1. Lab 1 Finding a relationship for mass and period
Ana Leyva, Christian Valencia
Completed on 2/27/17
2. With this experiment we are trying to find a correlation
between the period and the mass of an object. We are trying to do this by first
finding out how the period of an object is affected when weight is added to the
pendulum we are using to measure the period. Once this is found we will come up
with an equation that will allow us to approximate the mass of an object when
the period is known and will allow us to approximate the period when the mass
is known.
3. In this experiment we are trying to come up with an
equation that will do the best job at approximating the mass of an object when
the period is known and vice versa. In order to do this we first had to find
the period when mass was added to the pendulum that was being used to calculate
the period. Once we had that information we put it into a ln(M+Mtray) vs lnT
graph. By putting it in that graph and messing around with what we thought was
the mass of the tray we were able to get a linear fit on that graph with a
correlation of 0.998.We then got three different values of the Mtray(minimum,
intermediate, and maximum) that gave us a correlation of 0.998 and also gave us
the slope and y intercept of the graph.
4. At the beginning of this experiment we set up a pendulum
and photogate that would allow us to calculate the period of the pendulum. We
used Logger Pro, the pendulum, and the photogate to help us calculate the
period. We then started to record the period of the pendulum when there was no
mass added. Then we added 100g and once again calculated the period. We kept on
adding 100g to our pendulum and calculating our period until we got to 800g. When
we had the period for all the masses we created a ln(M+Mtray) vs lnT graph. We
then adjusted the values of the Mtray to try to get a near perfect correlation
of 0.998. With each value of Mtray that we got that gave us a near perfect
correlation we also got the slope and y intercept of the line when the Mtray
was a certain mass. The values that we got from our line allowed us to come up
with a mathematical model for the behavior of the pendulum.
With these graphs we were able to get the slope and the y intercept for two Mtray values. These two graphs and another one that is not pictured allowed us to come up the the equation in the pictures below. The slope value N and the y-intercept A were plugged into the equation:
lnT = n* ln(M+Mtray) + lnA Then the equation were maipulated to make finding T and M easier.
Conclusions:
Based on the last part of the experiment that asked us to find the mass of two unknowns my equations did not do that great of a job in predicting the mass of an object. I believe that the reason why my equations weren't very accurate has to do with maybe the way that the mass was put into the pendulum. When we were trying to calculate the period of my wallet it was very hard to place my wallet in a way that would distribute the mass of my wallet perfectly on the pendulum. I believe this is one of the reasons why my calculations were off. I believe that most of the errors that contributed to the uncertainty of my calculations had to do with human errors.
The lab isn't just a relationship between mass and period for any old object--it is for the inertial pendulum. You might move your (very good) picture up to right after you describe the purpose.
ReplyDeleteYour #2 and #3 repeat each other to a certain extent.
It isn't clear from your description why you are taking the natural log of the equation or what the graph is going to tell you or why adjusting the value of Mtray will give you a straight line.
You might consider an order like this:
--Power law equation
--ln form
--what will be plotted on the y axis and on the x-axis
--what the slope and y-intercept of that graph will tell you
--how you are going to find the mass of the tray
I don't see your actual mass and period data anywhere. If it is on the graph it is too small to read.
You don't make super clear why there are a range of Mtray values.
Your sample calculations ARE super clear.
Human errors are about being sloppy.
Experimental errors are different. In this case all of our known masses were compact cylinders not-quite-centered on the tray, and your experimental objects had a different shape than the one we used to develop our equation. We didn't test to see if different shapes and/or different placements on the tray affect the period or not.
The "error" was perhaps developing the equation one way and then using it another way.
Your calculations themselves shouldn't be uncertain. It doesn't look like they themselves were off in any way. It is our assumptions about the experiment that were off.