S ˆ A represent force systems exerted
A
on A from bodies external to A (S ) and from B (S ˆ A ). Similarly, let S and S ˆ B represent
A
B
forces on B from bodies external to B (S ) and from A (S ˆ B ). For equilibrium (whether static
B
or dynamic), the force systems on the individual and combined bodies must be zero
systems (see Chapter 7). Therefore, we have:
S + S = 0
A B
ˆ
S + S = 0 (6.7.12)
A A
ˆ
S + S = 0
B B

FIGURE 6.7.7
Bodies A and B exerting forces on
each other.

FIGURE 6.7.8
Free body diagrams of bodies A and B.