Physics 4A Inertia Balance

Physics 4A

Inertia Balance

Brett Mccausland

Purpose

Determine the relationship between mass in the tray of the inertial balance and its oscillation.Define an equation for the inertial balance that allows us to predict the weight of an unknown object.

Procedure

The inertial balance was clamped to a table, and a steel rod on a stand was placed directly in front of the inertial balance. A piece of tape was placed on the end of the inertial balance tray, such that it interrupted the laser in a photo gate attached to the steel rod. Masses were placed in the inertial balance tray and with use of a computer program we gathered data for the period of the inertial balance after giving it a nudge.

Calculations

For modeling are inertial pendulum period we used a equation of time, where t was equal to an inertial balance constant A times are mass M and the mass of the tray holding the mass represented by Mtray all two the n power. Are equation therefore had 5 variables but by using masses that were known and with the use of a photo timer we had only three unknowns. In order to bring the unknowns down to two we took data for 5 different masses and remolded are equation to resemble point slope form of y = mx + b then we plotted are data on a graph which allowed us to experiment with different values for Mtray  and by using a little “goldy locks physics” we found a upper and lower bound range for Mtray which gave us the best correlation possible. We then found are n (slope) and are inertial constant A (y intercept).Next we tested the model of the inertial balance by finding two unknown masses. In order to find the value of are masses we solved for M using are original equation by plugging in the values we found from the slope form. These values however were modeled to be the slope intercept form by taking the logarithm of are original equation therefore before plugging them back in we put e to the power of the variable.Since we used a little goldy locks physics and had no exact mass for Mtray but a range for Mtray we made the calculations for the upper and lower bounds of are range.

Data Analysis

Are calculations we not as accurate as we had hoped however reflecting on the methods I could see a few systematic errors that were occurring. First of all the nudge we were giving the inertial balance was inconsistent and likely led to error in the data. Additionally the masses that we placed in the tray were not secure and left to move about inside the tray making inconsistent resistance for the inertial balance to act on. There was error expected, since we had no exact value for Mtray and the best correlation that we could produce was 0.9994 slightly less than ideal.

Conclusion

The inertial balance gives you the ability to find the mass of an object independent of gravity. With the use of a scale that measures mass with the use of gravity, we were then able to describe the behavior of the inertial balance that allowed us to then determine mass independent of the force of gravity by using the values measured by the scale. We used one instruments measurement as a tool to describe another instruments much like math builds upon itself to make new operators by using method of previously defined and accepted ones.