Page 161 - Standard Handbook Of Petroleum & Natural Gas Engineering

146 General Engineering and Science

Transforming the integral to polar coordinates as shown in Figure 2-4:
dW, = L,@r cos 8dy

y = r sin 0
dy = r COS ede

= 14.5"= 0.253 rad

8, = 90" = 3 rad
2
cos = 0.968 rad

2L,yr3
7, = L, -(r - L,)+- sin 8 COS 8 de
W,

6.85
y, = 5.5+-
WZ

W, = 6.09 lb
Substituting W, into the equation for 7,

y2 = 6.62 in.

For the entire body
-
x=o

y= y,W, +y2W2 = 3x1.33+6.62x6.09
W, + W, 1.33 + 6.09
7 = 5.97 in.

When two bodies are in contact and there is a tendency for them to slide with
respect to each other, a tangential friction force is developed that opposes the motion.
For dry surfaces this is called dry friction or coulomb friction. For lubricated surfaces
the friction force is called fluidfriction, and it is treated in the study of fluid mechanics.
Consider a block of weight W resting on a flat surface as shown in Figure 2-5. The
weight of the block is balanced by a normal force N that is equal and opposite to the
body force. Now, if some sufficiently small sidewise force P is applied (Figure 2-5b) it
will be opposed by a friction force F that is equal and opposite to P and the block will
remain fixed. If P is increased, F will simultaneously increase at the same rate until