29-AUG-2016 Inertial Pendulum Relationship Between Mass and Period

In this experiment we will be trying to find the mass of object using the relationship of known masses and period with the use of a pendulum.

To begin this lab we will collect data specifically the period from known masses. We will use this data to come up with a relationship between mass and period. Using the slope that was formed from the mass of our known objects we can now use the formula T=A(mass+Mass(tray))^n. After a little algebra this equation will now become (T/ln(A))^(1/n)-Mass(tray)= the mass of the unknown object.

The aparatus we will be using in this experiment is a mounted pendulum that sways from left to right. We will also be using a a photogate and the application of logger pro to collect the period of the pendulum with the known weight. We will use this set up to collect data from several known weights to allow us to achieve an effective mass and period relationship.   This is how our set up looked.

Now using a data table we collected the mass of an object as well as the period it took that object to complete one cycle. In order to keep everything uniform we collected 15 seconds of each mass and then took the average period in those 15 seconds. Here is a copy of our data table.

Now we took this data and created a graph with ln(mass+mass(tray)) on the x axis and ln(seconds) on the y axis. This data will be used to calculate our slope. We will adjust the weight of the tray a little bit to try and achieve a correlation of 1. In this step the closest you may achieve is .999 and if so we need to create a low limit as well as a high limit. So for the weight of our tray to achieve this is a low limit of 240g and a high limit of 300g. here is a graph of our lower limit as well as higher limit.

The information needed in these graphs are the y-intercept and the slope which we will need in our calculations for the mass of the unknown.

A = y intercept      n = slope      T = period (s)       Mass(tray)=(upper limit 300) or (low limit=240) 

After collecting this data we will now collect the period of our unknown mass objects

T tape dispenser = 0.6198(s)

T stapler = 0.4974(s)

Here are the results of our calculations to find the unknown mass using the period. The following equation was used to calculate the mass. The objects that were used was a tape dispenser and a stapler. The period of the two objects are as follows.

T tape dispenser = 0.6198(s)

T stapler = 0.4974(s)

(T/ln(A))^(1/n) - Mass(tray) = Objects unknown mass

Upper Calculations:

tape dispenser (0.6198/0.00624)^(1/.6740) - 300 = 618.34(g)

stapler             (0.4974/0.00624)^(1/.6740) - 300 = 362.59(g)

Lower Calculations:

tape dispenser (0.6198/.01125)^(1/.5924) - 240 = 629.08(g)

stapler             (0.4974/.01125)^(1/.5924) - 240 = 359.48(g)

actual mass using a scale:

tape dispenser = 625(g)

stapler = 369(g)

Conclusion:

Although our calculations were close I found our results to be very interesting. One of the most important thing to keep in mind during this calculation is where you place the object on the pendulum which will affect your results tremendously. After calculating our results the tape dispensers actual weight fell between our calculations but the stapler was out by about 6/7(g). This could be affected by air resistance and exactly where we placed the stapler on the pendulum. Clearly this lab shows that there is in fact a relationship between the mass of an object and the period it takes that object to complete one cycle.