Let us illustrate these fundamentals of statics by analyzing the forces involved in a simple experiment. A bar is suspended from its ends by two spring scales which enable us to directly read out the forces required to keep the bar static. To make things interesting a mass hangs from a point in between the points of suspension. We want to write formulae predicting the forces at the points of suspension for an arbitrary location of the mass.
Clearly the bar can move through translation and it can move through rotation. Therefore we have a force and a torque equation to
satisfy if we want the bar to remain static. Denoting by
and 
the suspension forces from the
Left and Right side of the bar and by
the gravitational
force associated with the mass, m, hanging from the
bar, Newtons second law for the translational motion becomes
As always it is important to choose a positive direction
and we chose up to be positive.
We easily verify that indeed irrespective of the
location of the mass hanging from the bar the readings of the
spring scales add up to the same number. To predict the
individual reading we need the torque equation. Any point could
be chosen as reference. We choose one of the suspension points
as reference point because then the corresponding unknown
suspension force will drop out of the torque equation
because its moment arm and therefore its torque is zero.
Choosing the left suspension point as reference point and denoting
the location of the mass along the bar by x we have
Here L denotes the distance between the suspension
points and I chose torques inducing counter-clockwise rotation
as positive.
We now have to extract equations for 
and 
from these
two equations. We know that this must be possible because we have
as many unknowns as equations. From the torque equation we have
Inserting in Eq. 4 yields
Note that and are positive when
. Outside this interval the suspension forces
required for equilibrium
changes sign from positive to negative which may or may not be possible. If not the point beyond which
the sign changes is the point beyond which there can be no static equilibrium.