08/30/2016 : Inertial Pendulum - relationship between mass and period

Lab #1: Inertial Pendulum - Relationship between Mass and Period,
Name:   Charles Xu,
Partner: Anthony,
Date:     08/30/2016

Statement:
It was a laboratory that searching the relationship between mass and period using inertial balance and LabPro.

Theory:
Find the equation that relates time and mass by testing unknown mass of the inertial balance. Then, find a equation in a form of y = mx+b to express the relationship between time and mass. Do two experiments and calculations to find unknown mass.  Compare the final answer with the actual reading on the scale to prove your experimen.

Summary:
We used the Logger Pro to measure the different frequency about the movement of the inertial balance when there was different weight on it. We put 100 grams of mass on the inertial balance, and applied same amount of force on the inertial balance to make it start moving in a periodic movement. At the same time, we use Logger Pro measure the period and time. We then add 100 grams more on the inertial balance each time, and did the experiment rapidly. We collected data into a table and calculated the values of period per second for each weight. Then we turned the formula T = A(m + Mtray)^n into y=mx+b form, which is let = n*ln(m+Mtray) + lnA. At this moment, we had three unknown variables: A, n, Mtray. Then, we input data we recorded into Logger Pro and created three sets of data: m+Mtray, lnT, and ln(m+Mtray). Then we plot lnT vs. ln(m+Mtary) graph. After we adjusted the value of mTray that makes the correlation coefficient is close to one. According to the graph, we find the value of lnA, which is the y intercept; the value of n is the slope of the graph. For the second part of the lab, we use two different objects, golf ball and tennis ball. We measure the period of the inertial balance and time. Through calculation, we were able to find the mass of the golf ball and tennis ball.

Data table 

lnT vs. ln(m+Mtray) graph when Mtray= 220

lnT vs. ln(m+Mtray) graph when Mtray= 270

Experiment 1: measuring weight of golf ball

Experiment 2: measuring weight of tennis ball

Calculation to find the mass of golf ball and tennis ball

Conclusion:

This experiment successfully find the relationship between time and mass using LoggerPro. We found out that the relationship between time and mass is liner. It is in y=mx+b form, which is lnT = nln(m+Mtray) +lnA. We were able to find out the three unknown variables using testing pie method. We were also able to test our theory by measuring two unknown-mass objects and calculated the mass with error. The result from calculation is a little different than the exact reading on the scale. It might because when we released the inertial balance with force while golf ball or tennis ball is not static on the trail. It changed the force acting on the inertial balance and might change the data that recorded. Also, we did not include air resistance, which might cause error, too.