Inertial Balance

Challenge:  To design an inertial balance, or two, that can find the mass of unknown objects as precisely and accurately as possible.

Parameters: The balance(s) must be able to find the mass of two unknown objects.  One will be up to 2.5 kg, while the other will be a small object between 10 g and 100 g.  You will be given the unknown objects and will have 10 minutes to use your balance(s) to get as precise a measurement of the masses as possible.  You will report your masses with appropriate precision and specify your relative uncertainty.   

Scoring:  Your system will be scored based on the accuracy of your measurements and your estimate of your uncertainty, as follows:

        | % difference object one |  +  | % difference object two | + Confidence factor

* Confidence factor:  add one penalty point for incorrect uncertainty.  Incorrect uncertainty is an absolute uncertainty more than a factor of 3 away from your actual percent difference.

Rank will be based on score, with lowest score earning highest rank.

Physics:  Oscillatory motion can be measured to find the mass of an object.  This is how one could find the mass of any object while on a space-ship travelling to Mars.   Spring forces can be modelled mathematically, and can cause oscillatory motion.

Extensions: Calibration of your scale, and experimentation afterwards, can give you a good idea of its precision and accuracy, and help you determine your uncertainty.  Graph your calibration data and experimental results and draw a line of best fit.  Use the fit line to find unknown mass during the contest.

Help/Hints: The force of gravity can be balanced by a supporting force from underneath (Normal force), or from above (Tension force).  Try to make the oscillatory motion as horizontal as possible so that the vertical forces are always equal and opposite.

Quiz Topics:  Accelerated Motion, Oscillation, Newton’s Laws, Universal Law of Gravitation

Online Text:  3.1 - 3.2, 4.1 - 4.4, 5.5, 7.2