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

Inertial Balance Lab

Jae Yoo
8/29/16
Partners : John Demontano, Shawn Mazzio

Accomplishment
We were trying to find a relationship between mass and period for an inertial balance.

Theory/Introduction
We often use spring scales and balances to measure mass. These measuring devices are calibrated to make use of the Earth's gravitational pull in order to determine mass, and would be useless for measuring mass without the presence of gravity. Mass measured in this manner is known as gravitational mass.
Mass, however, is a quantitative measure of an object's inertia, and is not dependent upon gravity. Therefore, the mass of an object remains constant, regardless of the presence or strength of a gravitational pull.
The Inertial Balance is a device that is used to measure inertial mass by comparing objects' resistances to changes in their motion.

Procedure

1. Use a C-clamp to secure the inertial balance to the tabletop. Put a thin piece of masking tape on the end of the inertial balance.
2. Set up a photogate so the when the balance is oscillating the tape completely passes through the beam of the photogate.
3. Set up the LabPro with a power adapter, USB cable, and plug adapter plugged into the DIG/SONIC1 input.
4. Open the Logger Pro application.
5. Record the period with no mass in the tray.
6. Add more mass 100g - 800g and record the period of each of them.

Data


Calculated results/Graphs



Analysis
From the equation T = A(m+Mtray)^n, we took natural log on both sides and got lnT = n*ln(m+Mtray)+lnA.
From this equation, lnT = n*ln(m+Mtray)+lnA, n is slope ln A is y-intercept on our graph.
We got n as 0.7139 and lnT as -5.392 from when Mtray was 335g.
And n as 0.6658 and lnT as -5.034 from when Mtray was 295g.

Conclusions
We used the original equation, T = A(m+Mtray)^n, to find unknown mass 'm' since we know all the other values.
We got 169.655g and 167.106g when the actual mass was 169g,
And 45.5949g and 46.4746g when the actual mass was 46g.
As the result, we got very close calculated values from the actual values.