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Equilibrium and Free-body Diagrams

Objectives Construct a free-body diagram of a physical system.

A rigid body is in static equilibrium if the resultant force acting on the body is zero. For a system in static equilibrium, Newton's second law implies that the acceleration is zero. Notice this does not mean that the velocity of the body is zero; rather, it means that the velocity is a constant. If F and M are forces and moments on a system, then for a system in static equilibrium, Newton's second law may be written as follows:

The symbol is used to indicate a sum. In particular, F indicates the sum of all the forces acting on the rigid body.

Because Equation 3-12 is in terms of vectors, the equations are often written in terms of the components of the forces and moments. The solution of Equation 3-12 for different types of loading forms the crux of statics. To solve Equation 3-12, the forces and moments acting on a body must be represented within the context of what is happening physically to the body. This is accomplished by constructing a free-body diagram.

A free-body diagram is a sketch showing the loads acting on a rigid body. These loads may be forces and moments. The loads may be internally or externally applied. In solving problems involving rigid-body mechanics, it is imperative that an accurate free-body diagram be constructed.

Free-body diagrams represent the physical state of the rigid body. That is, the loads on the rigid body must be accurately represented so that the physical state of the body is represented.

Students often have difficulty constructing a proper free-body diagram. Because free-body diagrams are so important in statics and dynamics, such students will have difficulty with the courses.

When constructing free-body diagrams, use the following steps:

1. Isolate the body from its physical surroundings, and draw a simplified representation of the body.
2. Pick an appropriate coordinate system, and sketch on your drawing.
3. Add the appropriate loads to the sketch, bearing in mind what is happening physically to the body. Do not forget to add internal loads if needed.
4. Label known quantities with the magnitude and direction.