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contacting surface. In this section we will analyze the frictional forces
acting on a flat belt, although the analysis of other types of belts, such
as the V-belt, is based on similar principles.
Consider the flat belt shown in Fig. 1-66,a, which passes over a
fixed curved surface. The total angle of belt to surface contact in
radians is β, and the coefficient of friction between the two surfaces is
µ . We wish to determine the tension T in the belt, which is needed to
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pull the belt counterclockwise over the surface, and thereby overcome
both the frictional forces at the surface of contact and the tension T in
1
T
the other end of the belt. Obviously, T > .
2
1
Frictional Analysis. A free-body diagram of the belt segment in
contact with the surface is shown in Fig. 1-66,b. As shown, the normal
and frictional forces, acting at different points along the belt, will vary
both in magnitude and direction. Due to this unknown distribution, the
analysis of the problem will first require a study of the forces acting
on a differential element of the belt.

b

a

Fig. 1-66. c

A free-body diagram of an element having a length ds is shown
in Fig. 1-66,c. Assuming either impending motion or motion of the
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