8.4. Applications of Equilibrium Conditions http://www.ck12.org
8.4 Applications of Equilibrium Conditions
Objective
The student will:
- Use the conditions of equilibrium to solve problems.
Vocabulary
- fulcrum/pivot:The point about which a seesaw rotates.
Introduction
If you’re planning to study structural engineering or have hopes of becoming an architect, then at some point in
your education you will need to take up the study of statics. Structural engineers are involved in designing roads,
bridges, and large buildings. Architects must have an understanding of what is structurally possible when they
design a structure. It is not uncommon for beginning structural engineering students to design structures that fail.
The forces necessary to maintain the structure they have designed are improperly balanced and the conditions for
static equilibrium are not achieved. Fortunately, with the advent of computers, very fast feedback for students is
possible with the dynamic mathematical modeling of computer-aided design and drafting (CADD) software systems.
Students can quickly see if their designs are feasible.
The study of statics also involves topics such as the strength of the materials. A building may be designed correctly
and it may be in static equilibrium, but if the materials used in construction are of poor quality, failure may occur
from a “stress overload.” Very bad weather conditions may also add too much weight in the form of ice to a structure,
causing the structure to fail. Every once in a while, we hear about such tragedies on the news.
In this section we look at some simple systems that we wish to keep in static equilibrium. In solving the problems of
this section, we will always use the location of the center of mass of each object in order to determine the distance
between the axis of rotation and the applied force.
Illustrative Example 1: The Seesaw
InFigure8.9 Jessica has massmeof 27.0-kg and is located 0.500 m from the left end of the seesaw. Boris has a mass
mbof 33.0-kg and is located on the right end of the seesaw. If the seesaw is to remain balanced as inFigure8.9,
how far from the center of seesaw must Boris be seated? The seesaw is 5.50 m long and has a uniformly distributed
massmsof 8.30-kg.
Let us first draw a Free Body Diagram of the situation showing the forces on the seesaw.
The point,PinFigure8.10 is called thepivot, or thefulcrum. It is the point about which the seesaw rotates.
The axis of rotation is perpendicular to your computer screen, throughP. If we choose the pivotP, then the torque