Physics 103 : Fall 2005

Static Equilibrium

The figure below shows a physicists’ stylization of a bar (shown in black) subject to four forces:  F1and 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,

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.