February 27: Lab #1 Finding a Relationship Between Mass and Period for an Inertial Balance

Lab 1

 Finding a Relationship Between 

Mass and Period for an Inertial Balance

Ricardo Gonzalez

Josue 

2-27-17

The experiment was constructed in order to show that an unknown mass can be calculated by using the relationship between a measurable periods of an oscillating pendulum and known masses. 

1. Introduction

By using an oscillation pendulum and measuring the average periods with a variety of masses, the gathered data can be substituted into "power-law type of equation" that we derived. With the gathered data from the experiment, the data is plotted onto a graph. The slope of the line on the graph and the y intercept should be components of the equations derived. By doing so, we now have an equation we can use to calculate the mass of an unknown object. With the components of the Power-Law  equation found, we were instructed to find the mass of two unknown objects and use the Power-law equation to find a value. That calculated value would then be compared to the true measured value using a scale.  

2. Procedure
We first began by gathering a c-clamp to stabilize the inertial balance onto the table. By using a clamp and vertical stand, we placed a photogate in such a way that while the inertial balance would oscillate, the photogate would measure the period for each complete period. By connecting the photogate to the laptop, we were able to use the pendulum timer within the logger pro software to measure the period for each individual mass placed.Initially we measured the period (in seconds) of the inertial balance with no mass and proceeded to do the same for the masses (in grams); 100, 200, 300, 400, 400, 500, 600, 700, and 800 grams when placed onto the overhanging plate of the inertial balance.

3. Data
In the first and third column we have the masses used to measure a period. In columns 3 and 4 we have the periods measured for the masses.

4. Results

5. Analysis

We first graphed the Period vs. Mass as shown above. In our power law we took the natural log of both side and concluded that A=e^y-intercept and n=slope. In order to be able to find these values, we then added two additional columns to the graph for a Ln t vs. Ln (m+Mtray) which now gave us new properties of the slope of the line created. The slope of the line, as we know, is our n value and the y-intercept is provided. However we should be aware that because we are finding a relationship of Period to mass, the correlation of the points should be as close to 1 as possible. Therefore we must go back and try another mass chosen for the Mtray for our graph. Note, we chose three values for our Mtray, which essentially gives us a range of values for which our mass of the tray truly is.
We then changed the values of the Mtray on the logger pro which gave us new values for the y-intercept and the n value (the slope of the line). We chose only the upper bound and lower bound masses of the tray. As we can see in the calculations provided above. We placed a phone and clamp with unknown masses onto the inertial balance and measured a period. By using the power-law we have, we can find a lower bound value and an upper bound value by using the range of mass for the tray along with their corresponding n-value and y-intercept.
What we found was that the calculations were either 20 grams above or below the measured value of the two unknown masses using a scale. The measured mass of the Iphone we used, on a scale was 215 grams, however through the calculations, we got a range of 238-241 grams, nearly 20 grams above the true amount. Also, measured mass of the Clamp was 518 grams, however, through the calculations, we got a range of 500-502 grams, nearly 20 grams below the true mass.
6. Conclusion 
The experiment turned out fairly well in the aspect that we were able to find the necessary components of our Power-law equation that would be used to find the mass of two unknown objects simply by measuring  their period of oscillations on the inertial balance. However, our values calculated and the values measured on the scale were not by any means perfect. We believe there is some variation in the calculations because of a factor not taken account of. We are not sure if the location on the tray where the center of mass of the two objects would affect the overall period and therefore effecting our calculation. Another possible deviation, but possibly very unlikely, is the air resistance between the motion of the oscillation of the inertial balance and/or our two objects.