Free Bodies

6.3. Free Bodies#

A free body, for the purposes of engineering mechanics, is a collection of matter that is analyzed as a single object. This can be something simple like a rubber ball, or it can be something made of many parts such as a car.

What can count as a free body and what cannot count as a free body is dependent on the circumstances of the analysis. In engineering mechanics, it is sometimes useful to make certain assumptions about the bodies being analyzed. We usually need to assume the body is either rigid or deformable.

Rigid and Deformable Bodies#

Rigid bodies do not deform (stretch, compress, or bend) when subjected to loads, while deformable bodies do deform. No physical body is completely rigid, but most bodies deform so little that this deformation has a minimal impact on the analysis. For this reason, we usually assume that bodies in static analysis are rigid. When studying engineering strength of materials, we remove this assumption (that bodies are rigid) and examine how bodies deform and eventually fail under loading.

A hammer is a good example of a rigid body for analysis. It deforms little under regular use and does not have any pieces that move relative to one another.

hammer

Image Credit: Mechanics Map Textbook http://mechanicsmap.psu.edu/websites/1_mechanics_basics/1-1_bodies/bodies.html

There is no set boundary for determining if a body can be approximated as rigid, but there are two factors to look for that indicate that a rigid body assumption is not appropriate.

  • If the body is being significantly stretched, compressed, or bent during the period of analysis, then the body should not be analyzed as a rigid body.

  • If the body has parts that are free to move relative to one another, then the body as a whole should not be analyzed as a rigid body (this is instead a machine, comprised of multiple connected bodies that will each need to be analyzed separately).

The car below deformed significantly during a crash test. When analyzing the impact, we should not treat the car as a rigid body.

car crash

Image Credit: Mechanics Map Textbook http://mechanicsmap.psu.edu/websites/1_mechanics_basics/1-1_bodies/bodies.html Image by Brady Holt CC-BY-3.0.

Text Credit: Mechanics Map Textbook http://mechanicsmap.psu.edu/websites/1_mechanics_basics/1-1_bodies/bodies.html

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