Physics 103 : Fall 2005

**Static Equilibrium**

The figure below shows a physicists’ stylization of a bar
(shown in black) subject to four forces:
*F1*and *F2*, forces supporting it near its two ends; *mg*, its weight; and *Mg*, a
force due to a mass *M* hanging from
it.

The lever arms for these forces are also indicated, as
measured from the position where *F1*
acts. Notice that this position is close
to the end of the bar, but not exactly at the end. It is assumed that the lever arm for *mg* is *L/2*: that is not necessarily
true, and could be tested experimentally.
The lever arm for *Mg* is called
*x*, because this is variable: the mass *M*
can be moved along the bar to different positions *x*.

The forces *F1* and *F2* are applied by spring scales, and
hence can be read off the apparatus. The
position *x* of the mass M can also be
read off the bar (a meter stick, conveniently).
Thus one can easily measure *F1*,
*F2*, and *x* and see what their relationships are. It turns out that both *F1* and *F2* are linearly
related to *x*, and therefore F1 is
also linearly related to F2. Verify this
experimentally, using Excel to do plots and fits. Look at *F1*
vs *x*, *F2* vs *x*, and *F1* vs *F2*.

Why are these things linearly related, and what do the slopes and intercepts mean? Recall that we have a theory of this situation: the forces and torques should balance. In equations,

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What is the relationship between this theory and your experimental results?

Use the theory to say what the slopes and intercepts of all three of your graphs mean. Put your theoretical considerations below (algebraically, with expository sentences saying what is meant), then use the next page (worksheet) to organize your data, sketch graphs, and make sense of numbers.