I am designing an experiment where I will measure a value proportional to g, and determining if g then depends on the mass of the object falling. The particular problem explored is my choice, but I really like this one.
I plan on using a long ramp and either some cylindrical or spherical weights (of the same size and shape, different weights). I will do several runs with different weights and graph the data. A straight line indicates that g remains constant regardless of weight.
x = mgt2
The Attempt at a Solution
I will use the above equation (since initial velocity is zero) to graph a line of my data, where x is position, m is some unknown proportionality (due to the objects moving on a ramp, friction and other things), g is the acceleration due to gravity, t is time. With this set up, I will have a line with a slope of mgt going through the origin. I am NOT trying to find out what m or g is. Rather, what my experiment needs to show is that the slope is constant within my uncertainty (although if I can minimize all the factors affecting the motion, maybe I can get a good value for g).
The main problems:
Before I propose this to my instructor, I need to find out if things like moment of inertia can be neglected, or what dimensions of my ramp and size of weights need to be in order for such things to be negligible. I will also be waxing up my ramp to minimize friction, and since that should be constant I don't anticipate much a problem from that (although will it be constant? isn't friction proportional to normal force, which is proportional to mg? All that matters is that I minimize it, though).
Other potential ideas: What if I put flat weights on little cars? Would this help? If not that, what shapes would be best to minimize friction and energy from the rotation of the body?
So, how would I go about determining what the dimensions of my tools need to be in order to make these potential contaminates negligible? Are there any other factors that would effect my results that I am missing? Any help whatsoever would be appreciated.