Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 236

■ EXAMPLE 11.4
Problem : We have a 3000-lb load to be lifted with a two-leg sling whose legs are at a 30° angle from
the load. The load (force) on each leg of the sling is

Solution:

a
c

sin A =

sin 30 = 0 500 .

3000 lb

a = = 1500

2

a 15 00

05

c = = = 3000

sin A .

■ EXAMPLE 11.5
Problem : Given a two-rope sling supporting 10,000 lb, what is the load (force) on the left sling?
Sling angle to load is 60°.

Solution:

60
0 866

sin A =

.

10,000 lb

a = = 1500

2

a 5000

0

c = = = 5774

sin A . 866

11.3.1 r ated s ling l oads
In the preceding section we demonstrated simple math operations used to determine the rated sling
load that a particular sling can safely bear. In the field, on the job, knowing how to use simple math
to make sling angle-load determinations is important. It is also important to point out, however, that
many tables showing rated loads on slings are available. Table 11.1, for example, shows rated loads
for alloy steel chain slings.

11.4 INCLINED PLANE
Another common problem encountered by environmental engineers involved in the resolution of
forces occurs in material handling operations in moving a load (a cart, for example) up or down
an inclined plane (a ramp or tilted surface, in our example). The safety implications in this type of
work activity should be obvious. Objects are known to accelerate down inclined planes because of
an unbalanced force (anytime we deal with unbalanced forces, safety issues are present and must be
addressed). To understand this type of motion, it is important to analyze the forces acting upon an
object on an inclined plane. Figure 11.5 depicts the two forces acting upon a load positioned on an
inclined plane (assuming no friction). As shown in Figure 11.5, there are always at least two forces
acting upon any load that is positioned on an inclined plane—the force of gravity (also known as
weight) and the normal (perpendicular) force. The force of gravity acts in a downward direction; yet,
the normal force acts in a direction perpendicular to the surface. Let's take a look at a typical example
of how to determine the force needed to pull a fully loaded cart up a ramp (an inclined plane).