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

Lab Group

Carlos Hernandez

Ariel De Leon    

Dhalia 

 Finding a relationship between mass and period for an inertial balance. 

2.This experiment should allow us to understand how mass affects the period . Or how we can find the mass based of the period an object has.

3.  So we know there is a relationship between mass and period. My initial theory and thoughts to what would link them is the following. The period of something swinging is dependent on the mass and earths gravitational pull on it. If something has a greater mass it would slow down the period.

4. We first used a floppy metal piece that attaches to the table called an inertial balance. Using logger pro and a period detector device we manged to start the experiment. We first put weights on the metal piece (knowing the mass) to create a function.  We did this for a couple of masses to perfect the function. After this process we got a graph whose function looks like Y=mx+b. We know that the formula that relates mass and period is T= A(m+Mtray)^n. using algebra we managed to make it look like a y=mx+b function and it looked like the following: lnT=nln(m+Mtray)+lnA. Now after changing and adding a few features in logger pro , we were ready to measure the period of an object with an unknown mass. I will explain the the graphs and how we solved for the masses in step 7. step 5 will contain photos of date we compiled and lab equipment. while step 6 will contain photos of my calculations.

5)

6) 

7) So the graphs in step 5 are graphs of of the periodic movements of  two unknown objects whose masses we would try to find. The steps for doing this we first had to get an upper bound and lower bound of certainty for our original graph. our lower bound for Mtray was 280 and upperbound was 320. Anything below or above that would be to uncertain. Using only the period of the known objects we would plug that in to our power law equation . We ofcoarse solved for the mass twice , one with the lower bound date and the other with the upper bound data. One key feature is that the "B" in y=mx+b is actually a LnA. so to get the B or in other terms the A of the power law, we have to solve for A. We did this for both unknown objects. For unknown object 1 the 2 masses we got were 229g, and 240g. The mass of the object was actually 251. We were in a 10% margin of error which in my eyes isnt too bad. My beliefs for the uncertainty might include; human error, the object not being uniform, the object placed further or closer to the edge in respect to our weights trials. Our known object 2 was around the same margin of error and the same procedures were done. 

8) Overall I believe the lab was a success we learned how to use the power law equation for period and mass . It was also a great help understanding graphs which I believe will be useful in this coarse. I talked about uncertainty in step 7. Although I did no calculations on  it as I still don't have it clear how to do it. Thank you.