Subsection 4.1.4 Statics
When more than one force acts on a body in such a way that their net effects become zero is called an equilibrium. Equilibrium refers to a state of balance. An object is considered to be in a state of equilibrium when two opposing forces acting on the object balance each other. There may be two possible cases for a body in equilibrium,
- Static Equilibrium: sum of all forces, \(\sum F_{net} = 0,\) i.e., \(a=0,\quad v = 0\) and net torques \(\sum\tau_{net}=0,\) i.e., \(\alpha=0,\quad \omega = 0.\)
- Translational Equilibrium: sum of all forces, \(F_{net} = 0\text{,}\) i.e., \(a=0,\quad v \neq 0\text{.}\)
- Rotational Equilibrium: sum of all torques about a point on an object, \(\sum\tau_{net} = 0\text{.}\) (i.e., \(\alpha = 0,\quad \omega \neq 0\))
Subsubsection 4.1.4.1 Static Equilibrium
A system is in static equilibrium whenever no part of the system is moving. An example of static equilibrium is a spider web suspending one or more bugs. Any segment of the web (any bug, any strand, any junction, or any combination thereof) may be treated as a body.
- The vector sum of the forces acting on an object in static equilibrium is equal to zero. which is described by Newton First law \(\vec{F} = 0\) or, equivalently\begin{equation*} \vec{F}_{x} = 0 \quad \text{(x-component of force) and } \end{equation*}\begin{equation*} \vec{F}_{y} = 0 \quad \text{(y-component of force)}. \end{equation*}In static equilibrium, the total force acting on a body, \(\vec{F} = 0\text{,}\) \(\vec{a}=0,\) and also the velocity of a body \(\vec{v} = 0\text{.}\)
- Problem Solving Technique: To solve a static equilibrium problem one needs to:
- Read problem, list given quantities, draw a figure of the physical situation, and label the forces involved.
- Draw force diagrams (free-body diagrams) for each body in equilibrium.
- Resolve the forces into components.
- Sum the x- and y-components of forces and set them to zero.
- Solve equations simultaneously for the quantities of interest.
