# Suppose that a structure of arbitrary complexity has a number of forces applied to it (at various points) and yet is in static equilibrium.

Suppose that a structure of arbitrary complexity has a number of forces applied to it (at various points) and yet is in static equilibrium. The principle of virtual work allows one to write an equation that relates the applied forces. To find this relationship, you must imagine (hence the term “virtual” work) that the structure is disturbed slightly from its equilibrium position, and then calculate the ratio of the resulting displacements at the points where the forces are applied.We illustrate this principle by considering the two downward forces, and , applied to the ends of a massless lever (see the figure). Initially, the lever is in static equilibrium. Imagine that the lever starts in the horizontal position, shown in black, and then tilts infinitesimally to the position shown in blue. Under this infinitesimal rotation, the left end of the lever moves a distance , while the right end moves a distance .The net work done by the forces on the lever in this process is zero. (This is because equilibrium can also be defined as an energy extremum of the system. Therefore .)Find an expression for the force using arguments based on work (do not use a torque argument).Express F2 in terms of f1 ,h1 , and h2

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