V-belt or Rope:

The V-belt or rope make contact on the two sides of the groove as illustrated in fig

 (a)                                                             (b)

Assume the reaction be 'R_n' on each of the two sides of the groove. The resultant reaction shall be 2R_n sin α.

Determine all the forces tangentially in the Figure (b), we obtain

     . . . (8.8)

 Determining all the forces radially, we obtain

As δθ is very small

By neglecting the product of the two infinitesimal quantities 

By putting the value of R_n and utilizing the approximation

we obtain

Taking the limits and integrating between limits, we get

.........8.9