Hello, Franster!
Thank you for posting that sketch. It really helps us to understand what you are thinking about.
Is there a requirement to deterine the mass of the two objects simultaneously, as you have shown in your sketch? Or will you be examining the objects one at a time?
If the method described in your sketch is acceptable, it may also be acceptable to measure the mass by the length of a spring. If you hang objects of known mass from a spring and record the length of the spring for each, you can build a table of legths and masses. Then when you hang the unknowns from the spring, measure, and use the table to guess the mass. This is essentially using a scale, so I'm not sure that it is an acceptable solution.
I've been doing some reading about mass on the Internet. I did a Google search on "mass of an object" and found some interesting sites. I think the key to solving this problem is to note the relationship between mass and inertia.
I found this NASA site particularly interesting:
http://www-spof.gsfc.nasa.gov/stargaze/Smass.htm
and
http://www-spof.gsfc.nasa.gov/stargaze/Sskylab.htm
These sites talk about a method for determining body mass of astronauts in the zero-gravity environment of the SkyLab space station. Now, I know that you probably can't build a sophisticated oscillating chair the way NASA did, but their method suggests some interesting concepts.
The oscillating chair works because it takes more force to start and stop an object that has greater mass. Such an object requires more force to overcome its greater inertia. Therefore, objects with greater mass will take longer to decelerate, stop and then accelerate back at each end of the oscillation. The key for you might be to use the force required to accelerate an object at rest to determine its mass.
Here's an idea: Place an object on a nearly frictionless surface. Apply a nearly constant sideways force to the object and measure the amount of time it takes to move a fixed distance. The higher the mass, the longer it will take to cross. Like the spring example, above, you could test a number of known masses, build a table, and then test the unknowns.
For the nearly frictionless surface, you could use smooth plastic disks on a mirror or glass surface that has been waxed with car wax. (Think about air hockey!) For the nearly constant force, you could use a long thin string of rubberbands. (The force actually woudn't be constant, and you should probably talk about that in your report, but it doesn't substantially affect the results of this experiment...)
Make two lines on the glass surface - start and finish. Beyond the finish end, attach the rubberband to a piece of wood. Attach the other end of the rubberband to the plastic disk. You then pull back on the disk to stretch the rubberband to the start line, load the mass onto the disk, start the timer and release. Record the times for known masses to move from start to finish. Build your table of times for mass, run your unknowns, and you have it!
You must be careful to select a rubberband that isn't so strong that it just pulls the disk way too quickly. You also need to make sure the distance the disk travels is sufficient to give you measurements of say 5 seconds or more. You'll have to experiment with different lengths and bands to get good data.
Your report must talk about the relationship between mass and inertia and explain any potential sources of error, friction, etc.
I hope this helps.
