Statics

Summary

• Statics is the branch of mechanics dealing with forces acting on objects that are not accelerating.
• Equilibrium is a general concept that can refer to states of…
  • static equilibrium, which includes…
    • translational equilibrium (the equilibrium of forces)
    • rotational equilibrium (the equilibrium of torques)
  • dynamic equilibrium, which includes but is not limited to…
    • thermodynamic equilibrium (the equilibrium of internal energy transfer)
• An adjective before the noun is not needed when the type of equilibrium is known from context.
  • This section of this book is about translational equilibrium only.
  • Other forms of equilibrium will be dealt with in other sections of this book.
• An object is in translational equilibrium when…
  • it is not accelerating
  • the net force on it is zero.
• Tests for 2 forces in equilibrium
  • Two forces are in equilibrium if they are
    • equal (have equal magnitudes) and
    • opposite (180° apart).
• Tests for 3 forces in equilibrium
  • Resultant-equilibrant
    • Select two forces and find their resultant.
    • The remaining force is called an equilibrant if it is equal and opposite this resultant.
  • Triangle of forces
    • Three forces are in equilibrium if they can be arranged head-to-tail in any order to form a triangle.
• Tests for n forces in equilibrium
  • Polygon of forces
    • Three or more forces are in equilibrium if they can be arranged head-to-tail in any order to form a closed polygon.
  • No net force
    • Resolve all the forces acting on an object into components in some convenient coordinate system.
    • Combine all the components along each axis.
      • Add the components parallel to each axis.
      • Then subtract the components anti-parallel to each axis.
    • If the total along each axis is zero then the object is in equilibrium. For example…
      • All the longitudinal forces cancel (forward-backward)
      • All the lateral forces cancel (side to side).
      • All the vertical forces cancel (up and down).

      ∑Fx = 0		⎫ ⎪ ⎬ ⎪ ⎭	⇒	∑F = 0
      ∑Fy = 0
      ∑Fz = 0

  • Balanced forces
    • Resolve all the forces acting on an object into components in some convenient coordinate system.
    • Combine the components along each axis in the positive and negative directions separately.
      • Add just the components parallel to each axis.
      • Add just the components anti-parallel to each axis.
    • If the totals along each axis in opposite directions are equal, then the object is in equilibrium. For example…
      • All the forward forces equal all the backward forces.
      • All the leftward forces equal all the rightward forces.
      • All the upward forces equal all the downward forces.

      ∑F−x = ∑F+x		⎫ ⎪ ⎬ ⎪ ⎭	⇒	∑F = 0
      ∑F−y = ∑F+y
      ∑F−z = ∑F+z