Mechanics of Materials/Force-based Static Equilibrium/Free Body Diagrams

3.1 Free Body Diagrams

Figure 3.1: Free body diagram for a block on an inclined plane with the vector of magnitude mg broken down into orthogonal components.

In physics, we often employ free body diagrams (FBDs) to describe forces between objects and body forces. When thinking about the equilibrium of forces acting on an object/body, FBDs are a tremendous aid when used correctly. As shown in Figure 3.1, we can use a FBD on an object/body (the blue block on the inclined plane) to describe vectorial forces acting on the body (gravity, friction, and a normal force from the inclined plane). We can also describe action-reaction pairs of forces between objects using FBDs and remembering Newton's third law of motion. In the case of the block and inclined plane, we can envision one action-reaction pair as ${\vec {\mathsf {N}}}$ acting from the inclined plane against the blue block and the vectorial component from gravity with magnitude $mg\cos \theta$ acting from the block against the inclined plane. Another action-reaction pair would include the friction ${\vec {\mathsf {f}}}$ from the inclined plane acting on the block, along with the equal and opposite frictional force from the block acting on the inclined plane.

Identifying action-reaction pairs is key to understanding how the surrounding environment interacts with a structural object. When thinking of a free body as a particle or only having axial forces (i.e., forces going acting along an axis going through the centroid of a body), one might follow these steps:

1. Define appropriate coordinate systems (e.g., XYZ, xyz).
2. Draw vectors that describe the motion of the body -- usually none for stationary objects in statics/mechanics.
3. Draw vectors for body forces acting on the body.
4. Draw vectors for contact forces and surface forces acting on the body (i.e., select the force acting on the body from action-reaction pairs)

For this course, we envision most of our structures as fixed, unmoving sets of beams, trusses, or pressure vessels. Yes, these structures might be portions of moving vehicles, but the loading due to the acceleration will usually be minimal, unless there is rotation with high angular velocity (e.g. centripetal acceleration $r\omega ^{2}$ where $r$ is a radial distance and $\omega$ is an angular velocity).

Body Forces or Contact Forces?

These questions explore the characteristics of body forces and contact forces.

Body Forces?

Question Relating Rotational Power to Electrical Power and Current

Jumbo the Elephant would like to know which of the following are body forces. Gravity Friction Electrostatic attraction Centrifugal force
Jumbo the Elephant would like to know which of the following are surface forces or contact forces. Hydrostatic pressure. Friction Normal force Shear force

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