29-Aug-2016: Finding a relationship between mass and period for an inertial balance

Lab #1 Inertial Balance

Andrew Martinez
Lab Partners: Richard Mendoza

Statement: Use an inertial balance and power-law type equation to determine the mass and period and there relationship to each other.

Theory/Introduction: Measuring mass is usually done by spring scales and balances that depend on gravity to help in the measurement and is known as gravitational mass. However, there is another means of measuring mass by measuring inertial mass. This is done with an inertial balance and comparing the object resistance to change in its motions. We will also determine the relationship between mass and period by deriving a power-law type of equation.

Apparatus:

Left: Photogate attached to standing pole
Right: C-clamp holding inertial balance to table, tape placed on the open end to reach photogate
On table: Photogate attached to LabPro with USB connection to computer for data collection

Procedure: Set up apparatus by attaching the photogate to the standing pole at inertial balance level. Use C-clamp to hold inertial balance in place to the table. Next place a length of tape on open end of the balance to block the photogate laser. Using the LabPro connect to both the photogate and computer to begin collecting data. Using a series of 100g, two 200g, and one 500g masses to find the periods of 0g to 800g moving up every 100g. Once the data has been collected the data is organized under user parameters and into new calculated column where the data can be plotted. Once that is done the user can perform a linear fit and using the equations provided derive the estimated masses and periods. Finally use two random objects to measure using the inertial balance to determine their estimated masses and period ending with exactly finding the mass using a gravitational scale mass and period calculated from the computer.

Measured Data:
0-800g slotted masses









Calculated Results: Plot of ln(T) vs ln(m+Mtray)

Upper Mass: 360g Correlation: .9998 Slope: .7585 Y-intercept: -5.701s

Lower Mass: 280g Correlation: .9998 Slope: .6605 Y-intercept: -4.971s

Derived equation from the graphs

Calculated results of unknown mass of phone and water bottle

Conclusion: After finding the derived equation of the power-type problem in order to test out its accuracy two randomly selected objects were used to find the estimated mass and then were actually measure using a scale. The results were not within range of our estimated calculations. There are a number of reasons why this could be true such as the water in the bottle sloshing around and thus displacing the mass during its oscillations. The phone was not stable during the inertial balance oscillations either contributing to the inaccuracy of the results. Despite the inherit uncertainty of measurements these results are more likely user error and does not necessarily mean that the equation is wrong but that more suitable objects should have been used.