Translational Equilibrium

First condition of equilibrium: vanishing vector sum of all applied external forces.

General idea of the topic

A body is in translational equilibrium when the vector sum of the external forces acting on it is zero. Its acceleration is then zero: it can be at rest or moving at constant velocity. The condition is vectorial, so it is applied component by component.

The topic establishes that condition and uses it in typical situations: bodies resting on planes, loads held by symmetric or asymmetric cables and simple structures. The results are the tensions, normal forces and frictions needed to sustain the equilibrium.

What the student is expected to understand

By the end, the student should be able to set up the equilibrium equations by components, solve for unknown tensions and reactions and close the force polygon graphically.

The student should also be able to check whether an equilibrium is possible: for example, that the required friction does not exceed its maximum.

Recommended learning route

1. Net Force Balance Condition: states the zero-sum-of-forces condition, its component form and the closed force polygon.
2. Examples of Translational Equilibrium: applies the condition to supports, inclined planes and cable systems and computes the unknowns.

Essential physical criterion

The essential criterion is to draw the free body properly and project onto two axes. The number of unknowns cannot exceed the number of equations; if it does, the problem is not statically determinate and another condition is needed, such as the moments or a constitutive law of the material.

Connection with real problems

• loads hanging from cables.
• pictures and suspended lamps.
• bodies on inclined planes.
• frames and bar structures.

Final goal of the topic

The final goal is to solve any translational-equilibrium problem, justify the force diagram and check that the result is physically possible.