Complete COSMOS: Online Solutions Manual Organization System
Chapter 8, Solution 93.
Let normal force on A be N , and As in the text The total normal force P is
N k = A r
F = N , M = r F
2 R k P = lim N = 0 R 2 rdr d 1 r A 0
P = 2 R 2 kdr = 2 k ( R2 - R1 )
R
1
or
k =
P 2 ( R2 - R1 )
The total couple is
k 2 R M worn = lim M = 0 R 2 rdr r d A 0 r 1
R2 R1
M worn = 2 k
( rdr ) = k (
2 R2
-
R12
)=
2 P R2 - R12
2 ( R2 - R1 )
(
)
M worn =
1 P ( R2 + R1 ) 2
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.