Spinning Mass

Challenge: To design a device that can find the mass of unknown objects as precisely and accurately as possible by analyzing the dynamics of a horizontally rotating system.

Parameters: The device(s) must be able to find the mass of two unknown objects. One will be small (between 50 and 100 grams), while another will be larger (between 300 and 400 grams). The masses have eye hooks so you can attach them to your device. You cannot alter the masses in any way. Your method of mass determination must be based on centripetal force, not gravitational force! You can rely on angular momentum or add a motor to maintain constant circular motion. Please check with me before committing to a design. You must report your mass estimate with appropriate precision and include your absolute and 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 10 away from your actual percent difference.

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

Physics: The dynamics of centripetal acceleration can be analyzed to find the mass of an unknown object. See my notes for examples.

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. You may want to make it adjustable so that you can have a reasonable circular motion for the two very different masses.

Help/Hints: There are many ways to use circular motion to find the mass of an object. Use the equations for inspiration. Can you use period or frequency? Angle? Radius?

Can you incorporate a calibrated spring? Can your device be hung from the power drop-down? My example device is a good starting point, but far from perfected!

Quiz Topics: Circular Motion

Newton’s Laws

Universal Law of Gravitation

Online Text: chapter 6