Feb. 25, 2015. Finding a relationship between mass and period for an inertia balance. February 25, 2015

Purpose:
The purpose of this lab was to help us understand how mass can affected an oscillation period in a inertia balance.In order to help us find the relationship between mass and period for inertia balance, we set up a lab experiment with the equipment seen below.


Procedure:

Here we see our inertia balance held up by a C-clamp. Next to it we have the weights which we will use to load mass onto out balance for data recording. This data will be collected by the photogate which is held by the rod and another clamp. It will work by detecting the movement of the tape which is taped onto the inertia balance.                          





                                               

Mass was added in 100g and the values of the time each oscillation took with each mass was recorded until we had the oscillation of 800g.

Data analysis:

We then used logger pro to record the data and then set it up on a coordinate system with the values we recorded during the experiment.

In this form, it is possible to see a resemblance of a logarithmic function, because of this we will try to model this curve with the function: T = A*(m+Mtray)^n.

To achieve this, we set up a LnTime vs Ln(m+Mtray) graph and tried to approximate the equation as best as we could. Two graphs were recorded, one had the lowest possible value for the mass of the tray and the other had the highest value for which the function would be reasonably accurate.

Above:  Highest value for tray                         

M = 0.260g                                         

A = 0.6489                                         

m = n = 0.6180                        

Above: Lowest value for tray                      

M = 0.290g                                        

A = 0.6366                                          

m = n = 0.6512

With the new found data, it was now possible to solve for the logarithmic functions.The variables used were the y-intercepts and the mass values we evaluated for them respectively. 

Conclusion of experiment:

We concluded with the following two functions that were able to model the inertia balance periods where the following:

when  m = (mass added):

      For the lowest value: y = 0.6489 + (m+.260)^0.6180

      For the highest value: y = 0.6366 + (m+.290)^0.6512

It was clear at the end of the lab that increasing the mass in the inertia balance increases the period for each oscillation.