Look around you, and you see a world at rest. The monitor, desk, and chairâand the building that contains themâare in a state described as static equilibrium. Indeed, it is the fundamental objective of many branches of engineering to maintain this state in spite of the presence of obvious forces imposed by gravity and static loads or the more unpredictable forces from wind and earthquakes. The condition of static equilibrium is equivalent to the statement that the bodies involved have neither linear nor angular acceleration. Hence static mechanical equilibrium (as opposed to thermal or electrical equilibrium) requires that the forces acting on a body simultaneously satisfy two conditions: âF =0 and âÏ =0; that is, both external forces and torques sum to zero. You have the freedom to choose any point as the origin about which to take torques. Each of these equations is a vector equation, so each represents three independent equations for a total of six. Thus to keep a table static requires not only that it neither slides across the floor nor lifts off from it, but also that it doesn't tilt about either the x or y axis, nor can it rotate about its vertical axis.
Frequently, attention in an equilibrium situation is confined to a plane. An example would be a ladder leaning against a wall, which is in danger of slipping only in the plane perpendicular to the ground and wall. By orienting a Cartesian coordinate system so that the x and y axes are in this plane, choose which of the following sets of quantities must be zero to maintain static equilibrium in this plane.
A. âFx and âÏz and âFyB. âFz and âÏx and âÏyC. âÏx and âFx and âÏy and âFyD. âÏx and âFx and âÏy and âFy and âÏz