Lab 1: Finding a relationship between mass and period for an inertial balance
Author: Tiancih Jiao
Lab partners: Weisheng Zhang, Kitarou
Date: 2017/2/27
For this lab, we can measure the period of oscillation for a bunch of different masses, then we will use it to determine the unknown masses of many other objects.
Things to measure: The oscillation period of the inertial pendulum for a variety of known masses; The oscillation period of the inertial pendulum for a couple of unknown masses.
Theory/Introduction:
We are going to guess that the period is related to mass by the equation:
T = A(m + Mtray)^n
We have three unknowns--A, Mtray, and n. So we have to find them by the experiment.
Then we take the natural logarithm of both sides. Then we have:
lnT = n ln(m + Mtray) + lnA , which looks like y = mx + b
Y-intercept = lnA
X = ln(m + Mtray)
slope = n
We will try different values to get a straight line for Mtray.
Then we will come up with a range of A and n, and each value of Mtray will give us its own values for A and n.
Summary of our apparatus/experimental procedure:
We use a C-clamp to secure the inertial to the tabletop. Put a thin piece of masking tape on the end of the inertial balance just like the picture.
We use LabPro with a power adapter, USB cable, and plug adapter with laptop. Then we use them to measure and record the period with different mass on it.
Measured Data:
We enter these data into laptop, then we get a graph.
We guess 2 times for the Mtray, then we adjust the correlation to 0.9998, which is require to be from 0.9997-0.9999. The m = 0.8157, and the b = -6.175
Then we changed the value of Mtray to see the range of Slope and Y-intercept.
After we got the min and max of them, we can calculate the unknown items, so we use a pencil bag and an NDS as unknown items to test.
We use the n and lnA, and m is unknown, then we solve for m in the equation:
lnT = nln(m + Mtray) + lnA
Then we get the following table.
Analysis:
We measure and record data by changing the mass or the object, then we can get the range of the lnA and n. Then we can use the known lnA and n to calculate the unknown items mass. This is the lab purpose to find the relationship between the mass and the period.
Conclusion:
The purpose of the lab is to find the relationship between mass and period. So first we use laptop and C-clamp to record the period by increasing the mass. Then we find lnA and n by the given equation. After getting two unknown values of three, we can use these two values to find the rest one. So we can use the result to find out some other items' mass.
We measure and record data by changing the mass or the object, then we can get the range of the lnA and n. Then we can use the known lnA and n to calculate the unknown items mass. This is the lab purpose to find the relationship between the mass and the period.
Conclusion:
The purpose of the lab is to find the relationship between mass and period. So first we use laptop and C-clamp to record the period by increasing the mass. Then we find lnA and n by the given equation. After getting two unknown values of three, we can use these two values to find the rest one. So we can use the result to find out some other items' mass.
In the one graph shown, the linear fit doesn't include the first data point.
回复删除It is a little odd that the Mtray minimum gives mass values that are very far off from the other two values. Usually they are closer together than this. It turns out that a wide range of mass values will give you a correlation of 0.9997. It is a much narrower range that will give you a correlation of 0.9998. The idea was to find a value of Mtray that gives you the highest possible correlation and then to find the range of values of Mtray that gives you that highest value.
One thing that is missing is a discussion of sources of error or uncertainty in your lab. When we set up our original equation all of the masses were cylinders centered in the tray.
Our unknown objects had different shapes and perhaps different placement in the tray. We didn't test separately to see if placement or shape made a difference. This is an assumption (that mass is the only variable) that maybe turns out not to be true.