Partners: Kevin N, Jose Rodriguez
3 March, 2017
Finding a relationship between mass and period for an inertial balance
Purpose: Students will learn how to find unknown masses of other objects by using collective data.
Theory: By using different masses to measure the period of oscillation, students are able to use that data to create a mathematical model of the relationship between the masses and period. By using the created model, students can apply the model to determine the unknown masses of other objects. Students will use the oscillation period to measure the mass of the tray by applying the power-law type equation. (picture displayed below).
A= Amplitude
Mtray= The mass of the tray.
N= The slope
Procedure: In the figure below, students will place different amounts of weights (0g, 100g, 200g, 300g, 400g, 500g, 600g, 700g, 800g) on the metal tray. After, students will pull on the metal tray and will begin collecting data by using loggers pro. Students will measure the amount of oscillation within a certain time frame. We are trying to find the coefficient of determination by changing the values until we reach 0.997.
The picture below is the data that we have collected during the experiment.
We use the data to create a Mass(g)/ Period(s) graph. (picture provided below).
After the graph is created, the information should provide a curve fit equation. After getting the curve fit equation, students are able to find N(the slope) and the Y-intercept(displayed as amplitude). (Data collected). The X-axis represents the In mass plus mass tray and Y-axis is the In Period
After the graph is created, the information should provide a curve fit equation. After getting the curve fit equation, students are able to find N(the slope) and the Y-intercept(displayed as amplitude). (Data collected). The X-axis represents the In mass plus mass tray and Y-axis is the In Period
After finding your slope and y-intercept(shows as Amplitude), plug in the information into the power-law type equation (Equation is at the top of the page). We use "460g(minimum value), 530g(intermediate value), and 600g(maximum value)" as examples to find the best correlation possible closest to 0.9997. Afterwards, we will now try to find the mass of an unknown object, but we will use a cellphone as an example. (picture below).
We have collected data of the known period of the cellphone(0.3856 per/sec). By using this information, we will equal it to the power-law type equation with the given information of the slope and amplitude in the picture above. (process below).
With the data provided for us, we were able to find the mass of the cellphone, which is approximately 163g on average.
In addition, we used a wallet as another example for this lab. (No picture of wallet provided).
We will repeat the same process similar to the cellphone. We have the known period of the wallet(0.358 per/sec). We will apply the information and equal it to the power-law type equation(provided at the far top).
As a result, we used the known period of the wallet to find it's mass of 111g on average.
In conclusion, the lab turned out according to plan. We learned that students are able to find the unknown mass of an object by using oscillation periods and data. In addition, the power- law type equation helps us achieve the discovery of the unknown mass. After we got our approximate mass for both the cellphone and wallet, we weigh the two objects. In the end, we were off by a few grams but very close to the actual weight.
A lab blog is your record of what you did, told in the past tense. So rather than "Students will . . . " just tell what you did, or what the experiment was about.
ReplyDelete"A" isn't an amplitude, since the equation is for a period (time). It and "n" are just constants in our attempted fit equation.
You say that "
We use the data to create a Mass(g)/ Period(s) graph. (picture provided below)"
But the graph you provided is actually ln Period vs. ln (m + Mtray).
The "Amplitude" value in your table is actually the y-intercept (ln A).
Even before you show your data you might consider describing the approach you are taking in the lab:
--Power law equation
--natural log form of the equation
--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
So after you tell folks that your plot should be a straight line if Mtray has the "correct" value or range of values, then you can tell them how you are going to find the correct value for Mtray.
"Plug in the information" is pretty vague. Describe what gets plugged into what, and what the result tells you.
Your calculations are fine. The lab handout had a suggested format for reporting your results.
You have no discussion about uncertainties in your results. One thing we discussed in class is that 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 isn't a human error so much as an assumption (that mass is the only variable) that maybe turns out not to be true.