﻿ Adaptive Map - Bodies and Free Body Diagrams

# Bodies in Engineering Mechanics

## Bodies:

A 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 body and what cannot count as a body is dependent on the circumstances of the analysis. In some circumstances in engineering mechanics, it is useful to make certain assumptions about the bodies being analyzed. We will either need to assume the body is either rigid or deformable, and we will need to assume that the body is either a particle or an extended body.

### Rigid versus Deformable Bodies

Rigid bodies do not deform (stretch, compress, or bend) when subjected to loads, while deformable bodies do deform. In actuality, no physical body is completely rigid, but many bodies deform so little that this deformation has a minimal impact on the analysis. For this reason, we usually assume that bodies in the statics and dynamics courses are rigid. In the strengths of materials course we specifically remove this assumption and examine how bodies deform and eventually fail under loading.

There is no set boundary for determining if a body can be approximated as rigid, but there are two factors to to look for that indicate that a rigid body assumption is not appropriate. First, if the body is being visibly stretched, compressed, or bent during the period of analysis, then the body should not be analyzed as a rigid body. Second, 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).

 This bridge deforms very little under normal loading, and therefore can be analyzed as a rigid body. This car has been deformed significantly and should not be modeled as a rigid body during the impact The two halves of the scissors can move relative to one another, therefore the scissors cannot be considered a rigid body as a whole. Instead each half of of the scissors should be analyzed as its own separate body

### Particles versus Extended Bodies:

Particles are bodies where all the mass is concentrated at a single point in space. Particle analysis will only have to take into account the forces acting on the body and translational motion. Extended bodies on the other hand have mass that is distributed throughout a finite volume. Extended body analysis is more complex and also has to take into account moments and rotational motions. In actuality, no bodies are truly particles, but some bodies can be approximated as particles to simplify analysis. Bodies are often assumed to be particles if the rotational motions are negligible when compared to the translational motions, or in systems where there is no moment exerted on the body such as a concurrent force system.

 The rotation of this comet and the moments exerted on the comet are unimportant in modeling its trajectory through space, therefore we would treat it as a particle. The gravitational forces and the tension forces on the skycam all act through a single point, making this a concurrent force system that can be analyzed as a particle Rotation and moments will be key to the analysis of the crowbar in this system, therefore the crowbar needs to be analyzed as an extended body