Page 155 - Standard Handbook Of Petroleum & Natural Gas Engineering

140 General Engineering and Science

components along the coordinate axes. For the particle to be in equilibrium, the sum
of the force components along each of the axes must be zero. This yields an algebraic
equation to be solved for the forces in each coordinate direction.
Example 2-1
Block W, weighing 100 Ib (see Figure 2-2) is attached at point A to a cable, which is,
in turn, attached to vertical walls at points B and C. What are the tensions in segments
AB and BC?
Breaking down the diagram into the various forces (Figure 2-2b):

Force balance in the y direction:

F, = -100 + T, sin 45" + TAB sin 15" = 0
0.707T, + 0.259TA, = 100

Force balance in the x direction:

F, = T, cos 45" - TAB cos 15" = 0

0.707TA, - 0.966TA, = 0
and solving Example Equations a and b simultaneously yields

TAB 81.6 lb
=
T,, = 111.5 lb
If there are no unbalanced forces and no unbalanced moments acting on a rigid
body, the rigid body is said to be in static equilibrium. That is, Equation 2-4 must be
satisfied just as for particles, and furthermore:

TAB y

L

(b) 100 Ib

Figure 2-2. Diagram for Example 2-1.