**Belts**

When a belt slides on a surface, the friction
between the belt and the surface makes the tension in the belt change. If the
belt is sliding on a cylindrical surface, the tension will depend on the
contact angle and the coefficient of friction between the belt and the
cylinder.

To show this we can draw the free body
diagram of a segment of the belt

The equilibrium equations for this segment
are

Substitution of , using the small angle
approximations, and taking a limit yields

Combining the two equations to eliminate *N*
yields

Integrating this over the interval of contact
yields

The relation between tension on one side of
the contact and on the other side can be then calculated from the equation

where is the contact angle in radians
and is the
coefficient of friction.

ã Mehrdad Negahban and the

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Department of Engineering Mechanics,