Question

Ok. So we did an experiment with a meter stick balanced on the skinny side of a metal nut. We put 3 nuts on top of the meter stick and saw how moving the top nuts caused the center of mass to change. We got an equation: Position of center of mass = 0.63 X Position of nuts + 18 cm. Mass of the nuts: 87.8 g. Mass of the ruler: 143.9. We have to come up with an equation of how to write an equation in terms of general masses of nuts and ruler....i.e. an equation the would predict the changing of the center of mass no matter what the masses were. Any ideas on where to start??

Answer 1

I'm assuming this is your experiment setup. A meter stick is ideal because it's long and fulcrumy, and it's a cinch to measure the nut positions. Great experiment.

This experiment is about torque, which is force applied at a distance from a pivot. T=F*d where T is torque, F is force (weight of nut), and d is distance from the pivot. The forces exerted by the nuts are all downward forces due to gravity. Since the accelerations are all the same (g = 9.8m/s2) they all cancel out and you're left with just the masses of the nuts. So your simplified torque formula could be T=m*d. But it's not *really* torque, because the units are now inch*grams instead of inch*Newtons (or foot*pounds or Newton*meters or whatever).

For the meter stick to balance, you need equal torques on both sides. Assuming all nuts have the same mass, if you put two on one side and one on the other side, the single nut has to be twice as far from the fulcrum as the two nuts.
(2*m)*d = m*(2*d)

That's the physical principle at work. I don't understand exactly how you are applying the equation you gave, but this should give you a good start towards interpreting your data.