31-Aug-2016 . 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

Dahlia - Ariel - Carlos

29-Aug-2016

When I used an inertial balance with different mass of objects, each mass made different periods based on how heavy they were. The heavier of objects, the slower of period. Thus, there was a relationship between mass and period when using an inertial pendulum. In this lab, I tried to find equation that related period and mass in an inertial pendulum's movement.

Theory/introduction:
with some helps from professor, I had the relationship between mass (m-add and m-tray) and the period (T) by power-law type of equation with 3 unknown numbers: A-constant, n, and m-tray. With some changes from the first equation, the relationship of mass and period become a line (picture)

Now, I had to find the value of a and b for the line.

Apparatus/ experimental produce:

1. Set up:

       Used a C-clamp to secure the inertial balance to the tabletop. Put a thin piece of masking tape on the end of the inertial balance.

       Set up a photo-gate so when the balance was oscillating the tape completely passed through the beam of the photo-gate.

      Set up the LabPro in order to record data.

      Record the period with no mass in the tray.

      Repeat recording with mass of 100g, 200g, 300g, 400g, 500g, 600g, 700g, 800g.

2. Collected data:

The results of each mass, I recorded them to above data table.

3. Worked data:

In Logger Pro, I added 3 new columns: m+m-tray, lnT, and ln(m+m-tray)

I made a plot of lnT vs. ln(m+m-tray). 

To get m-tray, I tried several value until I got a straight-line plot ( correlation was almost 1)

From what I got, the mass of tray would have a value between 280-320 g. (in which the correlation=0.9999)

With the m-tray=280g, I got value for the equation:

And with the m-tray =320, I had:

Now, I had two equations about the relationship between mass and period in this experiment.

with m-tray =280 g, T=0.0073799 (m-add +280)^0.6464
with m-tray=320 g, T=0.0051539 (m-add + 320)^0.6948

Extension: 2 unknown objects

I had 2 unknown-mass objects, and I used them as the m-add. I left them on the pendulum. Based on relationship between mass and period, I calculated their mass as follow:

- Object 1 - a calculator:  Period: T = 0.418590 s

- Object 2 - a tape holder:  Period: T = 0.630202 s

Conclusion
    In this lab, I tried to figure out the relationship between mass and period in an inertial pendulum. Of course, each pendulum had different m-tray, and my m-tray in this experiment were between 280 and 320 g. From these mass, I came up with two different equations:
       with m-tray =280 g, T=0.0073799 (m-add +280)^0.6464
       with m-tray=320 g, T=0.0051539 (m-add + 320)^0.6948
Now, with 2 above equations, with an unknown object, I could easy to calculate its mass based on its period by the pendulum.
The experiment had some errors because of the position of unknown objects ( it was not stayed at the center of the inertial pendulum) and the effect of air friction,