27-FEB-2017 FINDING RELATIONSHIP BETWEEN MASS AND PERIOD

Art Mondragon

02-27-2017

Lab#1: Finding the relationship between mass and period for an inertial balance

Purpose: Though this experiment we are attempting to determine the mass of two unknown objects by the measured oscillation of the inertial pendulum and the added unknown masses.

Introduction:  The period of oscillation measured by the inertial pendulum will vary depending on how much mass is added. By measuring a range of different known masses we can establish a relationship between the period of oscillation and the mass of an object. We will use this relationship to determine the mass of unknown objects based  on their individual period of oscillation.

The inertial pendulum measures the period of oscillation by vibrating back and forth. A larger mass will produce an oscillation with a longer period. We are assuming the period of oscillation is related to mass by an equation similar to that of a power-law.

We need to find the values of A, m + Mtray , and n.


By taking the natural log of this equation we get similar to a equation in the form y=mx+b

 A graph of this natural equation will provide us with a line of slope n and a y-intercept equal to ln A.

 The value of Mtray  can be determined by trying different values of Mtray until they produce a straight line. Each value of Mtray will have its own values for A and n.
To achieve a straight line you need to manually adjust the value of Mtray so that it results in a correlation as close to the value of 1.00 because a value of 1 represent a perfect correlation. 
We adjusted the value of Mtray to 270g to get a correlation of 1.We also found two other values of Mtray one higher and one lower than 270g that gave us a correlation of .9999. These new values will help estimate the uncertainty in the value of Mtray.  

 Each possible value of Mtray has its own corresponding y-intercept value and slope value that will give you a straight line. Each one of these Mtray values give you an A and n value that can then be plugged into the power law.




If we rearrange the power law we get an equation that allows us to use the y-intercept and the slope values obtained by the graph of possible values of Mtray. This new equation will allow us to approximate the unknown mass value of the two objects. We measured the oscillation produced by two objects with unknown masses. The equation we will be using to approximate the mass value of two objects and the period of oscillation produced by the two objects are listed below.

An example of the calculation for the approximation mass value of the wallet is shown below using the period of oscillation of the wallet, the  Max value of "Mtray" and its corresponding values for A, n.

 Below is a data table with the calculated mass value using Mtray min, Mtray intermediate, and Mtray mas and all of there corresponding y-intercepts and slopes for each of the unknown masses and their period of oscillation. The results show the calculated and the measured mass of both the stapler and the wallet were within 2 grams of each other.

The 2 gram difference between the calculated mass of the staple and the measure mass of the stapler could be due to improper rounding during the calculation phase, debris left on the balance from previous experiment that we neglected to brush of the balance. Overall i believe our approximation of the mass of both the stapler and the wallet were fairly close to the true value of both objects.